JPH04302328A - Device and method for fuzzy processing - Google Patents

Abstract

PURPOSE:To generate the optimum membership function and fuzzy rule not depending on supplied sample data. CONSTITUTION:When sample data consisting of input and output data is supplied, learning by a neural network is performed at a learning processing part 1, and the membership functions are generated on arbitrary input and output axes, and an unrequited input variable is deleted at an input decision processing part 2. Then, the optimum spread width of an antecedent part membership function is decided at a resolution decision processing part 4, and also, the antecedent part membership is generated. The representative value of a generated antecedent part membership function is supplied to the learning processing part 1 as input data, and a consequent part membership function and a rule can be generated at a conversion processing part 3 by obtained output data.

Description

Description: FIELD OF THE INVENTION This invention relates to a fuzzy processing device and method, and more particularly to a fuzzy processing device and method for creating membership functions and rules through learning. In the present invention, the fuzzy processing device and method not only perform fuzzy inference operations, but also include so-called support devices and methods that are used only to create membership functions and rules for fuzzy inference. Also includes apparatus and methods for carrying out the procedures. [0002] Fuzzy inference has the characteristics that it is easy to reflect qualitative human knowledge and that the created knowledge (membership functions and rules) is easy to understand for humans. Generally, knowledge for fuzzy inference is created based on experts' know-how. [0003] However, on the other hand, even without human knowledge,
There is a known method of creating knowledge for fuzzy inference for systems with strong nonlinear input-output relationships through example learning. This is a method in which the input/output data obtained when the above system is operated is used as sample data and is directly reflected in knowledge. [0004] However, in this method, membership functions and rules directly depend on sample data, so membership functions and rules are created only for points or areas where sample data exists, and are not necessarily valid. It is not always possible to obtain a membership function that is Another problem is that accuracy is determined by variations in sample data. [0005] In order to solve these problems, we have developed a method for creating knowledge for fuzzy inference that is not affected by the quality of sample data for case learning by combining neural networks, which are a type of case learning, and fuzzy inference. has been proposed (for example, Hayashi et al. "Learning control of an inverted pendulum using neural network-driven fuzzy reasoning" 5th Fuz
zy System Symposium, Kobe
, June 2-3, 1989). [Problems to be Solved by the Invention] However, when this method is used in a real system, it requires software or hardware for both a case learning device and a fuzzy inference device, so the processing speed is slow and the fuzzy inference method is slow. Since the membership function of the device can only be expressed in a multidimensional input space, there is a problem that the knowledge of the fuzzy inference device after learning is difficult to understand. [0007] The present invention provides an apparatus and method for creating rules and membership functions for fuzzy inference that enable inference processing to be performed at a high processing speed and that are easy to understand. [Means for Solving the Problems] A fuzzy processing device for creating rules and membership functions according to the present invention processes input data regarding a plurality of given input variables and at least one type corresponding thereto. Using sample data that includes multiple pairs of output variables and output data, we can create a structure that allows output data corresponding to any set of input data regarding multiple types of input variables to be obtained through learning. The learning means to be constructed generates multiple sets of input data for multiple input variables, provides these to the learning means to obtain output data corresponding to them, and generates output data for each input variable in response to changes in input data. an antecedent part creation means for creating an antecedent membership function having a spread corresponding to the magnitude of change in data;
Also, an input data set consisting of a combination of input representative values for a plurality of input variables for the antecedent membership function created by the antecedent part creation means is given to the learning means, and correspondingly, the input data set is provided to the learning means. A consequent membership function is created based on the obtained output data, and an antecedent membership function with the input representative value included in the above input data set and a corresponding consequent membership function are created. The system is equipped with a rule creation means for creating a rule consisting of the following. [0009] In one embodiment of the present invention, a plurality of sets of input data regarding a plurality of input variables are generated, and output data corresponding to them is obtained by supplying these to the learning means, and these sets of input data and Further, input determining means is provided for determining whether there is an input variable whose correlation with the output data is smaller than a predetermined value based on the output data. [0010] If there is an input variable whose correlation with the output data is smaller than a predetermined value, it is determined as an input variable to be deleted, and data regarding the deleted input variable is deleted from the sample data to be given to the learning means. It is preferable to further include a control means which is applied to the learning means and causes the learning means to repeat the learning process again. [0011] It is preferable that the control means performs control such that data regarding the input variables to be deleted are repeatedly deleted from the sample data and learning is performed until there are no input variables to be deleted. [0012] It is preferable that the antecedent generation means and the rule generation means use the learning means in a state where there are no input variables to be deleted. [0013] It is preferable to further provide fuzzy inference means for performing fuzzy inference calculations according to the antecedent part membership function, consequent part membership function and rules created by the antecedent part creation means and rule creation means. [0014] In another embodiment of the present invention, fuzzy inference is performed to perform a fuzzy inference operation according to the antecedent part membership function, consequent part membership function, and rule created by the antecedent part creation means and rule creation means. generate a plurality of sets of input data regarding a means and a plurality of input variables, provide these to the fuzzy inference means to obtain corresponding output data, and based on these input data and output data, Input determining means is further provided for determining whether there is an input variable whose correlation with the output data is smaller than a predetermined value. [0015] If there is an input variable whose correlation with the output data is smaller than a predetermined value, it is determined as an input variable to be deleted, and data regarding the deleted input variable is deleted from the sample data to be given to the learning means. It is preferable to further include a control means which is applied to the learning means and causes the learning means to repeat the learning process again. [0016] The control means repeats the deletion of data regarding the input variables to be deleted from the sample data, the learning, the creation of the antecedent membership function, and the creation of rules until there are no input variables to be deleted. Preferably, it is controlled. [0017] It is preferable that the antecedent generation means and the rule generation means use the learning means in a state where there are no input variables to be deleted. The fuzzy processing method for creating rules and membership functions according to the present invention combines input data for a plurality of given input variables and corresponding output data for at least one type of output variable. Using sample data that includes multiple sets of Generate multiple sets of input data, give them to the above learning structure to obtain the corresponding output data, and for each input variable, calculate the spread according to the magnitude of change in output data with respect to change in input data. Create an antecedent membership function with Create a consequent membership function based on the output data obtained from the above learning structure, and create a consequent membership function with the input representative value included in the above input data set and the corresponding consequent membership function. This method creates rules consisting of subject membership functions. In one embodiment of the present invention, a plurality of sets of input data regarding a plurality of input variables are generated, output data corresponding to them is obtained by providing these to the learning structure, and these input data are and the output data, it is further determined whether there is an input variable whose correlation with the output data is smaller than a predetermined value. [0020] Then, if there is an input variable whose correlation with the output data is smaller than a predetermined value, it is determined as an input variable to be deleted, and data related to the deleted input variable is deleted from the sample data to be given to the above learning structure. is applied to the learning structure, and the learning structure is caused to repeat the learning process again. [0021] Further, the deletion of data regarding the input variables to be deleted from the sample data and the learning are repeated until there are no input variables to be deleted. Then, an antecedent membership function, a consequent membership function, and a rule are created using the above learning structure with no input variables to be deleted. In another embodiment of the present invention, a plurality of sets of input data for a plurality of input variables are generated, and the created antecedent membership function,
Corresponding output data is obtained by performing fuzzy inference operations according to the consequent membership function and rules, and based on these input data and output data, there is an input variable whose correlation with the output data is smaller than a predetermined value. Determine whether or not. [0023] Then, if there is an input variable whose correlation with the output data is smaller than a predetermined value, it is determined as an input variable to be deleted, and data regarding the deleted input variable is deleted from the sample data to be given to the learning structure. is applied to the learning structure, and the learning structure is caused to repeat the learning process again. [0024] Further, the deletion of data regarding the input variables to be deleted from the sample data, the learning, the creation of the antecedent membership function, and the creation of rules are repeated until there are no input variables to be deleted. Then, an antecedent membership function, a consequent membership function, and a rule are created using the above learning structure with no input variables to be deleted. [0025] The device for creating antecedent membership functions according to the present invention has a set of input data for a plurality of given input variables and corresponding output data for at least one type of output variable. A learning method for constructing a structure that can obtain output data corresponding to any set of input data regarding multiple types of input variables through learning using sample data that includes multiple sets, and regarding multiple input variables. an input generating means for generating a plurality of sets of input data; a means for controlling the learning means to supply the sets of input data given from the input generating means to the learning means to operate the learning means to obtain output data corresponding thereto; , means for calculating the amount of change in output data that occurs when input data fluctuates by a constant value for each input variable, and means for calculating the fluctuation range of input data so that the amount of change in output data maintains a constant value for each input variable. and means for allocating one antecedent membership function for each range of variation. Another apparatus for creating antecedent membership functions according to the invention includes means for storing a plurality of sets of input data for a plurality of input variables and their corresponding output data; means for calculating the amount of change in the output data that occurs when the input data fluctuates by a certain value, and for each input variable, the range of fluctuation of the input data so that the amount of change in the output data remains constant. and means for allocating one antecedent membership function for each range of variation. The device for deleting unnecessary input variables according to the present invention includes an input generating means for generating a set of input data regarding a plurality of input variables, and an output corresponding to the set of input data given from the input generating means. An output generation means that generates and outputs data, for each input variable, the input data of all other input variables except the target input variable are fixed, and the input data of the target input variable is changed. means for calculating the sum of variances of output data, and means for comparing the sum of variances with a predetermined reference value and determining that input variables whose sum of variances is smaller than the predetermined reference value should be deleted. We are prepared. [0028] The output generating means generates sample data that includes a plurality of sets of input data for a plurality of given types of input variables and corresponding output data for at least one type of output variable. Using,
Is it a learning method that constructs a structure in which output data corresponding to an arbitrary set of input data regarding multiple types of input variables can be obtained by learning, or is a learning method that uses preset antecedent membership functions and consequent membership functions? It is a fuzzy inference means that performs fuzzy inference operations according to functions and rules. Another apparatus for deleting unnecessary input variables according to the present invention includes means for storing a plurality of sets of input data for a plurality of input variables and output data corresponding thereto, for each input variable, Means for calculating the sum of the variances of output data when the input data of all input variables other than the target input variable are fixed and the input data of the target input variable is changed, and the total sum of the above variances and a predetermined reference value, and determines that input variables for which the sum of the variances is smaller than the predetermined reference value should be deleted. The method for creating an antecedent membership function according to the present invention is such that a set of input data for a plurality of given types of input variables and corresponding output data for at least one type of output variable is created. Using sample data that includes multiple sets, we construct a learning structure that can obtain output data corresponding to any set of input data regarding multiple types of input variables through learning. Generate multiple sets of input data, feed the generated sets of input data to the above learning structure, operate the above learning structure to obtain the corresponding output data, and keep the input data constant for each input variable. The amount of change in output data that occurs when the value fluctuates is calculated, and for each input variable, the fluctuation range of input data is determined so that the amount of change in output data remains constant, and one antecedent part is calculated for each of this fluctuation range. Antecedent membership functions are created by assigning membership functions. Another method for creating antecedent membership functions according to the present invention is to store in advance a plurality of sets of input data regarding a plurality of input variables and output data corresponding to these, and For the input variables, calculate the amount of change in the output data that occurs when the input data fluctuates by a constant value, and for each input variable, calculate the fluctuation range of the input data so that the amount of change in the output data remains constant. The antecedent membership function is created by assigning one antecedent membership function to each variation range. [0032] The method for deleting unnecessary input variables according to the present invention generates input data sets for a plurality of input variables, generates output data corresponding to the generated input data sets, and deletes each input variable. For, fix the input data of all input variables except the target input variable,
Calculate the total sum of variance of the output data when changing the input data of the target input variable, compare the sum of the variances with a predetermined reference value, and determine if the sum of the variances is greater than the predetermined reference value. It determines that small input variables should be deleted. [0033] Using sample data that includes multiple sets of input data for multiple types of given input variables and corresponding output data for at least one type of output variable, learning is performed using sample data. , construct a learning structure that can obtain output data corresponding to an arbitrary set of input data regarding multiple types of input variables, and generate output data by giving the set of input data to this academic financing structure, or generate the output data in advance. Output data may be generated by performing fuzzy inference calculations according to the set antecedent membership function, consequent membership function, and rules. Another method for deleting unnecessary input variables according to the present invention is to store in advance a plurality of sets of input data regarding a plurality of input variables and their corresponding output data, and , fix the input data of all other input variables except the target input variable, calculate the sum of the variance of the output data when the input data of the target input variable is changed, and calculate the sum of the above variances. is compared with a predetermined reference value, and it is determined that input variables for which the sum of the variances is smaller than the predetermined reference value are to be deleted. [Operation] Using sample data that includes a plurality of sets of input data for a plurality of given types of input variables and corresponding output data for at least one type of output variable. Through learning, a learning structure is constructed that can obtain output data corresponding to any set of input data regarding multiple types of input variables. By generating a plurality of sets of input data regarding a plurality of input variables and supplying them to the learning means, output data corresponding to them can be obtained. and,
For each input variable, an antecedent membership function is created whose spread corresponds to the magnitude of change in output data with respect to change in input data. Further, an input data set consisting of a combination of input representative values for a plurality of input variables for the created antecedent membership function is given to the learning means, and an output obtained from the learning means is correspondingly given to the learning means. A consequent membership function is created based on the data, and an antecedent membership function with an input representative value included in the above input data set and a corresponding consequent membership function are created. A rule consisting of is created. Effects of the Invention: According to the apparatus and method for creating membership functions and rules according to the present invention, since learning is performed using the given sample data, output data for arbitrary input data can be obtained. It will be done. Therefore, valid membership functions for the preceding and consequent parts can be created on arbitrary input and output variable axes. Furthermore, even if there are variations in the sample data, the accuracy will not be significantly reduced. Since the created membership functions and rules can be set in any fuzzy inference device, the fuzzy inference device can be realized by either software or hardware, which simplifies the configuration and increases processing speed. Furthermore, since the membership function is expressed on one axis (each input variable axis), the created knowledge is easy to understand. According to the antecedent membership function creation device and method according to the present invention, the spread range of the antecedent membership function is determined so that the fluctuation width of the output data is approximately constant, so that detailed processing can be performed easily. Processing can be performed at a fine resolution in the necessary range and at a coarse resolution in a range where coarse processing is sufficient, and an optimal antecedent membership function is created without waste. According to the device and method for deleting unnecessary input variables according to the present invention, unnecessary input variables are deleted;
Since it does not appear in the final fuzzy inference rules, unnecessary processing can be omitted and processing speed can be improved. Embodiments First Embodiment A first embodiment of the fuzzy processing apparatus according to the present invention will be described. FIG. 1 is a functional block diagram of the fuzzy processing device, and FIG. 2 is a flow chart showing an overview of its operation. [0045] As shown in FIG. 1, the fuzzy processing device
It is composed of a learning phase processing section 1, an input determination phase processing section 2, a conversion phase processing section 3, a resolution determination phase processing section 4, and an execution phase processing section 5. The fuzzy processing device is specifically constituted by a computer system, and each of the processing units 1 to 5 described above is realized by programming this computer system to execute operations to be described in detail later. As shown in FIG. 2, this program is executed in the order of the processing units 1 to 5 described above. The configuration and operation or function of each processing section will be explained in detail below. In order to simplify the explanation, this example basically has two input variables (input 1 and input 2) and one output variable (two inputs and one output).
shall be. Learning Phase Processing Unit The learning phase processing unit 1 performs learning based on given sample data (consisting of input data and expected output data corresponding to it), and obtains an output corresponding to any input. This is to build a structure that can be used. In this embodiment, this structure is a neural network constructed by combining a large number of neurons. A functional block diagram showing the configuration of the learning phase processing section 1 is shown in FIG. Learning phase processing unit 1
are a sample data storage unit 11 and a case learning execution unit 12.
and a learning result storage section 13. Sample data consisting of input data and expected output data corresponding thereto is input and stored in the sample data storage section 11. This sample
An example of sample data stored in the data storage section 11 is shown in Table 1. Input data x for input 1
s1j, input data xs2j for input 2, and the corresponding expected output data dsj are one sample.
Construct a data set. N sets of such sample data are set. [0050] [Table 1] [0051] The example learning execution unit 12 executes learning in the neural network. sample·
The sample data stored in the data storage unit 11 is sequentially read out one set at a time, the input data of which is input to the input side of the case learning execution unit 12, and the expected output data is input to the execution unit 12.
are given to the output side of each. As is well known, a neural network is constructed by combining a large number of neurons, and the weights of connections between neurons are modified through learning. This learning is performed, for example, by a backpropagation method. The weights are modified so that the difference between the output data obtained from the neural network given the input data and the given expected output data is reduced. Learning is performed by sequentially providing sample data one set at a time until the value of the evaluation function (sum of squared errors) expressed by the above difference becomes less than or equal to a predetermined value. When the learning in the case study execution unit 12 is completed, the learning result, that is, the internal state of the case study execution unit 12, is stored in the learning result storage unit 13. When learning about a neural network is executed as described above, the internal state of the example learning execution unit 12 is represented by the structure of the neural network and the weights of connections between neurons. Parameters representing the structure of this neural network and the weights of connections between neurons are stored in the learning result storage section 13. By using a structure constructed as a result of such learning (for example, a neural network structure), an output can be obtained for any input. FIG. 4 shows the relationship between input and output obtained through learning. The × marks are sample data, and the solid curve represents the input-output relationship of the learning results. As will be seen later, in order to create a fuzzy rule, it is necessary to set the membership function of the antecedent part for the input variable. One parameter that characterizes the membership function is the coordinates of its vertices (the input value at which the membership function value is the maximum value) (this is referred to as a representative value or set value). Assuming that these set values are T1, T2, T3,..., Tj, Figure 4
is shown. [0057] If the input data that constitutes the sample data always matches the set value, the output data corresponding to the set value is included in the sample data, so fuzzy rules can be created relatively easily. It is. However, the input data in the sample data does not always match the set value; rather, the input data and the set value for the optimal fuzzy rule often differ. The learning result in the learning phase processing section 1 has an interpolation function for sample data, and since an output can be obtained for any input, output data can be obtained for any set value. In this way,
It becomes possible to create appropriate membership functions and create rules using them. Furthermore, even if there are variations in sample data, an average input-output relationship can be obtained through the above learning, so there is an advantage that output errors due to variations in sample data are reduced. Input Decision Phase Processing Unit The input decision phase processing unit 2 determines whether there are input variables that have no correlation with the output or are very small, and deletes such input variables, if any. , which ultimately determines the necessary input variables. This input determination phase processing is particularly effective when there are many types of input variables. When creating rules for fuzzy inference, there are generally a large number of possible input variable types (input variable candidates). However, not all of these input variable candidates are useful for obtaining a desired inference result (output). The greater the number of types of input variables included in a created fuzzy rule, the greater the amount of computation required for fuzzy inference according to that rule, and the longer the computation time. The input decision phase process removes unnecessary input variables in advance. The configuration of the input determination phase processing section 2 is shown in FIG. The input determination phase processing section 2 includes an input variation instruction section 21, an output variance monitoring section 22, a deletion input storage section 23, and the above-mentioned example learning execution section 12 and learning result storage section 13. The output distribution monitoring section 22 creates an input/output matrix as shown in Table 2. [0065] In order to create such an input/output matrix, the output dispersion monitoring unit 22 instructs the input fluctuation instructing unit 21 to generate input data for all input variables. In accordance with this instruction, the input variation instruction section 21 creates input data for all input variables, and provides the input data to the example learning execution section 12 and the output variance monitoring section 22. Preferably, the input data constitutes an arithmetic line number. Input data is also created to cover the entire range of the input variable. [0067] The case learning execution unit 12 includes an input variation instruction unit 21.
A set of input data from (each one for all input variables)
When a set of input data (each set of input data) is given, output data for that set of input data is calculated using the learning results stored in the learning result storage unit 13, and the output data is sent to the output distribution monitoring unit. Give to 22. Output data is created for every set of input data. The output variance monitoring unit 22 creates the input/output matrix shown in Table 2 using the set of input data and the output data for this, and also calculates the standard deviation (or variance) σij for each input and its Total value Si
Calculate. [0069] The standard deviation for an input variable is determined by changing the input data of the target input variable while fixing the input data of all other input variables except the target input variable. It is determined as the standard deviation of the output data obtained. Therefore, this standard deviation can be obtained by the number of input data combinations of other fixed input variables. The sum of all the standard deviations regarding the target input variables determined in this way is the total value. That is, in the case of two inputs, the standard deviation σij is obtained by Equation 1 and Equation 2, and the total value Si is obtained by Equation 3. ##EQU1## In the output variance monitoring unit 22, the total value of standard deviations for each input variable obtained in this way is compared with a predetermined reference value a for input deletion. , the input variables whose total value is smaller than the reference value a are determined to be deleted. Table 3 shows a specific example of the input/output matrix. If the reference value for input deletion is 10, the total value of standard deviations for input 1, 8, is smaller than this reference value, so input 2 is deleted. [0073] The fact that the standard deviation or the total value of a certain input variable is small means that even if the input data for that input variable is changed within that range, the output data will not change at all or the change will be small. This means that the input variable has no or little effect on the output data. therefore,
There is no need to consider the input variables. In this way, all input variables are evaluated. If an input variable to be deleted is found, that input variable is stored in the deletion input storage unit 23 as a deletion input. If there is an input variable to be deleted (YES in step 103 in FIG. 2), the learning phase processing section 1 is notified of this input variable to be deleted. In the learning phase processing unit 1, the above-described learning is executed again after excluding sample data regarding the input variables determined to be deleted. After the learning is completed, the processing in the input determination phase processing section 2 is repeated again. If there are no input variables to be deleted, or if there are no input variables to be deleted after the learning phase and input determination phase processes are repeated again or three or more times, the process moves to the next resolution determination phase process. In this input decision phase processing, input variables with low correlation with the output are deleted, so the amount of tasks in subsequent processing is reduced, the fuzzy inference rules are simplified, and the inference processing according to these rules is simplified. Increases speed. Resolution Determination Phase Processing Unit The resolution determination phase processing unit 4 determines the magnitude of change in output data with respect to change in input data for each input variable, and determines the above-mentioned set value according to this magnitude. This creates a membership function for the antecedent part. The configuration of the resolution determination phase processing section 4 is shown in FIG.
is shown. The resolution determination phase processing section 4 is composed of an input generation section 41, an antecedent membership function (MF) determination section 42, and the above-mentioned example learning execution section 12 and learning result storage section 13. The antecedent membership function determination unit 42 creates an input/output matrix as shown in Table 4. [Table 4] In order to create such an input/output matrix, the antecedent membership function determination unit 42 instructs the input generation unit 41 to generate input data for all input variables. do. The input generation unit 41, like the input variation instruction unit 21 described above, creates input data for all input variables according to this instruction, and uses the input data to the case learning execution unit 12 and the antecedent membership function. It is given to the determining unit 42. Preferably, the input data constitutes an arithmetic line number. Input data is also created to cover the entire range of the input variable. When the case learning execution section 12 is given a set of input data (one set of input data for all input variables) from the input generation section 41, the case learning execution section 12 stores the set of input data in the learning result storage section 13. Using the learning results, output data for the set of input data is calculated, and the output data is provided to the antecedent membership function determining unit 42. Output data is created for every set of input data. [0084] The antecedent membership function determination unit 42 is
The input/output matrix shown in Table 4 is created using the given set of input data and the corresponding output data, and for each input variable, the maximum value ( This is called the maximum value of the difference). For example, if there is an input/output matrix as shown in Table 4, the maximum value of the difference between input 1 and input 2 K1
i and K2j are determined by Equation 4 and Equation 5, respectively. [Equation 2] The antecedent membership function determining unit 42 is
Next, the resolution of the membership function of the antecedent is determined from the maximum value of the difference for each of the input variables described above, and the membership function is determined. At this time, the larger the maximum value of the difference (the larger the change in the output data), the more finely the membership function is set (the finer the input resolution).
The smaller the maximum value of the difference (the smaller the change in output data), the coarser the membership function (the coarser the input resolution) is set. FIG. 7 shows an example of a membership function set for a certain input variable. The spread of the membership function is set to be small in areas where the amount of change in the output value is large, and the spread of the membership function is set to be large in areas where the amount of change in the output value is small. When the membership function to be created is triangular, the procedure for determining the membership function will be explained using a specific example. The triangular membership function is uniquely determined when the coordinates (setting values) T1, T2, T3, . . . , Tj of its vertices are determined. That is, the membership function is created such that it has a peak at a setting value and a bottom point at an adjacent setting value (excluding those located at the edges). Then, each setting value is determined so that the lengths of the bases of the triangular membership functions are equal for all membership functions (excluding those located at the ends). Assume that an input/output matrix as shown in Table 5 has been obtained. [Table 5] [0093] Looking at input 1, the maximum value of the difference is 6.
,9,7,... Therefore, a length corresponding to a difference of 8 is assigned to the interval (length of the base) of each membership function. Referring to FIG. 8, if the value of input 1 is 1.0 ~
The maximum value of the difference is 6 when the value of input 1 is between 2.0 and 3.0, and the maximum value of the difference is 9 when the value of input 1 is between 2.0 and 3.0. In order to assign a difference of 8 to the first section M1 starting from the position where the value of input 1 is 1.0, the value of input 1 is 2.
Find the length corresponding to a difference of 2 from between 0 and 3.0,
Add this difference 2 between 1.0 and 2.0. For this purpose, a length corresponding to a difference of 2 between 2.0 and 3.0 is determined by proportional distribution. Since the difference between 2.0 and 3.0 is 9, the end point B of this section M1 can be found as follows. [Equation 3] B=2.0 + (3.0 −2.0 )×(2
/9) ...Formula 6 0097
] The width of section M1 is given by the following equation. [Equation 4] M1 = (2.0 - 1.0 ) + (3.0
−2.0 )×(2/9) Equation 7 [0099] When this idea is extended to the general case, the following algorithm is obtained. Here, each symbol is defined as follows. Difference assigned to the interval of membership function: A
Membership function interval width: M1, M
2 ,...,Me Input data when calculating the difference
:x1,x2,...,xi,...,xm
Maximum value of difference between input data: K1 , K2 ,
. . , Ki , . Tjs is the start point of the section, and Tje is the end point of the section (j=1 to e). First, the interval M of the first membership function
Find 1. FIG. 9(A) shows the case of Equation 8. [Equation 5] [0104] Interval M of the second and subsequent membership functions
Find j. However, the end point of the section of the previous membership function is between the input data xk and x(k+1), and the remaining floor difference of the section at that time is assumed to be B. Figure 9 (B
) shows the case of Equation 11. ##EQU6## The above operation is repeated until B<A. The final remaining difference B constitutes the final membership function (interval width: Me) (see FIG. 9(C)). [Formula 7] Me =B
...Formula 14 [0108] Therefore, i
The starting point Tjs and ending point Tje of the th membership function are expressed by the following equation. [Equation 8] Conversion phase processing unit The conversion phase processing unit 3 uses the membership function of the antecedent obtained as described above to create a membership function of the consequent. , which creates a set of rules for fuzzy inference. The configuration of the conversion phase processing section 3 is shown in FIG. The conversion phase processing unit 3 includes an antecedent membership function storage unit 31, a consequent membership function storage unit 32, a rule storage unit 33, and the above-mentioned antecedent membership function determination unit 42 and learning result storage unit 13.
and a case study execution unit 12. [0112] The antecedent membership function determining unit 42 is
A label (a kind of symbol for identifying a membership function, preferably given as linguistic information) is assigned to all the membership functions obtained as described above. An example of a label is NL (Negative Lar).
ge: Negatively large), NM (Negative Med
ium: Medium negative), NS (Negative)
Small: Negatively small), ZR (Zero: Almost zero)
, PS (Positive Small)
, PM (Positive Medium), PL (Positive Large), etc. may be linguistic information, or MF11, MF12,
..., MFij, etc. may be used. [0113] The antecedent membership function determination unit 42 is
Data representing each antecedent membership function (may be a setting value indicating the vertex of the membership function, or a value representing the start point and end point of the above-mentioned interval; however, data representing these setting values and the start point and end point of the interval) value) is given to the antecedent membership function storage section 31 and the rule storage section 33 along with the fuzzy label assigned to it. Data representing these antecedent membership functions and fuzzy labels are stored in these storage units 31,
33. [0114] The antecedent membership function determining unit 42 also creates combinations for all input variables of setting values (input data) corresponding to the vertices of the determined antecedent membership function, and sequentially calculates the combinations of the set values (input data) for all input variables. It is given to the learning execution unit 12. The case learning execution section 12 outputs output data corresponding to the given set of input data, and provides the output data to the consequent membership function storage section 32 and the rule storage section 33. The membership function of the consequent part is represented by the output data obtained from the case learning execution unit 12. The consequent membership function is represented by a singleton, as shown in FIG. 12, and is represented by one bar (grade 1) standing at the position of the output data. FIG. 12 shows only a part of the created consequent membership function. However, the consequent membership function may be realized by a triangular function. In this case, the triangular membership function is formed to take a value of grade 1 at the position of the output data and to have a base of an appropriate length. The consequent membership function created in this manner is stored in the consequent membership function storage section 32. The rule storage unit 33 creates and stores a set of fuzzy rules based on the fuzzy label of the given antecedent part and the output data. Each rule has a label of a membership function represented by a set of input data given to the case learning execution unit 12 as an antecedent part, and a corresponding output data obtained from the execution unit 12 as a consequent part. . An example of the rule created in this way is shown in FIG. FIG. 11 expresses the following rules. If input 1 is PL and input 2 is NL, set the output to 1.0
Let it be. If input 1 is PL and input 2 is NM, set the output to 5.0
Let it be. If input 1 is PL and input 2 is NS, the output is 4.8
Let it be. If input 1 is PM and input 2 is NL, set the output to 2.3
Let it be. If input 1 is PM and input 2 is NM, the output is 4.5
Let it be. If input 1 is PM and input 2 is NS, the output is 5.6
Let it be. If input 1 is PS and input 2 is NL, set the output to 1.5
Let it be. If input 1 is PS and input 2 is NM, the output is 3.2
Let it be. If input 1 is PS and input 2 is NS, the output is 6.7
Let it be. Execution Phase Processing Unit The execution phase processing unit 5 executes fuzzy inference calculations based on the rules created as described above, and its configuration may be of a known type. As shown in FIG. 13, the execution phase processing unit 5 includes a fuzzy operation execution unit 51, the aforementioned antecedent membership function storage unit 31, consequent membership function storage unit 32, and rule storage unit 33. It consists of When input data is given, the antecedent membership functions according to the rules stored in the rule storage section 33 are read out from the storage section 31, and the degree of compatibility of the input data with each membership function is determined. The minimum fitness value is calculated for each rule. On the other hand, the consequent membership function of each rule is read out from the consequent membership function storage unit 32, and its height is determined by the minimum value of the fitness of the corresponding rule. A centroid calculation is performed on the calculation results (cut consequent membership functions) obtained for all rules, and final output data is calculated and output. [0124] The fuzzy inference operation is the MIN-MA described above.
It goes without saying that there are various methods other than calculating the center of gravity. It goes without saying that such execution phase processing section 5 may itself be an independent fuzzy inference device. Second Embodiment Next, a second embodiment will be explained. FIG. 14 is a functional block diagram of the fuzzy processing device of the second embodiment, and FIG. 15 is a flow chart showing an outline of its operation. As can be seen from the comparison of FIGS. 1 and 2 with FIGS. 14 and 15, in the second embodiment, after creating fuzzy rules, fuzzy inference is performed according to the fuzzy rules, and the fuzzy The inputs to be deleted are determined based on the results of the inference. In FIGS. 14 and 15, the same components as those shown in FIGS. 1 and 2 are denoted by the same reference numerals, and the explanation thereof will be omitted. The learning phase processing unit 1, resolution determination phase processing unit 4, and conversion phase processing unit 3 calculate the antecedent membership function, Consequent membership functions and fuzzy rules are created and stored in each of the storage units 31, 32 and 33. Next, input variable deletion processing is performed in the input determination phase processing section 6. The configuration of the input determination phase processing section 6 is shown in FIG. In this figure as well, the same components as those shown in FIGS. 5 and 13 are given the same reference numerals. [0132] In response to instructions from the output variance monitoring unit 22, the input fluctuation instructing unit 21 sequentially generates input data consisting of combinations of all input variables, and provides the input data to the execution phase processing unit 5 and the output variance monitoring unit 22. The execution phase processing unit 5 uses the given input data to perform fuzzy inference according to the antecedent membership function, consequent membership function, and fuzzy rules stored in each storage unit 31, 32, and 33. and output the corresponding output data. This output data is given to the output distribution monitoring section 22. [0133] The output distribution monitoring unit 22 creates an input/output matrix as shown in Table 2 or Table 3 using the input data and output data provided, and outputs it in the same manner as in the first embodiment described above. It is decided that input variables that have a small correlation with the input variables should be deleted. The input variables to be deleted are stored in the deletion input storage section 23. [0134] When there is an input to be deleted, the process returns to the learning phase processing section 1 again (step 108 in Fig. 15).
(return to 101), using the sample data excluding the sample data related to the input variables to be deleted,
Again, the learning phase processing section 1, the conversion phase processing section 3, and the resolution determination phase processing section 4 create an antecedent part membership function, a consequent part membership function, and a fuzzy rule. If there is no input variable to be deleted, the process proceeds to the execution phase processing unit 5 (although this process is not necessarily required).

[Brief explanation of drawings]

FIG. 1 is a functional block diagram showing the configuration of a fuzzy processing device according to a first embodiment.

FIG. 2 is a flow chart showing the operation of the fuzzy processing device according to the first embodiment.

FIG. 3 is a functional block diagram showing the configuration of learning phase processing and the like.

FIG. 4 is a graph showing the relationship between input and output obtained through learning.

FIG. 5 is a functional block diagram showing the configuration of an input determination phase processing section.

FIG. 6 is a functional block diagram showing the configuration of a resolution determination phase processing section.

FIG. 7 is a graph showing how the width of the section of the membership function created changes depending on the amount of change in output.

FIG. 8 shows how the width of the interval of the antecedent membership function is determined.

FIGS. 9A, 9B, and 9C illustrate processing according to an algorithm for determining the interval of the antecedent membership function.

FIG. 10 is a functional block diagram showing the configuration of a conversion phase processing section.

FIG. 11 is a table showing an example of created fuzzy rules.

FIG. 12 is a graph showing a consequent membership function represented by a singleton.

FIG. 13 is a functional block diagram showing the configuration of an execution phase processing section.

FIG. 14 is a functional block diagram showing the configuration of a fuzzy processing device according to a second embodiment.

FIG. 15 is a flow chart showing the operation of the fuzzy processing device according to the second embodiment.

FIG. 16 is a functional block diagram showing the configuration of an input determination phase processing section.

[Explanation of symbols]

1 Learning phase processing section 2, 6 Input decision phase processing unit 3 Conversion phase processing section 4 Resolution determination phase processing unit 5 Execution phase processing unit

[Table 3]

Claims (40)

[Claims] [Claim 1] Using sample data that includes a plurality of sets of input data for a plurality of given types of input variables and corresponding output data for at least one type of output variable, A learning means for constructing a structure in which output data corresponding to an arbitrary set of input data regarding a plurality of types of input variables can be obtained by learning, generating a plurality of sets of input data for a plurality of input variables,
By giving these to the above learning means, output data corresponding to them is obtained, and for each input variable, an antecedent membership function is created whose spread corresponds to the magnitude of change in output data with respect to change in input data. An antecedent part creation means and an input data set consisting of a combination of input representative values for a plurality of input variables for the antecedent membership function created by the antecedent part creation means are provided to the learning means, and the input data set is provided to the learning means. A consequent membership function is created based on the output data obtained from the above learning means, and an antecedent membership function having the input representative value included in the above input data set and the corresponding antecedent membership function are created. A fuzzy processing device comprising a rule creation means for creating a rule consisting of a consequent membership function. [Claim 2] Generate a plurality of sets of input data regarding a plurality of input variables, provide these to the learning means to obtain output data corresponding to them, and based on these input data and output data, 2. The fuzzy processing device according to claim 1, further comprising input determining means for determining whether there is an input variable whose correlation with output data is smaller than a predetermined value. [Claim 3] If there is an input variable whose correlation with the output data is smaller than a predetermined value, it is determined as an input variable to be deleted, and the sample or sample to be given to the learning means is determined.
3. The fuzzy processing apparatus according to claim 2, further comprising control means for deleting data regarding the deleted input variables from the data and providing the data to the learning means, and causing the learning means to repeat the learning process again. 4. The control means according to claim 3, wherein the control means performs control to repeatedly delete data regarding input variables to be deleted from the sample data and learning until there are no input variables to be deleted. Fuzzy processing device. 5. The fuzzy processing device according to claim 4, wherein the antecedent part creation means and the rule creation means use the learning means in a state where there are no input variables to be deleted. 6. Claim 1, further comprising fuzzy inference means for performing fuzzy inference operations in accordance with the antecedent part membership function, the consequent part membership function, and the rules created by the antecedent part creation means and the rule creation means. Fuzzy processing device described in. 7. Fuzzy inference means for performing fuzzy inference operations according to the antecedent part membership function, consequent part membership function and rules created by the antecedent part creation means and rule creation means, and a plurality of input variables. Generate multiple sets of input data for , provide these to the fuzzy inference means to obtain corresponding output data, and based on these input data and output data, the correlation for the output data is a predetermined value. 2. The fuzzy processing device according to claim 1, further comprising input determining means for determining whether there is an input variable smaller than . [Claim 8] If there is an input variable whose correlation with the output data is smaller than a predetermined value, it is determined as an input variable to be deleted, and the sample or sample to be given to the learning means is determined.
8. The fuzzy processing apparatus according to claim 7, further comprising control means for deleting data regarding the deleted input variables from the data and providing the data to the learning means to cause the learning means to repeat the learning process again. 9. The control means deletes data regarding input variables to be deleted from sample data, learns, creates antecedent membership functions, and creates rules until there are no input variables to be deleted. 9. The fuzzy processing device according to claim 8, wherein the fuzzy processing device performs repeated control. 10. The fuzzy processing apparatus according to claim 9, wherein the antecedent part creation means and the rule creation means use the learning means in a state where there are no input variables to be deleted. 11. The learning means includes a first storage means for storing sample data, a neural network means for performing learning by being given the sample data, and a learning result by the neural network means. The fuzzy processing device according to claim 1, comprising: second storage means. 12. The antecedent generating means includes input generating means for generating a plurality of sets of input data regarding a plurality of input variables, and output data corresponding to the sets of input data given from the input generating means. the above-mentioned learning means for calculating and outputting; means for calculating the amount of change in output data that occurs when input data fluctuates by a constant value for each input variable; means for determining a fluctuation range of the input data so as to maintain the same, and assigning one antecedent membership function to each of the fluctuation ranges;
The fuzzy processing device according to claim 1, comprising: 13. The input determining means includes input generating means for generating a plurality of sets of input data regarding a plurality of input variables, and output data corresponding to the sets of input data given from the input generating means. For each input variable, the input data of all other input variables except the target input variable are fixed, and the output data when the input data of the target input variable is changed. consisting of means for calculating the sum of variances, and means for comparing the sum of variances with a predetermined reference value and determining that input variables for which the sum of the variances is smaller than the predetermined reference value should be deleted. The fuzzy processing device according to claim 2. 14. The input determination means includes an input generation means for generating a plurality of sets of input data regarding a plurality of input variables, and provides the set of input data generated by the input generation means to the fuzzy inference means, Correspondingly, the output data obtained from the above fuzzy inference means is taken in, and for each input variable, the input data of all other input variables except the target input variable are fixed, and the input data of the target input variable is means for calculating the sum of the variances of the output data when changing the value, and comparing the sum of the variances with a predetermined reference value, and deleting input variables for which the sum of the variances is smaller than the predetermined reference value. 8. The fuzzy processing device according to claim 7, further comprising: means for determining that the fuzzy processing device is a kimono. [Claim 15] Using sample data that includes a plurality of sets of input data for a plurality of given types of input variables and corresponding output data for at least one type of output variable, Learning means for constructing a structure capable of obtaining output data corresponding to arbitrary sets of input data regarding multiple types of input variables through learning; input generating means for generating multiple sets of input data regarding multiple input variables; means for supplying the set of input data given from the input generation means to the learning means and controlling the learning means to operate and obtain output data corresponding thereto; for each input variable, when the input data fluctuates by a constant value; A means for calculating the amount of change in output data that occurs, and a range of variation in input data for each input variable so that the amount of change in output data remains constant, and one antecedent membership function for each range of variation. means of allocating
A fuzzy processing device equipped with 16. Means for storing a plurality of sets of input data regarding a plurality of input variables and output data corresponding thereto, a means for storing a plurality of sets of input data regarding a plurality of input variables, and a means for storing the output data that occurs when the input data fluctuates by a constant value for each input variable. For each input variable and the means for calculating the amount of change, determine the range of variation of the input data so that the amount of change in the output data remains constant, and assign one antecedent membership function to each range of variation. A fuzzy processing device equipped with means. 17. Input generation means for generating a set of input data regarding a plurality of input variables, output generation means for generating and outputting output data corresponding to the set of input data given from the input generation means, and each input. Regarding variables, means for calculating the sum of variances of output data when the input data of all input variables other than the target input variable is fixed and the input data of the target input variable is changed, and the above. A fuzzy processing device comprising means for comparing a total sum of variances with a predetermined reference value and determining that input variables for which the sum of the variances is smaller than the predetermined reference value should be deleted. 18. A sample in which the output generation means includes a plurality of sets of input data for a plurality of given types of input variables and corresponding output data for at least one type of output variable. 18. The fuzzy processing device according to claim 17, wherein the fuzzy processing device is a learning means that uses data to construct, through learning, a structure that can obtain output data corresponding to a set of arbitrary input data regarding a plurality of types of input variables. 19. The fuzzy processing according to claim 17, wherein the output generation means is a fuzzy inference means that performs fuzzy inference calculations according to preset antecedent part membership functions, consequent part membership functions, and rules. Device. 20. Means for storing a plurality of sets of input data regarding a plurality of input variables and output data corresponding to these, and for each input variable, inputting of all other input variables except the target input variable. Means for calculating the sum of variance of output data when the data is fixed and input data of a target input variable is changed, and comparing the sum of the variance with a predetermined reference value, a fuzzy processing device, comprising: means for determining that input variables for which the sum of the variances is smaller than , are to be deleted; [Claim 21] Using sample data that includes a plurality of sets of input data for a plurality of given types of input variables and corresponding output data for at least one type of output variable, Through learning, a learning structure is constructed in which output data corresponding to an arbitrary set of input data regarding multiple types of input variables can be obtained, multiple sets of input data regarding multiple input variables are generated, and these are combined into the above learning structure. For each input variable, we created an antecedent membership function whose spread corresponds to the magnitude of the change in the output data with respect to the change in the input data. An input data set consisting of a combination of input representative values for a plurality of input variables for the antecedent membership function is given to the above learning structure, and the consequent member is correspondingly determined based on the output data obtained from the above learning structure. A fuzzy processing method that creates a ship function and creates a rule consisting of an antecedent membership function with an input representative value included in the above input data set and a corresponding consequent membership function. . [Claim 22] Generating a plurality of sets of input data regarding a plurality of input variables, providing these to the learning structure to obtain output data corresponding to them, and based on these input data and output data. 22. The fuzzy processing method according to claim 21, further comprising determining whether there is an input variable whose correlation with the output data is smaller than a predetermined value. [Claim 23] If there is an input variable whose correlation with the output data is smaller than a predetermined value, it is determined as an input variable to be deleted, and data regarding the deleted input variable is deleted from the sample data to be given to the learning structure. 23. The fuzzy processing method according to claim 22, wherein the learning process is applied to the learning structure and the learning process is repeated again. 24. The fuzzy processing method according to claim 23, wherein the deletion of data regarding the input variables to be deleted from the sample data and the learning are repeated until there are no input variables to be deleted. [Claim 25] Using the above learning structure with no input variables to be deleted, the antecedent membership function,
25. The fuzzy processing method according to claim 24, further comprising creating a consequent membership function and a rule. 26. The fuzzy processing method according to claim 21, wherein fuzzy inference calculations are performed according to the created antecedent part membership function, consequent part membership function and rules. [Claim 27] Generate multiple sets of input data regarding multiple input variables, and use these to perform fuzzy inference operations according to the created antecedent membership function, consequent membership function, and rules. 22. The fuzzy processing method according to claim 21, wherein corresponding output data is obtained by performing the above steps, and based on these input data and output data, it is determined whether there is an input variable whose correlation with the output data is smaller than a predetermined value. . [Claim 28] If there is an input variable whose correlation with the output data is smaller than a predetermined value, it is determined as an input variable to be deleted, and data regarding the deleted input variable is deleted from the sample data to be given to the learning structure. 28. The fuzzy processing method according to claim 27, wherein the learning process is applied to the learning structure and the learning process is repeated again. [Claim 29] According to claim 28, the deletion of data regarding the input variables to be deleted from the sample data, the learning, the creation of the antecedent membership function, and the creation of the rules are repeated until there are no input variables to be deleted. Fuzzy processing method described. [Claim 30] Using the above learning structure with no input variables to be deleted, the antecedent membership function,
30. The fuzzy processing method according to claim 29, further comprising creating a consequent membership function and a rule. 31. The fuzzy processing method according to claim 21, wherein the learning structure is constituted by a neural network that performs learning by being given sample data. [Claim 32] Generate a plurality of sets of input data for a plurality of input variables, give the generated sets of input data to the learning structure to calculate output data corresponding to these, and for each input variable, Calculate the amount of change in output data that occurs when input data fluctuates by a certain value,
For each input variable, the variation range of the input data is determined so that the amount of change in the output data remains constant, and one antecedent membership function is assigned to each variation range to calculate the antecedent membership function. 22. The fuzzy processing method according to claim 21. 33. Generate a plurality of sets of input data for a plurality of input variables, provide the generated sets of input data to the learning structure to calculate corresponding output data, and for each input variable, The input data of all other input variables except the target input variable are fixed, and the sum of the variances of the output data when the input data of the target input variable is changed is calculated, and the sum of the above variances and the predetermined value are calculated. 23. The fuzzy processing method according to claim 22, wherein input variables having a total sum of variances smaller than the predetermined reference value are determined to be deleted. [Claim 34] Generating a plurality of sets of input data regarding a plurality of input variables, using the generated sets of input data, and following the created antecedent membership function, consequent membership function, and rule. When output data is obtained by performing fuzzy inference operations, and for each input variable, the input data of all other input variables except the target input variable is fixed, and the input data of the target input variable is changed. A total of the variances of the output data is calculated, the total variance is compared with a predetermined reference value, and it is determined that an input variable whose total variance is smaller than the predetermined reference value is to be deleted. The fuzzy processing method described in 27. [Claim 35] Using sample data that includes a plurality of sets of input data for a plurality of given types of input variables and corresponding output data for at least one type of output variable, Through learning, we construct a learning structure that can obtain output data corresponding to any set of input data regarding multiple types of input variables, generate multiple sets of input data regarding multiple input variables, and calculate the output data of the generated input data. The set is given to the learning structure, the learning structure is operated and controlled to obtain the corresponding output data, and for each input variable, the amount of change in the output data that occurs when the input data fluctuates by a certain value is calculated, For each input variable, determine the variation range of the input data so that the amount of change in the output data remains constant, and create an antecedent membership function by assigning one antecedent membership function to each variation range. Fuzzy processing method. [Claim 36] A plurality of sets of input data for a plurality of input variables and output data corresponding to these are stored in advance, and for each input variable, the above-mentioned output that occurs when the above-mentioned input data fluctuates by a certain value The amount of change in the data is calculated, and for each input variable, the range of variation in the input data is determined so that the amount of change in the output data remains constant, and one antecedent membership function is assigned to each range of variation. A fuzzy processing method that creates antecedent membership functions by [Claim 37] Generate a set of input data for a plurality of input variables, generate output data corresponding to the generated set of input data, and for each input variable, calculate the output data for all other input variables except the target input variable. The input data of the input variable is fixed, and the sum of the variances of the output data when the input data of the target input variable is changed is calculated, the sum of the variances is compared with a predetermined reference value, and the sum of the variances of the output data is calculated. A fuzzy processing method that determines that input variables whose total sum of variance is smaller than a reference value should be deleted. [Claim 38] Using sample data that includes a plurality of sets of input data for a plurality of given types of input variables and corresponding output data for at least one type of output variable, Claim 37: constructing a learning structure that can obtain output data corresponding to an arbitrary set of input data regarding a plurality of types of input variables through learning, and generating output data by giving the set of input data to this learning structure. Fuzzy processing method described. 39. The fuzzy processing method according to claim 37, wherein the output data is generated by performing fuzzy inference calculations according to preset antecedent part membership functions, consequent part membership functions, and rules. [Claim 40] A plurality of sets of input data regarding a plurality of input variables and output data corresponding to these are stored in advance, and for each input variable, all other input variables except the target input variable are stored. Calculate the sum of the variances of the output data when the input data of the target input variable is fixed and change the input data of the target input variable, compare the sum of the variances with a predetermined reference value, and calculate the sum of the variances of the output data when the input data of the target input variable is changed. A fuzzy processing method that determines that input variables for which the sum of the above variances is smaller than are to be deleted.