JPH05108357A - Back-up device for decision of neuro-fuzzy model - Google Patents

Abstract

PURPOSE:To effectively decide en optimum neuro-fuzzy model. CONSTITUTION:An automatic fuzzy modeling part 20, an automatic neuro-modeling part 22, and an automatic neuro-fuzzy modeling part 24 perform each modeling operation based on the input/output data received from an input/output data memory 12. A fuzzy model evaluating part 40, a neuro-model evaluating pert 42, and a neuro-fuzzy modeling part 44 calculate each prescribed evaluation item and store these calculated items in a fuzzy modeling result memory 46, a neuro-modeling result memory 48, and a neuro-fuzzy modeling result memory 50 respectively. At a selected optimum model decision back-up part 52 using the information quantity standard, a fuzzy model information quantity standard calculation part 54, a neuro-model information quantity standard calculation part 60, and a neuro-fuzzy model information quantity standard calculation part 66 calculate each standard based on the stored evaluation items. Then an optimum fuzzy model deciding part 56, an optimum neuro-model deciding part 62, and an optimum neuro-fuzzy model deciding part 68 decide each optimum model and stores these models in an optimum fuzzy model memory 58, an optimum neuro- model memory 64, and an optimum neuro-fuzzy model memory 70 respectively. These stored optimum models are shown at a general evaluation graph display part 72. At the part 52 using no information standard, two items are selected out of those evaluation items stored in the memories 46, 48 and 50. Then a non-deteriorated model is selected at a non-deteriorated model extracting part. This process is repeated for decision of an optimum model.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a neuro-fuzzy model decision support device, and more particularly to, for example, a fuzzy model, a neuro model or a neuro-fuzzy model for household appliances to realize an ideal input / output response. The present invention relates to a neuro-fuzzy model decision support device for assisting a designer in adopting the.

[0002]

2. Description of the Related Art Various models such as a fuzzy model, a neural net model, and a neuro-fuzzy fusion model have been proposed as a method for modeling a nonlinear input-output relationship. When actually designing, when various evaluation items and constraint conditions (model accuracy, memory capacity, learning speed, calculation speed, etc.) are considered from all methods of fuzzy model, neuro model and neuro fuzzy model. , We have to consider which model is best. However, product designers and development engineers rely on experience and intuition to select fuzzy models, neuromodels and neurofuzzy models, and to determine the model structure based on only preliminary examination work that is not always sufficient by trial and error. The current situation is to determine the parameters.

[0003]

In such a conventional method, it takes a long time to determine a model, and the reliability of whether or not the model is the best is not sufficient. was there. Therefore, a main object of the present invention is to provide a neuro-fuzzy model decision support device capable of efficiently supporting which model should be adopted.

[0004]

A first aspect of the present invention is an input / output data memory for holding input / output data, a fuzzy structure, a neuro structure and a structure parameter setting means for setting respective structure parameters of the neuro fuzzy structure. Automatic modeling means for determining optimum parameters for input / output data for each structure set by the means, evaluation means for calculating a model obtained by the automatic modeling means for each predetermined evaluation item,
A result storage memory that holds the results calculated by the evaluation means, an information amount reference calculation unit that refers to the contents of the result storage memory to calculate a predetermined information amount reference for the model, and a calculation result of the information amount reference calculation unit. A neuro-fuzzy model decision support device comprising an optimum fuzzy model, an optimum neuro model, and an optimum model decision means for deciding the optimum neuro fuzzy model based on the above.

A second aspect of the present invention is an input / output data memory for holding input / output data, a fuzzy structure, a neuro structure, and a structure parameter setting means for setting respective structure parameters of the neuro fuzzy structure, and each set by the structure parameter setting means. Automatic modeling means for determining optimum parameters for input / output data with respect to structure, evaluation means for calculating a model obtained by the automatic modeling means for each predetermined evaluation item, result storage memory for holding results calculated by the evaluation means, and A neuro-fuzzy model decision support device comprising a non-inferior model extraction means for extracting a plurality of non-inferior models by referring to the contents of a result storage memory.

[0006]

The required input / output data (to be learned) is previously input to the input / output data memory. In the structural parameter setting means, for example, the number of fuzzy divisions for each input is specified for a fuzzy model, the number of hidden layer units is specified for a neuro model, and the number of antecedent neural networks and antecedent neural for a neuro fuzzy model. Specify the number of networks and the structure of these neural nets. In the automatic modeling means, for each structure set by the structure parameter setting means,
Optimal parameters are determined for the input / output data stored in the input / output data memory, and a model is obtained for each structure. The evaluation unit evaluates the model obtained by the automatic modeling unit with predetermined evaluation items such as model accuracy (error regarding learning input / output data and error regarding evaluation data), required memory capacity, learning speed corresponding to various microprocessors, Calculate the calculation speed. The result is held in the result storage memory.

The information amount reference calculation means of the first invention calculates the information amount reference value for each evaluation item, and the determination means determines the optimum fuzzy model, the optimum neuro model and the optimum neuro fuzzy model based on the calculated information content reference value.
Preferably, the evaluation display means displays the comprehensive evaluation for each optimum model in the radar chart format, for example. Therefore, the designer may look at it and decide which model to adopt.

The non-inferior model extracting means of the second invention extracts a plurality of non-inferior models by referring to the contents of the result storage memory.
Then, the support means provided as needed interactively supports the determination of the optimum selection model from the plurality of non-inferior models based on the selection criteria of the designer.

[0009]

According to the present invention, the fuzzy, neuro, or neuro-fuzzy structure is automatically determined when input / output data is given, and a model is obtained for each structure. It is only necessary to select a preferred optimal model from among, and therefore, a model to be efficiently incorporated can be determined in a very short time as compared with the conventional method. Further, since the model is extracted based on the result evaluated by the evaluation means, it is possible to trust that the selection optimum model determined thereby is the best model.

The above-mentioned objects, other objects, features and advantages of the present invention will become more apparent from the following detailed description of the embodiments with reference to the drawings.

[0011]

BEST MODE FOR CARRYING OUT THE INVENTION The neuro-fuzzy model decision support apparatus 10 of the embodiment shown in FIG. 1 is best suited for modeling a nonlinear input-output relationship by using any of a fuzzy model, a neuro model and a neuro-fuzzy fusion model. And includes an input / output data memory 12 for storing input / output data. Further, the neuro-fuzzy model determination support device 10 uses the fuzzy model structure parameter designating unit 14 that designates, for example, the number of fuzzy divisions for each input / output data input, for example, the number of intermediate layer units in the case of a three-layer hierarchical neural network. A neuro model structure parameter designating unit 16 for designating, and a neuro fuzzy model structure parameter for designating the number of antecedent neural nets, the number of consequent neural networks, and the structures of these neural networks in the case of, for example, fuzzy inference driven by a neural network. Designating part 18
including.

[0012] It should be noted that such structural parameters can be changed in accordance with the use of fuzzy, neuro, or different neuro-fuzzy structures. The automatic fuzzy modeling unit 20, the automatic neuro-modeling unit 22 and the automatic neuro-fuzzy are respectively set for the model structures determined by the fuzzy model structure parameter specifying unit 14, the neuro model structure parameter specifying unit 16 and the neuro fuzzy model structure parameter specifying unit 18. The modeling unit 24 uses the input / output data stored in the input / output data memory 12 to perform modeling.

First, the algorithm of the automatic fuzzy modeling unit 20 will be described. In the automatic fuzzy modeling unit 20, for example, a fuzzy inference method using a gradient method is used to input x X = (x ₁ , ..., x _i , ..., x
_m ) ∈ R ^m , the function y = f such that the output is y ∈ R ¹
When identifying ( x ), it is assumed that the input x _i is standardized to be included in the section X _{i as} shown in Equation 1. However, in this specification, the symbol " ] Indicates a vector value.

[0014]

[Equation 1]

In the section X _i , L _i points a _i are taken as shown in equation 2.

[0016]

[Equation 2]

[0017] Then, as membership function matters section before FIG 2 (when _{L i = 4), a i} j (i) a vertex x
A triangle membership function A _i ^{j (i)} (x, where _i is the _i- coordinate, and the adjoining membership function intersects with a grade value of 0.5
_i ) is defined as L _i . At this time, the number of rules s for the simplified fuzzy inference is n as shown in Formula 3, and the n rules s are given by Formula 4.

[0018]

[Equation 3]

[0019]

[Equation 4]

The fitness μ _s of the antecedent part of the rule s is given by the equation 5, and the inference result y of the simplified fuzzy inference is calculated by the equation 6.

[0021]

[Equation 5]

[0022]

[Equation 6]

The consequent parameter w_s, S = 1,
2, ..., n and antecedent parameter a _i, I = 1, 2,
…, M, for example,
Therefore, the parameters are updated. In addition, P is a penalty
Tee function.

[0024]

[Equation 7]

[0025]

[Equation 8]

Next, the algorithm of the automatic neuromodeling unit 22 will be described. As the neuro model, various models have been proposed depending on the way in which the units that make up the model are connected. Here, among the generally well-known hierarchical structure models shown in FIG. 3, the input layer 26
A three-layer neuro model including the intermediate layer 28 and the output layer 30, that is, a neuro model having a hierarchical three-layer structure will be described. In this neuro model, based on the steepest descent method, for example, in the direction of reducing the error of the equation 9,
And changing the weighting factor of the network according to Eq.

[0027]

[Equation 9]

[0028]

[Equation 10]

[0029]

[Equation 11]

Here, N is the number of data, y ^p is the target value of the p-th learning data, / y ^p is the model output value using the p-th input data, and ω _ij ^k is the i-th unit of the k-th layer. To the j-th unit of the k + 1-th layer, α and β are learning parameters. Equation 8 represents the load change at the t-th time, and the t + 1-th load is the load at the t-th learning,
Equal to the addition of Δω _ij ^k (t).

Next, the algorithm of the automatic neuro-fuzzy modeling unit 24 will be described with reference to the neuro-fuzzy model structure example shown in FIG. The operation amount y _i ^* for the inference rule and the input data x _i is obtained from the following procedure. First, as the procedure 1, the input variable x related to the output y
₁ , x ₂ , ..., X _n are set. Input / output data (y _i , x _i ) = (y _i , x _i1 , x _i2 , ..., X _in ), i
It is assumed that = 1, 2, ..., N are obtained. Here, the input data x _ij , j = 1, 2, ..., N indicates the i-th data of the j-th input variable.

Next, in procedure 2, the input / output data is r
Split, R_s, S = 1, 2, ..., R. Where each
Split means inference rule, each R_sInput and output data of
(Y_i ^s, X_i ^s), I = 1, 2, ..., N^sIt is represented by. Was
But N^sIs each R_sIs the number of input / output data of. That
Then, as the procedure 3, the NN of FIG._memTo use the
The shape of the umbership function is determined, and in step 4, NN₁，
NN₂, ..., NN_rIs used to identify the structure of the consequent part,
Then, as step 5, the estimated value y_i ^*Is obtained by
It

[0033]

[Equation 12]

Where mey_isIs the optimal obtained in step 4
This is an estimated value based on a simple back propagation learning model. Sanawa
Then, in Fig. 4, the membership value of the antecedent part of each inference rule
μ_As(X_i1, X _i2, ..., x_in) And the estimated value mey of the consequent part
_isAnd are multiplied by accumulators 32, 34 and 36,
Estimated from the result of the sum operation between the rules in the adder 38
Constant y_i ^*Is obtained. However,
Then Σμ_As(X_i1, X_i2, ..., x _in) = 1
ing.

Then, the automatic fuzzy modeling unit 20,
The outputs from the automatic neuro modeling unit 22 and the automatic neuro fuzzy modeling unit 24 are output to the fuzzy model evaluation unit 40, the neuro model evaluation unit 42, and the neuro fuzzy model evaluation unit 44, respectively. The fuzzy model evaluation unit 40, the neuro model evaluation unit 42, and the neuro fuzzy model evaluation unit 44 respectively include error calculation units 40a, 42a and 44a that calculate an error, and storage capacity calculation units 40b, 42b and 44b that calculate a storage capacity. , A learning speed calculation unit 40c for calculating a learning speed,
42c and 44c and operation speed calculators 40d, 42d and 44d for calculating operation speed, and each model is evaluated based on, for example, an error (approximation accuracy), a storage capacity, a learning speed, and an evaluation index of the operation speed.

First, the error calculators 40a, 42a and 4
As the error calculated in each of 4a, for example, a value obtained by dividing the value of Expression 7 by the total number of input / output data is used as shown in Expression 13.

[0037]

[Equation 13]

Next, the storage capacities calculated by the storage capacities calculating units 40b, 42b, and 44b are the storage capacities required when the neuro model and the fuzzy model are installed in the microcomputer application product. It can be calculated from the capacity required to define the structure, the capacity of neuro-calculation and fuzzy inference processing programs, and the capacity to store learning data.

First, in the fuzzy model evaluation section 40, the structure and variables of fuzzy knowledge necessary for fuzzy modeling are shown in FIG. In FIG. 5, variables such as membership functions, fuzzy sets of antecedent parts, structures of fuzzy rules and variables for storing inference results, the number of inputs necessary for inference, the number of outputs, and the number of rules are defined. The number of bytes of the structure required for one membership function is 8 bytes, the number of bytes of the structure required for one antecedent part fuzzy set is 14 bytes, and the number of bytes of the structure required for one fuzzy rule is ( 2 · m + 4 · Q + 4) bytes, the number of bytes required to store one inference output value is 4 bytes, and the number of bytes required to store the number of inputs, the number of outputs and the number of rules is 6 bytes. When the total number of membership functions is set to 14 and the total number of fuzzy rules is set to 15, the storage capacity Fe of fuzzy knowledge required at the time of execution can be obtained by the following formula 16.

[0040]

[Equation 14]

[0041]

[Equation 15]

[0042]

[Equation 16]

At the time of learning, in addition to the equation (14), variables for storing learning coefficients and variables for storing learning data are required. When the number of learning data is d, the number of bytes required to store the learning data is (m + q) · d · 4 bytes, and the number of bytes required to store the learning coefficient is 4 bytes. The storage capacity Fs of fuzzy knowledge is

[0044]

[Equation 17]

FIG. 6 shows variables required for neuromodeling in the neuromodel evaluation unit 42. The variables include the output value of the input layer 26, the output value of the intermediate layer 28, the output value of the output layer 30, the offset value of the intermediate layer 28, the offset value of the output layer 30, the input layer 26 and the intermediate layer 2.
8, the load factor value between the intermediate layer 28 and the output layer 30, the delta value of the intermediate layer 28, and the output layer 3
There are 9 delta values of 0. The number of bytes required for a float type variable is 4 bytes, the number of bytes required for a short int type variable is 2 bytes, the number of units in the input layer 26 (the number of inputs) is m, and the number of units in the middle layer 28 is h. And the number of units (the number of outputs) of the output layer 30 is q, a variable for storing the output value of the unit of each layer is 4 · (m + h +
q) bytes, 4.2. (h + q) bytes as variables for storing offset values and delta values of all units of the intermediate layer 28 and the output layer 30, respectively, and a load coefficient between the input layer 26 and the intermediate layer 28. The variable to be stored is 4 · (m · h) bytes, and the variable to store the weighting factor between the intermediate layer 28 and the output layer 30 is 4 · (h · q) bytes, and the storage capacity Ne required at the time of execution is Ne. Can be obtained by Equation 18.

[0046]

[Equation 18]

At the time of learning, in addition to the equation 18, variables for storing learning coefficients and variables for storing learning data are required. If the learning data is d, the number of bytes required to store the learning data is (m + q) · d · 4 bytes, and the number of bytes required to store the learning coefficient is 8 bytes. Storage capacity N
s can be obtained by Equation 19.

[0048]

[Formula 19]

Further, the neuro-fuzzy model evaluation unit 44
Can be calculated in the same manner as in the case of the above-mentioned neuro model or fuzzy model. Next, with respect to the learning speeds calculated by the learning speed calculation units 40c, 42c, and 44c, the number of times of addition, subtraction, multiplication, and division required for each learning of the neuro operation or fuzzy inference is calculated. The speed is calculated by multiplying the calculated number of calculations and the number of instruction clocks of the CPU required for each calculation. This operation is repeated a predetermined number of times to obtain an average value of speeds, and this average value is used as the learning speed. In this way, it is possible to calculate the learning speed required until the learning is completed when the variation Δε of the value of Expression 13 reaches the set value. Note that any of the fuzzy model, the neuro model, and the neuro fuzzy model can be calculated by the same method.

The operation speeds calculated by the operation speed calculators 40d, 42d, and 44d, that is, the speeds for giving data to the learned model and obtaining the model output value can be calculated as follows. First, in the fuzzy model evaluation unit 40, the central value of the j (i) th membership function of the antecedent part fuzzy set corresponding to the i-th input value is x i, and the i-th input value is a _i ^{j (i).} , The membership function is A _i ^{j (i)} (x _i ), and the fitness of the antecedent part of the fuzzy rule s is μ _s , the inference result y of the simplified fuzzy inference is It is calculated by Equation 6.

[0051]

[Equation 20]

From the equation (20), the calculation required for one membership function is three times of subtraction and one division, and the total number of membership functions is the equation (21). Therefore, it is necessary to calculate the grade values of all the membership functions. Calculation clock number Gc is
Can be obtained with.

[0053]

[Equation 21]

[0054]

[Equation 22]

From Equation 5, the calculation of the antecedent part conformance required for one rule requires multiplication (number of inputs-1) times,
Since the total number of rules is given by equation 23, the number of operation clocks Rc required to calculate the fitness of all rules can be obtained by equation 24.

[0056]

[Equation 23]

[0057]

[Equation 24]

From Equation 6, the calculation required for one output value calculation is that the sum of the product of the rule conformance and the real value of the consequent part is divided by the sum of the rule conformance. The calculation clock number Oc is calculated by the equation 25.

[0059]

[Equation 25]

Operation clock number Fc in fuzzy inference
Is calculated by Equation 26, which is obtained by adding Equations 22, 24 and 25.

[0061]

[Equation 26]

Further, in the neuro model evaluation section 42, when the output from each unit is the sum of the input to that unit and the load added with an offset value, the transfer function f of the unit is input. Is the output value of. Let m be the number of units (the number of inputs) of the input layer 26, h be the number of units of the intermediate layer 28, and q be the number of units (the number of outputs) of the output layer 30. The output of the i-th unit is Ii, the load between the i-th unit of the input layer 26 and the j-th unit of the intermediate layer 28 is Wji, the load between the j-th unit of the intermediate layer 28 and the k-th unit of the output layer 30 is Vkj, When the offset of the jth unit of the intermediate layer 28 is θj and the offset of the kth unit of the output layer 30 is γk, the output value Hj of the jth unit of the intermediate layer 28 is
7, the output value Pk of the k-th unit of the output layer 30
Is calculated from Eq.

[0063]

[Equation 27]

[0064]

[Equation 28]

To obtain the sum of the inputs to the j-th unit of the hidden layer 28, the addition is performed m-1 times, the multiplication is performed m times, and the hidden layer 2 is used.
To obtain the output from the j-th unit of 8
1 times, 13 times multiplication and 1 time division are required. Output layer 30
Summation of the inputs to the k-th unit of
−1 times, multiplication is performed h times, addition 10 times, multiplication 13 times, and division 1 are required to obtain the output from the k-th unit of the output layer 30. Therefore, assuming that the number of clocks required for addition is Ac, the number of clocks required for subtraction is Sc, the number of clocks required for multiplication is Mc, and the number of clocks required for division is Dc, the operation clocks required for neuro computation are The number Nc is represented by the number 29.

[0066]

[Equation 29]

Further, in the case of the neuro-fuzzy model, it can be calculated by the same method as in the case of the neuro-model or the fuzzy model. The number of learnings is as follows for fuzzy model, neuro model and neuro fuzzy model.
It can be defined by terminating the learning when the change Δε in the value of the equation 13 becomes smaller than the preset δ and counting the number of learnings up to that time.

Next, the process of evaluating the modeling result of each model will be described. In the case of the fuzzy model evaluation unit 40, the error calculated by the error calculation unit 40a, the storage capacity calculated by the storage capacity calculation unit 40b, and the learning speed calculation unit 4
The learning speed calculated at 0c and the result calculated at the calculation speed calculation unit 40d are held in the fuzzy modeling result storage memory 46. In the case of the neuro model evaluation unit 42, the error calculated by the error calculation unit 42a, the storage capacity calculated by the storage capacity calculation unit 42b, and the learning speed calculation unit 42c.
The learning speed calculated in the above and the result calculated in the calculation speed calculation unit 42d are stored in the neuro modeling result storage memory 48.
Hold on. In the case of the neuro-fuzzy model 44, the error calculated by the error calculation unit 44a, the storage capacity calculated by the storage capacity calculation unit 44b, and the learning speed calculation unit 44
The learning speed calculated in c and the result calculated in the calculation speed calculation unit 44d are held in the memory 50 for storing the neuro-fuzzy modeling result.

Then, the fuzzy modeling result storage memory 46, the neuromodeling result storage memory 48, and the neurofuzzy modeling result storage memory 50.
The respective outputs of the above are sent to the preference optimal model determination support unit 52. As a method for determining the preference optimum model of the preference optimum model determination support unit 52, for example, AIC or MPLP is used.
Among them, the information standard of AIC is used. AIC is one of the indexes for comprehensively evaluating whether the model is good or bad from the memory capacity and the error, and is defined by Equation 30.

[0070]

[Equation 30]

Here, N is the number of data used for modeling, and ε _i ² is the squared error between the model output value and the output data value. The first term of Expression 30 represents the badness of the model itself from the sum of squared errors, and the second term adds the influence of the number of parameters. When the approximation performances of the models are almost the same, the number of parameters of the second term acts and a model having a small number of parameters is selected.

In the case of a fuzzy model, the fuzzy modeling result storage memory 46 is referred to, and the fuzzy model information amount reference calculation unit 54 calculates the information amount reference value from the storage capacity and the error. Next, the optimum fuzzy model determination unit 56 determines the model with the smallest value of the information amount reference as the optimum model, and holds the result in the optimum fuzzy model storage memory 58.

In the case of the neuro model, the neuro model information amount reference calculation unit 60 refers to the contents of the neuro modeling result storage memory 48 to calculate the information amount reference value from the storage capacity and the error. Next, the optimum neuro model determination unit 62 determines the model having the smallest value of the information amount reference as the optimum model, and holds the result in the optimum neuro model storage memory 64.

Further, with reference to the contents of the neuro-fuzzy modeling result storage memory 50, the neuro-fuzzy model information amount reference calculator 66 calculates the information amount reference value from the storage capacity and the error. Next, the optimal neuro-fuzzy model determination unit 68 determines the model with the minimum value of the information amount reference as the optimal model, and stores the result in the optimal neuro-fuzzy model storage memory 70.

Finally, in the comprehensive evaluation graph display section 72 for a plurality of evaluation items, the optimum fuzzy model storage memory 58,
Based on the evaluation items of the error, the storage capacity, the learning speed, the calculation speed, and the learning frequency, the optimum model of each model structure held in the optimum neuro model storage memory 64 and the optimum neuro fuzzy model storage memory 70,
It is displayed in a radar chart as shown in FIG. The designer determines a preferred optimal model from among the respective optimum models according to the preference criteria possessed by the designer based on the results displayed in the graph. It should be noted that in the display of the radar chart, the fact that the figure extends outward indicates that it is a good model.

In this embodiment, the optimum model of each model structure is displayed on the comprehensive evaluation graph display section 72. However, a non-inferior model is extracted from the optimum model of each model structure and only the non-inferior model is comprehensively evaluated. You may display on the graph display part 72. Further, referring to FIG. 8, a neuro-fuzzy model decision support device 10 ′ according to another embodiment, instead of the preference optimum model decision support unit 52 of the neuro-fuzzy model decision support device 10 according to the previous embodiment, Non-inferior model extraction unit 7
4 and the preference optimal model determination support unit 76. The preference optimum model determination support unit 76 includes a non-inferior model storage unit 78, an evaluation item coordinate designating unit 80, a non-inferior point projection display unit 82 on the evaluation item coordinate system, a constraint condition designating unit 84 in the evaluation item coordinate system, a constraint. A non-inferior point exclusion unit 86 that does not satisfy the condition and a display unit 88 that displays the number of non-inferior points are included.

Neuro-fuzzy model decision support device 1
In the operation at 0 ', the processing up to the fuzzy modeling result storage memory 46, the neuromodeling result storage memory 48, and the neurofuzzy modeling result storage memory 50 is performed in the same manner as in the previous embodiment, and therefore the description thereof is omitted. Is omitted. The outputs from the fuzzy modeling result storage memory 46, the neuromodeling result storage memory 48, and the neurofuzzy modeling result storage memory 50 are the non-inferior model extracting unit 7.
Input to 4. Here, the concept of the non-inferior model will be described. When there are n evaluation items represented by a plurality of real values, each model is represented by an n-dimensional vector. Now 2
Two models p = (p ₁ , p ₂ , ..., _pn ), q =
For (q ₁ , q ₂ , ..., Q _n ), all i = 1, ...,
For n, we will write the formula 31.

[0078]

[Equation 31]

Memory 4 for storing fuzzy modeling result
6. All of the models stored in the neuromodeling result storage memory 48 and the neurofuzzy modeling result storage memory 50 have n evaluation items as components.
A set of all n-dimensional vectors (models) represented by a dimensional vector (points in the n-dimensional space R ⁿ ) is M
And At this time, the perfect optimal model and the non-inferior model are defined as follows. (Definition of Perfect Optimal Model) The model p ∈ M is all p ∈ M
On the other hand, if p ^o ≤ p , then p ^o is a "perfect optimal model". (Definition of non-dominated model) to the model p'∈M, p <p '
(I.e. p ≦ p 'and p ≠ p') when it becomes p ∈M absence, p 'is a non-dominated model.

Using this definition, the non-inferior model set N is generated from the non-inferior model candidate set M as follows. First,
Using the definition of the perfect optimum model, it is checked whether or not the perfect optimum model p ^o εM exists in the non-inferior model candidate set M. If the perfect optimal model p ^o exists, this is adopted as the preferred optimal model, and the whole process is terminated. On the other hand, when the perfect optimal model p ^o does not exist (which corresponds to this case in most cases), the non-inferior model set is extracted by the procedure shown in FIG. First, in step S1, the number of elements of the non-inferior model candidate set M is checked, and the number of elements ≦ 0
If so, end. If the number of elements> 0, step S3
In, one non-inferior model candidate p _j is taken from the non-inferior model candidate set M. At this time, p _j is excluded from M. Then, in step S5, this p _j is compared with all the elements included in the non-inferior model candidate set M, that is, all other elements, that is, all other non-inferior model candidates. Then, in step S7, a model vector pεM superior to p _j (that is, p ≤ p _j and p ≠ p _j )
Is present, in step S9, p _j is not a non-inferior model and is rejected. better model than p _j
If the p ∈M does not exist, since p _j is a non-dominated model by definition, is added p _j as elements of nondominated model set N in step S11. If this process is continued until there are no elements in the non-inferior model candidate set M, all non-inferior models can be extracted from the non-inferior model candidate set M, and all of them are included in the set N.

The output from the non-inferior model extraction unit 74 is the preference optimum model determination support unit 7 which does not introduce the information amount criterion.
6 to the non-inferior model storage unit 78. Note that, here, there are four model evaluation items of the neuro-fuzzy model determination support device 10 ', and p1: error due to evaluation data, p2: storage capacity, p3: execution time calculation time, and p4: learning time, respectively. To do. Further, as a result of extracting the non-inferior model, a total of 12 non-inferior models including five non-inferior fuzzy models, three non-inferior neuro models, and four non-inferior neuro-fuzzy models are stored in the non-inferior model storage unit 78. It is assumed to be remembered. Considering this as a candidate for the optimal preference model, the only optimal preference model is determined from the candidates according to the preference criteria of the designer.

First, the designer sequentially selects two evaluation items that are considered important from the evaluation items p1 to p4. This is performed by using the menu selection means provided by the evaluation item coordinate designating unit 80, such as a mouse or a keyboard and a display, and is represented as evaluation item coordinates. Here, the designer has p1 (error due to evaluation data) and p2
Suppose that (storage capacity) is selected. Non-inferior point projection display unit 82
Then, as shown in FIG. 10, 12 non-inferior models (four-dimensional points) are projected and displayed as non-inferior points on the selected two evaluation item coordinate systems. In addition, in this embodiment, a display unit 88 is provided above the non-inferior point projection display unit 82, and the display unit 88 displays two of the 12 optimal preference model candidates.
The number of non-inferior models, that is, non-inferior points, that satisfy one of the constraints is dynamically displayed. As a result, even if the number of original non-inferior models is very large, the relation between the specified constraint conditions and the number of candidates for the optimal preference model that satisfy this condition, and the optimal preference model when the constraint value is slightly changed. It is possible to know the sensitivity regarding the number of candidates.

Next, the designer, for the time being, focuses only on these two evaluation items p1 and p2 and narrows down the number of model candidates. As a means for that, it is considered that the upper limit value with respect to the evaluation item value is interactively set as a constraint condition regarding the preference optimal model and the candidates for the preference optimal model are narrowed down. FIG. 11 shows this interactive process, in which the designer uses the mouse and the display means provided in the constraint condition designating unit 84 in the evaluation item coordinate system, that is, the value of p1 on the p1 axis, that is, A limit value p1max at which an error value based on the evaluation data is allowable is interactively designated. Similarly, the limit value p2max regarding the storage capacity p2 is designated. The non-inferiority excluding unit 86 rejects the non-inferior model that does not satisfy the specified constraint condition. FIG. 12 shows only the preference optimal model satisfying the constraint conditions concerning p1 and p2 designated in this way, and in this example, the number of non-inferior models satisfying the constraint is narrowed down to five.

Next, the designer selects another evaluation item.
That is, it is assumed that the designer again selects p3 (run time calculation time) and p4 (learning time) by the evaluation item coordinate designating unit 82. In the same way as before, the non-inferior point projection display unit 84 on the evaluation item coordinate system displays p3-p4.
FIG. 13 shows what is projected and displayed on a plane. Figure 1
Similarly to FIG. 11, 3 indicates a process of designating the upper limit value p3max regarding the runtime calculation time p3 and the upper limit value p4max regarding the learning time p4. In this example, finally only the non-inferior neurofuzzy model □ ⁶ is p
Satisfying the constraint conditions regarding 3 and p4, it becomes a preference optimal model based on the designer's preference criteria. FIG. 14 shows this preference optimum model.

[Brief description of drawings]

FIG. 1 is a block diagram showing an embodiment of the present invention.

FIG. 2 is a graph showing a membership function of an antecedent part of a fuzzy model.

FIG. 3 is an illustrative view showing a structural example of a neuro model.

FIG. 4 is an illustrative view showing a structural example of a neuro-fuzzy model.

FIG. 5 is an illustrative view showing a structure and variables of fuzzy knowledge necessary for fuzzy modeling.

FIG. 6 is an illustrative view showing variables necessary for neuromodeling.

FIG. 7 is a radar chart showing an optimum model of each model structure based on evaluation items.

FIG. 8 is a block diagram showing another embodiment of the present invention.

FIG. 9 is a flowchart showing the operation of the non-inferior model extraction unit.

FIG. 10 is a graph showing a state in which 12 non-inferior models are projected onto two evaluation item coordinate systems.

FIG. 11 is a graph showing a process of narrowing down the number of preference optimal model candidates by focusing on only two evaluation items p1 and p2.

FIG. 12 is a graph showing only the preference optimal model that satisfies the constraint condition regarding the evaluation items p1 and p2.

FIG. 13 is a graph showing a process of narrowing down the number of preference optimum model candidates by focusing on only two evaluation items p3 and p4.

FIG. 14 is a graph showing a preference optimal model.

[Explanation of symbols]

10, 10 '... Neuro-fuzzy model determination support device 12 ... Input / output data memory 14 ... Fuzzy model structure parameter designation unit 16 ... Neuro model structure parameter designation unit 18 ... Neuro fuzzy model structure parameter designation unit 20 ... Automatic fuzzy modeling unit 22 ... automatic neuro-modeling section 24 ... automatic neuro-fuzzy modeling section 40 ... fuzzy model evaluation section 42 ... neuro-model evaluation section 44 ... neuro-fuzzy model evaluation section 46 ... fuzzy modeling result storage memory 48 ... neuro-modeling result storage memory 50 ... neuro Memory for storing fuzzy modeling results 54 ... Fuzzy model information amount reference calculation unit 56 ... Optimal fuzzy model determination unit 60 ... Neuro model information amount reference calculation unit 62 ... Optimal neuro model determination Part 66 ... Neuro-fuzzy model information amount reference calculation part 68 ... Optimal neuro-fuzzy model determination part 74 ... Non-inferior model extraction part

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[Procedure amendment]

[Submission date] January 7, 1992

[Procedure Amendment 1]

[Document name to be amended] Statement

[Name of item to be corrected] Claim 1

[Correction method] Change

[Correction content]

[Procedure Amendment 2]

[Document name to be amended] Statement

[Correction target item name] 0004

[Correction method] Change

[Correction content]

[0004]

A first aspect of the present invention is an input / output data memory for holding input / output data, a fuzzy structure, a neuro structure and a structure parameter setting means for setting respective structure parameters of the neuro fuzzy structure. Automatic modeling means for determining optimum parameters for input / output data for each structure set by the means, evaluation means for calculating a model obtained by the automatic modeling means for each predetermined evaluation item,
Result storage memory for storing results of calculation by the evaluation unit, respectively, the calculation result of the result of referring to the contents of the storage memory you calculate predetermined information criterion for model information criterion calculation means, and the information criterion calculation means On the basis of,
A neuro-fuzzy model decision support device comprising an optimum fuzzy model, an optimum neuro model, and an optimum model decision means for deciding the optimum neuro fuzzy model.

[Procedure 3]

[Document name to be amended] Statement

[Correction target item name] 0007

[Correction method] Change

[Correction content]

The information amount reference calculation means of the first invention is a fuzzy
Model, neuro model and neuro fuzzy model
The information standard value is calculated for each of the parameters, and the determining means determines the optimum fuzzy model, the optimum neuro model, and the optimum neuro fuzzy model based on the calculated information standard value. Preferably, the evaluation display means, for each optimal model,
For example, the comprehensive evaluation is displayed in a radar chart format.
Therefore, the designer may look at it and decide which model to adopt.

[Procedure amendment 4]

[Document name to be amended] Statement

[Correction target item name] 0026

[Correction method] Change

[Correction content]

Next, the algorithm of the automatic neuromodeling unit 22 will be described. As the neuro model, various models have been proposed depending on the way in which the units that make up the model are connected. Here, among the generally well-known hierarchical structure models shown in FIG. 3, the input layer 26
A three-layer neuro model including the intermediate layer 28 and the output layer 30, that is, a neuro model having a hierarchical three-layer structure will be described. In this neuro-model, for example, error reverse transfer
Based on the carrying method (back propagation) , the weighting factor of the network is changed according to equations (10) and (11 ) in the direction of reducing the error of equation ( 9 ) .

[Procedure Amendment 5]

[Document name to be amended] Statement

[Correction target item name] 0039

[Correction method] Change

[Correction content]

First, in the fuzzy model evaluation section 40, the structure and variables of fuzzy knowledge necessary for fuzzy modeling are shown in FIG. In FIG. 5, variables such as membership functions, fuzzy sets of antecedent parts, structures of fuzzy rules and variables for storing inference results, the number of inputs necessary for inference, the number of outputs, and the number of rules are defined. The number of bytes of the structure required for one membership function is 8 bytes, the number of bytes of the structure required for one antecedent part fuzzy set is 14 bytes, and the number of bytes of the structure required for one fuzzy rule is ( 2 ・ m + 4 ・q ＋4) bytes (however,
m is the number of inputs, q is the number of outputs) , the number of bytes required to store one inference output value is 4 bytes, and the number of bytes required to store the number of inputs, outputs and rules is It will be 6 bytes. The total number of membership functions is 14
Assuming that the total number of fuzzy rules is 15, the storage capacity Fe of the fuzzy knowledge required at the time of execution can be obtained by the formula 16.

[Procedure correction 6]

[Document name to be amended] Statement

[Correction target item name] 0049

[Correction method] Change

[Correction content]

Further, the neuro-fuzzy model evaluation unit 44
Can be calculated in the same manner as in the case of the above-mentioned neuro model or fuzzy model. Calculated in this way
Each model is added to the knowledge storage capacity (Fs, Ns) of each model
By adding the program capacity required for processing
Storage capacity is calculated. Next, the learning speed calculation unit 40c,
With respect to the learning speeds calculated by 42c and 44c, the number of times of addition, subtraction, multiplication and division required for each learning of the neuro operation and fuzzy inference is calculated. The speed is calculated by multiplying the calculated number of operations and the number of CPU instruction clocks required for each operation. This operation is repeated a predetermined number of times to obtain an average value of speeds, and this average value is used as the learning speed. In this way, it is possible to calculate the learning speed required until the learning is completed when the variation Δε of the value of Expression 13 reaches the set value. In addition,
The same method can be applied to any of the fuzzy model, the neuro model, and the neuro fuzzy model.

[Procedure Amendment 7]

[Document name to be amended] Statement

[Correction target item name] 0069

[Correction method] Change

[Correction content]

Then, the fuzzy modeling result storage memory 46, the neuromodeling result storage memory 48, and the neurofuzzy modeling result storage memory 50.
The respective outputs of the above are sent to the preference optimal model determination support unit 52. As a method of determining the preference optimal model preferences optimal model determination supporting unit 52, for example, AIC and M D LP
Among them, the information standard of AIC is used. AIC is one of the indexes for comprehensively evaluating whether the model is good or bad from the memory capacity and the error, and is defined by Equation 30.

Claims (5)

[Claims] 1. An input / output data memory for holding input / output data, a fuzzy structure, a neuro structure and a structure parameter setting means for setting respective structure parameters of the neuro fuzzy structure, and each structure set by the structure parameter setting means. Automatic modeling means for determining optimum parameters for the input / output data, evaluation means for calculating a model obtained by the automatic modeling means for each predetermined evaluation item, result storage memory for holding results calculated by the evaluation means, respectively An information amount reference calculation means for calculating a predetermined information amount reference for the model by referring to the contents of the result storage memory, and an optimum fuzzy model, an optimum neuro model and an optimum information calculation method based on the calculation result of the information amount reference calculation means. Neurofuzz Provided the best model determining means for determining a model, Neuro-Fuzzy Model determination assisting device. 2. The neuro-fuzzy model decision support device according to claim 1, further comprising evaluation display means for displaying evaluation items for said optimum fuzzy model, optimum neuro model and optimum neuro fuzzy model. 3. An input / output data memory for holding input / output data, a fuzzy structure, a neuro structure, and a structure parameter setting means for setting respective structure parameters of the neuro fuzzy structure, and each structure set by the structure parameter setting means. Automatic modeling means for determining optimum parameters for the input / output data, evaluation means for calculating a model obtained by the automatic modeling means for each predetermined evaluation item, result storage memory for holding results calculated by the evaluation means, respectively And extraction means for extracting a plurality of non-inferior models with reference to the contents of the result storage memory,
Neuro-fuzzy model decision support device. 4. The neuro-fuzzy model determination support device according to claim 3, further comprising a support means for supporting interactively to determine a preference optimum model from the plurality of non-inferior models. 5. The support means is an evaluation item coordinate designating means for sequentially selecting an evaluation item having a high degree of importance among a plurality of evaluation item coordinates for the plurality of non-inferior models, and each of the non-inferior models is assigned to the selected evaluation item coordinate system. Non-inferior point projection display means for projecting and displaying inferior points, constraint condition designating means for designating specific evaluation item values as constraint conditions on the selected evaluation item coordinate system, and the constraint condition designating means. A non-inferior point excluding means for automatically excluding non-inferior points not satisfying the specified evaluation item value, and a display means for displaying the number of non-inferior points satisfying the specific evaluation item value, Item 4. The neuro-fuzzy model decision support device according to item 4.