JPH05298109A - Fuzzy inference system - Google Patents

Abstract

PURPOSE:To have the ambiguity of input environments reflected in a conclusion and to easily expansion/integration an inference system under the environment requiring temporary setting in the case of performing information processing based on fuzzy inference. CONSTITUTION:In the case of calculating one output based on a lot of fuzzy rules, alpha entropy scale is calculated by a fuzzy entropy function corresponding to each grade decided by an input value, respective conclusion part fuzzy sets due to the fuzzy inference based on the respective fuzzy rules are calculated and integrated by performing the alpha-cut of consequent parts corresponding to this alpha entropy scale, and the integrated output fuzzy set is made non-fuzzy. On the other hand, alphai is selected based on the maximum value of fuzzy entropy corresponding to the respective grades, and the alpha-cut of the consequent parts can be performed based on this grade alphai as well.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to information processing such as control of plants and other large-scale equipment, or identification of characters and figures.

[0002]

2. Description of the Related Art Today, various information processing based on fuzzy inference called an expert system is performed. For example, in order to perform process control by this fuzzy inference, the antecedent membership function is defined as a fuzzy set of the deviation of the current controlled variable, which is the state of the controlled device, from the target value, and the variation of the deviation. ,
Moreover, the consequent part membership function that defines the fuzzy set of the manipulated variables is defined, and the observed value (measured value) is associated with the antecedent part membership function to obtain the grade of the measured value. Fuzzy inference is performed so that the membership function of the subject part is α-cut.
-The fuzzy set is calculated by performing the defuzzification operation by calculating the center of gravity of the consequent part fuzzy set, and the operation state of the device to be controlled is controlled so as to approximate the ideal state.

Further, in order to perform the control and judgment by the fuzzy inference more accurately, the responsiveness of the control by the inference device is improved (for example, Japanese Patent Laid-Open No. 63-113.733) and the measurement value is included. Noise removal (for example, Japanese Patent Laid-Open No. 119.803
No.) is being tried. Although fuzzy inference is already performed in many fields for some of the operations for control and information processing in large-scale devices, there are many control rules for controlling plants and complicated information processing.
There will be a need to overlay many rules.

However, when a large number of rules are superposed on the basis of fuzzy inference and inference is performed, an unexpected inference result is calculated, which makes it difficult to obtain appropriate control and judgment results. .. Therefore, the applicant of the present application obtains each conclusion part fuzzy set based on each fuzzy rule, combines each conclusion part fuzzy set into an output fuzzy set, and when performing the defuzzification operation on this output fuzzy set, the fuzzy entropy Has proposed an inference method using (JP-A-4-80826).

[0005]

The inference method that uses the fuzzy entropy to form the output fuzzy set after the conclusion part fuzzy set is obtained and to defuzzify the output fuzzy set in an environment that requires temporary setting. Although it is useful to develop the reasoning of, there were cases where it was not enough to reflect the ambiguity in the input environment in the conclusion part.

[0006]

According to the present invention, when calculating a conclusion part fuzzy set by each fuzzy rule based on fuzzy inference, the grade of each IF antecedent part fuzzy set corresponds to each grade instead of the conventional MIN operation. The fuzzy entropy function E (αi) is used for weighting and the α entropy scale 1 is Σαi × E (αi) / ΣE (αi)
Then, each conclusion part fuzzy set is obtained by α-cutting the output fuzzy set by this α entropy scale l, and each conclusion part fuzzy set is combined to derive the output fuzzy set. The output value is obtained by performing a defuzzification operation based on the Sasa method, the area method, the center of gravity method, or the like.

Further, in calculating the conclusion part fuzzy set by each fuzzy rule based on the fuzzy inference, each IF
The grade of the antecedent part fuzzy set is not the conventional MIN operation, but αi (∃α) is calculated using the maximum value of the fuzzy entropy corresponding to each grade αi as an index, and the output fuzzy set is α-cut by this grade αi. Each conclusion part fuzzy set is obtained by using, and each conclusion part fuzzy set is combined to derive the output fuzzy set, and the defuzzification operation based on the conventional height method, area method, or centroid method is performed from the output fuzzy set. It may be necessary to go and obtain the output value. However, if the fuzzy entropy is the same, select the one with higher fitness.

When performing the defuzzification operation from the output fuzzy set, the output fuzzy set may be defuzzified based on the fuzzy entropy method.

[0009]

[Operation] According to the present invention, the output fuzzy set is α− by the α entropy scale 1 using the fuzzy entropy function corresponding to the grade of each input fuzzy set for weighting.
Since the output value is obtained by performing the defuzzification operation on the output fuzzy set after cutting, it is possible to obtain the output value with emphasis on the intermediate grade level.

Further, when the maximum value of the fuzzy entropy corresponding to the grade of each input fuzzy set is used as an index, the intermediate grade level is first emphasized, and if there are those having the same entropy, the one having a high degree of conformity is selected. It is possible to obtain a priority output value.

[0011]

The first embodiment of the present invention is a method for deriving one output based on a plurality of fuzzy rules. As shown in the flowchart of FIG. 1, an α entropy scale 1 by weighting with a fuzzy entropy function is used. The fuzzy set of the consequent part is calculated using this α entropy scale l
-Cut out the conclusion part fuzzy set, and defuzzify the conclusion part fuzzy set to obtain the output value ω0.
In the defuzzification operation, the output value δ is calculated by inference by the area method or the barycentric method, or the output value ω0 is calculated by inference by the fuzzy entropy method with the fuzzy entropy as a parameter. Is also done.

This fuzzy entropy function E (αi)
The α entropy scale 1 used for weighting is calculated by the following equation.

[0013]

[Equation 1]

The centralized language headed entropy as a fuzzy entropy function is a centralized language headed potential.

[0015]

[Equation 2]

[0016]

[0017]

[Equation 3]

In

[0019]

[Equation 4]

Is called a centralized language heading N of μ (x).

[0021]

[Equation 5]

Of

[0023]

[Equation 6]

Is a centralized language of μ (x), which is called a headed entropy N, and a membership function is

[0025]

[Equation 7]

Represented as In addition, the expanded language head potential

[0027]

[Equation 8]

And

[0029]

[Equation 9]

In

[0031]

[Equation 10]

Is called an expanded language heading N of μ (x).

[0033]

[Equation 11]

Of

[0035]

[Equation 12]

The membership function is called the enlarging language headed entropy N of μ (x).

[0037]

[Equation 13]

It is represented by Furthermore, the bright and dark enhanced language head potential

[0039]

[Equation 14]

And

[0041]

[Equation 15]

In

[0043]

[Equation 16]

The membership function of μ (x) is called the bright and dark enhanced language headed entropy N

[0045]

[Equation 17]

It is represented by And the λ-complement by Sugno

[0047]

[Equation 18]

Then, the inevitable headline entropy

[0049]

[Formula 19]

And normalize this

[0051]

[Equation 20]

And the possibility headline entropy

[0053]

[Equation 21]

And normalize this

[0055]

[Equation 22]

Then, as an expression of the fuzzy set by the modal heading entropy,

[0057]

[Equation 23]

Or

[0059]

[Equation 24]

Can be expressed as, and as a representation of the modal operator by modal headed entropy

[0061]

[Equation 25]

Or

[0063]

[Equation 26]

Can be expressed as Inevitability operator

[0065]

[Outer 1]

Possibility operator

[0067]

[Outside 2]

Modal operator using

[0069]

[Outside 3]

And

[0071]

[Outside 4]

Is

[0073]

[Equation 27]

And

[0075]

[Equation 28]

It is represented as In the present embodiment which uses such a fuzzy entropy function for weighting, in order to derive one output from a plurality of fuzzy rules, first, inference is performed by each fuzzy rule. Is used to calculate the α entropy scale 1 from the fuzzy entropy function E corresponding to the grade of the antecedent membership function, and the α-cut of the antecedent membership function is performed by the α entropy scale 1 to obtain the conclusion part fuzzy set. For example, in the case of two inputs and one output, ξ is the first input, μX is the first membership function, η is the second input, μY is the second membership function, ω is the output, and the conclusion part If the membership function is μA, the fuzzy rule is IF ξ is X and η is Y THEN ω is
A, the value of the first input ξ is ξ0, and the value of the second input η is η0, the fuzzy entropy function of μX (ξ0) is used to obtain the composite fuzzy set μA '(conclusion part fuzzy set A'). Is E (μX (ξ0)), and the fuzzy entropy function of μY (η0) is E (μY (η0)), the α entropy scale l is

[0077]

[Equation 29]

Is represented by, and the synthetic fuzzy set is

[0079]

[Equation 30]

Then, as shown in FIG. 2, the first input value ξ
If the grade of 0 is 0.8 and the grade of the second input value η0 is 0.7, and the centralized language headed entropy shown in the following Table 1 is used, E (μX (ξ0)) becomes 0. 16
And E (μY (η0)) becomes 0.21,

[0081]

[Equation 31]

Therefore, the consequent part fuzzy set B is α-cut at 0.74 to form the conclusion part fuzzy set A.

[0083]

[Table 1]

The entropy function in the case of using the expanded language headed entropy is as shown in the following table.

[0085]

[Table 2]

Tables 3 and 4 show the case of using the possibility head entropy.

[0087]

[Table 3]

[0088]

[Table 4]

Similarly, for the n-input 1-output fuzzy rule, IF ξ1 is X1 and ξ2 is X2 and ξ3 is
X3 and ………… ξn is Xn THEN ω i
s A and the α entropy scale l is

[0090]

[Equation 32]

It becomes When the consequent part fuzzy set A is obtained by cutting the consequent part membership function by the α entropy scale l, the consequent part fuzzy set B is compressed by the α entropy measure l as shown in FIG. In some cases, the conclusion part fuzzy set A may be obtained. When the number of fuzzy rules is n, the conclusion part fuzzy set A is first calculated.
1, A2, A3, ..., An are to be obtained respectively.

Further, in another embodiment of the present invention, as shown in the flow chart of FIG. 4, the grade used for MIN calculation calculates the maximum value by fuzzy entropy, and the grade corresponding to the maximum value of this entropy (identical If there is more than one that has the maximum value, select the one with the highest grade) to obtain the conclusion part fuzzy set by α-cutting the consequent part fuzzy set, and calculate the area when defuzzifying the conclusion part fuzzy set. Method is used to calculate the output value .delta., Or the fuzzy entropy method with the fuzzy entropy as a parameter is also used to calculate the output value .omega.0.

The maximum value by this fuzzy entropy is calculated, and the output fuzzy set is α-cut using a large grade corresponding to this maximum value. In order to α-cut the fuzzy entropy corresponding to each grade αi of the IF antecedent part, Then, α i (∃ i) is selected and the grade α is obtained. To obtain the grade α by this fuzzy entropy, for example, in the case of the centralized language headed entropy,

[0094]

[Expression 33]

And using extended language headed entropy

[0096]

[Equation 34]

In the case of fuzzy entropy by the possibility operator in the modal theory,

[0098]

[Equation 35]

By using, the fuzzy entropy of each input section can be obtained. Therefore, 2 inputs 1
In the case of output, if the first input is a, the first membership function μX, the second input is b, the second membership function μY, the output is ω, and the conclusion part membership function μB, the fuzzy rule Is the same as in the first embodiment, IF a is X and b is Y THEN ω is
As shown in FIG. 5, when the grade of the first input a is 0.7 and the grade of the second input b is 0.6, the centralized language headed entropy is

[0100]

[Equation 36]

Using, the entropy d (0.7) of the first input a is 0.84 because the grade of the first input a is 0.7, as shown in the second column of Table 1 above. Since the grade of the second input b is 0.6, the entropy d (0.6) of the second input b is 0.96, which is the grade αi of the second input having a large fuzzy entropy of 0.6. Is used to α-cut the consequent part membership function B.

Incidentally, when the consequent part membership function is α-cut with the value of the grade αi of the second input, the consequent part membership function may be compressed by the grade αi. When a plurality of conclusion part fuzzy sets calculated according to the first and second embodiments are calculated, defuzzification operation is performed after combining them to form an output fuzzy set. The output value ω0 is calculated,
The calculation of this output value is performed by setting the value δ 1 of the area center β of the output fuzzy set as the first output value δ, or, as shown in FIG. 7, of each conclusion part fuzzy set which constitutes the output fuzzy set. The output value δ can be obtained by combining the centers of gravity γ1, γ2.
0 is calculated as the first output value δ.

As another example of calculation, there is a case where the fuzzy entropy method is used for defuzzifying the output fuzzy set. This fuzzy entropy method is defined by the Younger's definition when each membership function of each of the n fuzzy sets of conclusion part Aα (α = 1,2, ... n) is μAα (α = 1,2, ... n). The entropy d (Aα) of each conclusion part fuzzy set by

[0104]

[Equation 37]

Since it is represented by, each conclusion part fuzzy set Aα
Let ωα be each representative point corresponding to each centroid of

[0106]

[Equation 38]

It is calculated by Note that μAα represents the membership function of the complementary set Aα of the fuzzy set Aα. The output value ω 0 with this fuzzy entropy as a parameter takes into account the intermediate grade level, and it is unclear whether or not the measurement fact conforms to the antecedent fuzzy set, and a fuzzy set of the conclusion part of low grade occurs. In this case, the output value is obtained by increasing the weight of the conclusion part fuzzy set having a low grade, and when the grades of the conclusion part fuzzy sets are both high, the output value approximates to the first output value δ by the area method or the center of gravity method. However, when the conclusion part fuzzy set includes a low-grade fuzzy set, the fluctuation range of the output value is suppressed to be smaller than that of the area method or the center of gravity method.

The definition of fuzzy entropy is not limited to the definition of Younger.

[0109]

[Formula 39]

Based on the definition of and, each input part fuzzy set,
It is also possible to find the entropy of each conclusion part fuzzy set. In addition, when performing the defuzzification operation with the fuzzy entropy as a parameter, the width of the bottom of the conclusion part fuzzy set is also taken into consideration together with the fuzzy entropy.
As shown in the figure, let the width of the bottom of each conclusion part fuzzy set that constitutes the output fuzzy set be lα.

[0111]

[Formula 40]

The output value ω 0 can also be calculated by

[0113]

The fuzzy inference method according to the present invention uses the fuzzy entropy function E according to each fuzzy rule.
(Αi) is used to obtain the α entropy scale 1, and the α entropy scale 1 is used to α-cut the consequent part fuzzy set to obtain the conclusion part fuzzy set, and the defuzzification operation based on the conclusion part fuzzy set is performed. , Inference method that emphasizes intermediate grade level, suitable for tuning in an environment where trial-and-error rules and membership functions must be given, and development and integration of an inference method in an environment that requires hypothesis setting It facilitates thinking.

Further, when finding the conclusion part fuzzy set by each fuzzy rule, the grade is selected by the maximum value of the fuzzy entropy corresponding to the grade of the IF antecedent part fuzzy set, and the consequent part membership function is α-cut. In this case, since the higher grade is given priority while focusing on the intermediate grade level, the hypersensitivity reaction to extremely high or low grade input is suppressed compared to the past grade history, and the extreme level due to noise is suppressed. Robust reasoning that avoids adverse effects can be performed.

[Brief description of drawings]

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

FIG. 2 is a diagram showing fuzzy inference.

FIG. 3 is a diagram showing fuzzy inference.

FIG. 4 is a flowchart showing another embodiment according to the present invention.

FIG. 5 is a diagram showing fuzzy inference.

FIG. 6 is a diagram showing defuzzification by the area method.

FIG. 7 is a diagram showing defuzzification by the centroid method.

FIG. 8 is a diagram showing a fuzzy entropy method.

─────────────────────────────────────────────────── ───

[Procedure amendment]

[Submission date] September 7, 1992

[Procedure Amendment 1]

[Document name to be amended] Statement

[Name of item to be amended] Detailed explanation of the invention

[Correction method] Change

[Correction content]

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to information processing such as control of plants and other large-scale equipment, or identification of characters and figures.

[0002]

2. Description of the Related Art Today, various information processing based on fuzzy inference called an expert system is performed. For example, in order to perform process control by this fuzzy inference, the antecedent membership function is defined as a fuzzy set of the deviation of the current controlled variable, which is the state of the controlled device, from the target value, and the variation of the deviation. ,
Moreover, the consequent part membership function that defines the fuzzy set of the manipulated variables is defined, and the observed value (measured value) is associated with the antecedent part membership function to obtain the grade of the measured value. Fuzzy inference is performed so that the membership function of the subject part is α-cut.
-The fuzzy set is calculated by performing the defuzzification operation by calculating the center of gravity of the consequent part fuzzy set, and the operation state of the device to be controlled is controlled so as to approximate the ideal state.

Further, in order to perform the control and judgment by the fuzzy inference more accurately, the responsiveness of the control by the inference device is improved (for example, Japanese Patent Laid-Open No. 63-113.733) and the measurement value is included. Noise removal (for example, Japanese Patent Laid-Open No. 119.803
No.) is being tried. Although fuzzy inference is already performed in many fields for some of the operations for control and information processing in large-scale devices, there are many control rules for controlling plants and complicated information processing.
There will be a need to overlay many rules.

However, when a large number of rules are superposed on the basis of fuzzy inference and inference is performed, an unexpected inference result is calculated, which makes it difficult to obtain appropriate control and judgment results. . For this reason, the applicant of the present application obtains each conclusion part fuzzy set based on each fuzzy rule, combines each conclusion part fuzzy set into an output fuzzy set, and when performing the defuzzification operation on this output fuzzy set, the fuzzy entropy Has proposed an inference method using (JP-A-4-80826).

[0005]

The inference method that uses the fuzzy entropy to form the output fuzzy set after the conclusion part fuzzy set is obtained and to defuzzify the output fuzzy set in an environment that requires temporary setting. Although it is useful to develop the reasoning of, there were cases where it was not enough to reflect the ambiguity in the input environment in the conclusion part.

[0006]

According to the present invention, when calculating a conclusion part fuzzy set by each fuzzy rule based on fuzzy inference, the grade of each IF antecedent part fuzzy set corresponds to each grade instead of the conventional MIN operation. The fuzzy entropy function E (αi) is used for weighting and the α entropy scale 1 is Σαi × E (αi) / ΣE (αi)
Then, each conclusion part fuzzy set is obtained by α-cutting the output fuzzy set by this α entropy scale l, and each conclusion part fuzzy set is combined to derive the output fuzzy set. The output value is obtained by performing a defuzzification operation based on the Sasa method, the area method, the center of gravity method, or the like.

Further, in calculating the conclusion part fuzzy set by each fuzzy rule based on the fuzzy inference, each IF
The grade of the antecedent part fuzzy set is not the conventional MIN operation, but αi (∃α) is calculated using the maximum value of the fuzzy entropy corresponding to each grade αi as an index, and the output fuzzy set is α-cut by this grade αi. Each conclusion part fuzzy set is obtained by using, and each conclusion part fuzzy set is combined to derive the output fuzzy set, and the defuzzification operation based on the conventional height method, area method, or centroid method is performed from the output fuzzy set. It may be necessary to go and obtain the output value. However, if the fuzzy entropy is the same, select the one with higher fitness.

When performing the defuzzification operation from the output fuzzy set, the output fuzzy set may be defuzzified based on the fuzzy entropy method.

[0009]

[Operation] According to the present invention, the output fuzzy set is α− by the α entropy scale 1 using the fuzzy entropy function corresponding to the grade of each input fuzzy set for weighting.
Since the output value is obtained by performing the defuzzification operation on the output fuzzy set after cutting, it is possible to obtain the output value with emphasis on the intermediate grade level.

Further, when the maximum value of the fuzzy entropy corresponding to the grade of each input fuzzy set is used as an index, the intermediate grade level is first emphasized, and if there are those having the same entropy, the one having a high degree of conformity is selected. It is possible to obtain a priority output value.

[0011]

The first embodiment of the present invention is a method for deriving one output based on a plurality of fuzzy rules. As shown in the flowchart of FIG. 1, an α entropy scale 1 by weighting with a fuzzy entropy function is used. The fuzzy set of the consequent part is calculated using this α entropy scale l
-Cut out the conclusion part fuzzy set and defuzzify the conclusion part fuzzy set to obtain the output value ω0
In the defuzzification operation, the output value δ is calculated by inference by the area method or the center of gravity method, or the output value ω0 is calculated by inference by the fuzzy entropy method with the fuzzy entropy as a parameter. Is also done.

This fuzzy entropy function E (αi)
The α entropy scale 1 used for weighting is calculated by the following equation.

[0013]

[Equation 1]

The centralized language headed entropy as a fuzzy entropy function is a centralized language headed potential.

[0015]

[Equation 2]

[0016]

[0017]

[Equation 3]

In

[0019]

[Equation 4]

Is called a centralized language heading N of μ (x).

[0021]

[Equation 5]

Of

[0023]

[Equation 6]

Is a centralized language of μ (x), which is called a headed entropy N, and a membership function is

[0025]

[Equation 7]

Represented as In addition, the expanded language head potential

[0027]

[Equation 8]

And

[0029]

[Equation 9]

In

[0031]

[Equation 10]

Is called an expanded language heading N of μ (x).

[0033]

[Equation 11]

Of

[0035]

[Equation 12]

The membership function is called the enlarging language headed entropy N of μ (x).

[0037]

[Equation 13]

It is represented by Furthermore, the bright and dark enhanced language head potential

[0039]

[Equation 14]

And

[0041]

[Equation 15]

In

[0043]

[Equation 16]

The membership function of μ (x) is called the bright and dark enhanced language headed entropy N

[0045]

[Equation 17]

It is represented by And the λ-complement by Sugno

[0047]

[Equation 18]

Then, the inevitable headline entropy

[0049]

[Formula 19]

And normalize this

[0051]

[Equation 20]

And the possibility headline entropy

[0053]

[Equation 21]

And normalize this

[0055]

[Equation 22]

Then, as an expression of the fuzzy set by the modal heading entropy,

[0057]

[Equation 23]

Or

[0059]

[Equation 24]

Can be expressed as, and as a representation of the modal operator by modal headed entropy

[0061]

[Equation 25]

Or

[0063]

[Equation 26]

Can be expressed as Inevitability operator

[0065]

[Outer 1]

Possibility operator

[0067]

[Outside 2]

Modal operator using

[0069]

[Outside 3]

And

[0071]

[Outside 4]

Is

[0073]

[Equation 27]

And

[0075]

[Equation 28]

It is represented as In the present embodiment which uses such a fuzzy entropy function for weighting, in order to derive one output from a plurality of fuzzy rules, first, inference is performed by each fuzzy rule. Is used to calculate the α entropy scale 1 from the fuzzy entropy function E corresponding to the grade of the antecedent membership function, and the α-cut of the antecedent membership function is performed by the α entropy scale 1 to obtain the conclusion part fuzzy set. For example, in the case of two inputs and one output, ξ is the first input, μX is the first membership function, η is the second input, μY is the second membership function, ω is the output, and the conclusion part If the membership function is μA, the fuzzy rule is IF ξ is X and η is Y THEN ω is
A, the value of the first input ξ is ξ0, and the value of the second input η is η0, the fuzzy entropy function of μX (ξ0) is used to obtain the composite fuzzy set μA '(conclusion part fuzzy set A'). Is E (μX (ξ0)), and the fuzzy entropy function of μY (η0) is E (μY (η0)), the α entropy scale l is

[0077]

[Equation 29]

Is represented by, and the synthetic fuzzy set is

[0079]

[Equation 30]

Then, as shown in FIG. 2, the first input value ξ
If the grade of 0 is 0.8 and the grade of the second input value η0 is 0.7, and the centralized language headed entropy shown in the following Table 1 is used, E (μX (ξ0)) becomes 0. 16
And E (μY (η0)) becomes 0.21,

[0081]

[Equation 31]

Therefore, the consequent part fuzzy set B is α-cut at 0.74 to form the conclusion part fuzzy set A.

[0083]

[Table 1]

The entropy function in the case of using the expanded language headed entropy is as shown in the following table.

[0085]

[Table 2]

Tables 3 and 4 show the case of using the possibility head entropy.

[0087]

[Table 3]

[0088]

[Table 4]

Similarly, for the n-input 1-output fuzzy rule, IF ξ1 is X1 and ξ2 is X2 and ξ3 is
X3 and ………… ξn is Xn THEN ω i
s A and the α entropy scale l is

[0090]

[Equation 32]

It becomes When the consequent part fuzzy set A is obtained by cutting the consequent part membership function by the α entropy scale l, the consequent part fuzzy set B is compressed by the α entropy measure l as shown in FIG. In some cases, the conclusion part fuzzy set A may be obtained. When the number of fuzzy rules is n, the conclusion part fuzzy set A is first calculated.
1, A2, A3, ..., An are to be obtained respectively.

Further, in another embodiment of the present invention, as shown in the flow chart of FIG. 4, the grade used for MIN calculation calculates the maximum value by fuzzy entropy, and the grade corresponding to the maximum value of this entropy (identical If there is more than one that has the maximum value, select the one with the highest grade) to obtain the conclusion part fuzzy set by α-cutting the consequent part fuzzy set, and calculate the area when defuzzifying the conclusion part fuzzy set. Method is used to calculate the output value .delta., Or the fuzzy entropy method with the fuzzy entropy as a parameter is also used to calculate the output value .omega.0.

The maximum value by this fuzzy entropy is calculated, and the output fuzzy set is α-cut using a large grade corresponding to this maximum value. In order to α-cut the fuzzy entropy corresponding to each grade αi of the IF antecedent part, Then, α i (∃ i) is selected and the grade α is obtained. To obtain the grade α by this fuzzy entropy, for example, in the case of the centralized language headed entropy,

[0094]

[Expression 33]

And using extended language headed entropy

[0096]

[Equation 34]

In the case of fuzzy entropy by the possibility operator in the modal theory,

[0098]

[Equation 35]

By using, the fuzzy entropy of each input section can be obtained. Therefore, 2 inputs 1
In the case of output, if the first input is a, the first membership function μX, the second input is b, the second membership function μY, the output is ω, and the conclusion part membership function μB, the fuzzy rule Is the same as in the first embodiment, IF a is X and b is Y THEN ω is
As shown in FIG. 5, when the grade of the first input a is 0.7 and the grade of the second input b is 0.6, the centralized language headed entropy is

[0100]

[Equation 36]

Using, the entropy d (0.7) of the first input a is 0.84 because the grade of the first input a is 0.7, as shown in the second column of Table 1 above. Since the grade of the second input b is 0.6, the entropy d (0.6) of the second input b is 0.96, which is the grade αi of the second input having a large fuzzy entropy of 0.6. Is used to α-cut the consequent part membership function B.

Incidentally, when the consequent part membership function is α-cut with the value of the grade αi of the second input, the consequent part membership function may be compressed by the grade αi. When a plurality of conclusion part fuzzy sets calculated according to the first and second embodiments are calculated, defuzzification operation is performed after combining them to form an output fuzzy set. The output value ω0 is calculated,
The calculation of this output value is performed by setting the value δ 1 of the area center β of the output fuzzy set as the first output value δ, or, as shown in FIG. 7, of each conclusion part fuzzy set which constitutes the output fuzzy set. The output value δ can be obtained by combining the centers of gravity γ1, γ2.
0 is calculated as the first output value δ.

As another example of calculation, there is a case where the fuzzy entropy method is used for defuzzifying the output fuzzy set. This fuzzy entropy method is defined by the Younger's definition when each membership function of each of the n fuzzy sets of conclusion part Aα (α = 1,2, ... n) is μAα (α = 1,2, ... n). The entropy d (Aα) of each conclusion part fuzzy set by

[0104]

[Equation 37]

Since it is represented by, each conclusion part fuzzy set Aα
Let ωα be each representative point corresponding to each centroid of

[0106]

[Equation 38]

It is calculated by still,

[0108]

[Formula 39] Is the complement of the fuzzy set Aα

[0109]

[Formula 40] Represents the membership function of. The output value ω 0 with this fuzzy entropy as a parameter takes into account the intermediate grade level, and it is ambiguous whether or not the measurement fact conforms to the antecedent fuzzy set, and a fuzzy set of the conclusion part of low grade occurs. In this case, the output value is obtained by increasing the weight of the conclusion part fuzzy set having a low grade, and when the grades of the conclusion part fuzzy sets are both high, a value similar to the first output value δ by the area method or the center of gravity method Narumo
Conclusion When the fuzzy set with a low grade is included in the fuzzy set, the fluctuation range of the output value is suppressed to be smaller than that of the area method or the center of gravity method.

The definition of fuzzy entropy is not limited to the definition of Younger.

[0111]

[Formula 41]

Based on the definition of and, each input part fuzzy set,
It is also possible to find the entropy of each conclusion part fuzzy set. In addition, when performing the defuzzification operation with the fuzzy entropy as a parameter, the width of the bottom of the conclusion part fuzzy set is also taken into consideration together with the fuzzy entropy.
As shown in the figure, let the width of the bottom of each conclusion part fuzzy set that constitutes the output fuzzy set be lα.

[0113]

[Equation 42]

The output value ω 0 can also be calculated by

[0115]

The fuzzy inference method according to the present invention uses the fuzzy entropy function E according to each fuzzy rule.
(Αi) is used to obtain the α entropy scale 1, and the α entropy scale 1 is used to α-cut the consequent part fuzzy set to obtain the conclusion part fuzzy set, and the defuzzification operation based on the conclusion part fuzzy set is performed. , Inference method that emphasizes intermediate grade level, suitable for tuning in an environment where trial-and-error rules and membership functions must be given, and development and integration of an inference method in an environment that requires hypothesis setting It facilitates thinking.

Further, when obtaining the conclusion part fuzzy set by each fuzzy rule, the grade is selected according to the maximum value of the fuzzy entropy corresponding to the grade of the IF antecedent part fuzzy set, and the consequent part membership function is α-cut. In this case, since the higher grade is given priority while focusing on the intermediate grade level, the hypersensitivity reaction to extremely high or low grade input is suppressed compared to the past grade history, and the extreme level due to noise is suppressed. Robust reasoning that avoids adverse effects can be performed.

Claims (2)

[Claims] 1. When obtaining one output based on a large number of fuzzy rules, each grade αj determined by an input value
By the fuzzy entropy function E (αi) corresponding to, the α entropy scale 1 is Σαi × E (αi) / ΣE (α
i), the consequent part is α-cut by this α entropy measure l to obtain each conclusion part fuzzy set by fuzzy inference based on each fuzzy rule, and each conclusion part fuzzy set is combined and output A fuzzy set,
A fuzzy inference method characterized in that the output fuzzy set is defuzzified to obtain an output value ω0. 2. When obtaining one output based on a large number of fuzzy rules, each grade αi determined by an input value
Based on the maximum value of the fuzzy entropy corresponding to
i (∃i) is selected, the consequent part is α-cut by this grade αi, each conclusion part fuzzy set is obtained by fuzzy reasoning based on each fuzzy rule, and each conclusion part fuzzy set is combined. A fuzzy inference method, characterized in that an output fuzzy set is obtained, and the output fuzzy set is defuzzified to obtain an output value ω0.