JPH05181985A - Non-fuzzy device - Google Patents

Abstract

PURPOSE:To improve variation in final output due to a noise and an error in inference grade by providing a means which applies an optional bias value to each inference output grade and calculates the value of center of gravity of each inference output grade after the bias application. CONSTITUTION:The outputs of inference blocks 1 provided by rules are integrated by a maximum value arithmetic block 2 by singletons of a consequent part. The integrated inference grade is denoted as mui. Here, (i) is a number indicating each singleton. A bias addition block 4 adds the output mui of the maximum arithmetic block 2 and the output muo of a bias value generation block 3 together. This value is inputted to the weighted addition block 5 and simple addition block 6 in a trailing stage to find the values of expressions I. A division block 7 performs division between the two values to calculate a final determination output V0 shown by an equation II. Then when fuzzy inference is performed by hardware, the vairation in final output due to the noise and error in inference grade can be improved.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION The present invention relates to control, pattern recognition,
The present invention relates to a defuzzification device for realizing fuzzy reasoning based on ambiguous information and knowledge such as decision making as hardware.

[0002]

2. Description of the Related Art An outline of simplified fuzzy inference is shown in FIG. Generally, in fuzzy inference, an inference rule is described by a so-called “if then rule” in the form of “if it is then”. The "if-" part is the antecedent part, and the "-
The part of "is" is called the consequent part. In fuzzy reasoning, the above "-" part is expressed by a membership function as a fuzzy set, which enables reasoning based on ambiguous knowledge.

Recently, it has been confirmed that there is no inconvenience in the inference result even if the consequent part "-" is not a fuzzy set but a constant (singleton). This method is called the simplification method, and since the calculation process is greatly omitted,
Many are being put to practical use in various fields including control.

An inference algorithm of simplified fuzzy inference will be described with reference to FIG. The given input x is compared and collated with the membership function described in the antecedent part for each rule 1, 2 and 3, and a value corresponding to the input is calculated. This value is called the goodness of fit, and by further truncating the consequent part with the goodness of fit, the inference result for each rule is obtained.

In the simplified fuzzy inference, since the consequent part is composed of a singleton, the fitness itself of the antecedent part itself becomes the grade of the inference result.

Next, the grades of inference results obtained from a plurality of rules are integrated by, for example, maximum value calculation.
In many practical cases, it is necessary to output only one deterministic value from the integrated inference result. This operation is called defuzzification, and is generally performed by obtaining the weighted average of the integrated inference results, that is, the center of gravity. This calculation is expressed by equation (1).

[0007]

[Equation 1] In equation (1), i represents each singleton that constitutes the consequent part, and n is the sum of singletons. w _i represents the position of each singleton in the horizontal axis direction, that is, a constant value. μ _i is the inference grade corresponding to each singleton. The numerator is the weighted addition value of each inference grade, and the denominator is the simple addition value. By performing these divisions, the centroid value is obtained, and this value becomes the definite output of fuzzy inference.

[0008]

However, there are some problems in the above inference method, especially in the defuzzification part. As shown in FIG. 4, however small the grade of the inference result is, if the finite value other than 0 is taken, the centroid value is the same. This means that, from another viewpoint, there may be a large change in the center of gravity value, that is, the final output, with only a small change in the inference grade. If the inference hardware is realized by an electric circuit or the like, the output may deviate significantly from the normal value due to a slight noise as shown in FIG. Similar to noise, the same problem occurs when there is an error in the inference grade.

If the input value does not match any of the rules, all the inference grades are 0, and the numerator and denominator of equation (1) are 0, so that an abnormal value is output from the actual circuit. It

Therefore, the problem to be solved by the present invention is to improve the fluctuation of the final output caused by noise or inference grade error in simplified fuzzy inference hardware.
It is also intended to prevent abnormal output that occurs when the input value does not match any rule.

[0011]

In order to solve the above-mentioned problems, the defuzzification device of the present invention is a defuzzification device in which the consequent part of an inference rule is represented by a singleton. And a means for calculating the barycentric value of each inference output grade after applying the bias value.

[0012]

The inference grade is corrected by applying an appropriate bias value in advance to each inference result grade, and then the center of gravity is calculated. Since the magnitude of the bias value can be arbitrarily adjusted, it is possible to improve the fluctuation of the final output value due to the noise or the error by setting an appropriate bias value according to the magnitude of the noise or the error. Further, even if the input does not match any of the rules, the inference grade does not become 0, so that the occurrence of abnormal output can be prevented.

[0013]

EXAMPLES The present invention will be specifically described below based on examples.

FIG. 1 is a block diagram showing an example in which the present invention is implemented as hardware. In the figure, the output of the inference grade calculation block 1 provided for each rule is integrated by the maximum value calculation block 2 for each singleton of the consequent part. Let the integrated inference grade be μ _i . i is a number representing each singleton.

On the other hand, in the bias value generation block 3, an appropriate bias value μ ₀ selected from the outside is generated.
Output mu ₀ Output mu _i and the bias value generation block 3 of the bias adder block 4 in the maximum value calculation block 2 is added, and outputs the values of μ _i + μ _0. This value is input to the weighted addition block 5 and the simple addition block 6 in the next stage, and

[Equation 2] The value of is obtained. By performing division of the above two values by the division block 7, the final confirmed output V ₀ shown by the equation (3) is obtained.
To calculate.

[0016]

[Equation 3] If there is an error Δμ in μ _i , change the bias value to μ
_By setting ₀ = −Δμ, the error is corrected and the deviation of the final confirmed output V ₀ can be prevented. The error of μ _i is i
In the case where it is different for each i, the bias value may be set for each i. Further, by intentionally applying a positive bias value in advance and shifting μ _i , it is possible to improve the fluctuation of V ₀ with respect to noise.

FIG. 6 shows this example. When the bias value is not applied, V ₀ fluctuates greatly due to the influence of noise as shown in FIG. On the other hand, when the bias value μ ₀ is applied as shown in FIG. 6B, the deviation of V ₀ due to noise is improved. Further, even if the input does not match any rule, the input of the division block does not become 0, so that no abnormal output occurs. In this case, V ₀ is represented by the following equation.

[0018]

[Equation 4] This expression means that V ₀ takes the average value of w _i , and if w _i is bilaterally symmetric, the median value thereof is calculated. In typical fuzzy control, the median value is equivalent to the control amount being zero. This means that no operation is performed unless there is a matching rule, which is consistent with human's natural judgment. This is shown in FIG. In this example, the bias value employs the same mu ₀ for each mu _i, it is also possible to set different bias values for each mu _i.

FIG. 2 shows an example in which the defuzzification hardware according to the present invention is configured as an analog electric circuit. Each of the weighted addition block 11 and the simple addition block 12 is composed of a group of n resistors and an operational amplifier. The inference grade voltage μ _i and the bias voltage μ ₀ generated from the bias voltage generation circuit 13 are two addition blocks 11 and 1.
2 are input respectively. As a result, the outputs X and Y of the weighted addition block 11 and the simple addition block 12 are expressed by the following equations.

[0020]

[Equation 5] This value is input to the division circuit 14, and finally the finalized output voltage V ₀ is output as follows.

[0021]

[Equation 6] Considering 1 / R _i in equation (6) as w _{i in} equation (3), R ₀
When treated as a coefficient, becomes equivalent to the equation (3).

In this example, even if noise or an error exists in the inference grade voltage μ _i , the fluctuation of the output voltage V ₀ can be improved by setting an appropriate bias voltage μ ₀ .

If μ ₀ is a negative voltage, the input of the divider circuit will not be 0 V, so that an abnormality in V ₀ can be prevented even if there is no matching rule.

[0024]

As described above, according to the present invention, when the fuzzy inference is implemented by hardware, the fluctuation of the final output due to noise or inference grade error can be improved. Further, even when the input does not match any rule, the abnormal output can be prevented.

[Brief description of drawings]

FIG. 1 is a block diagram showing a basic configuration of the present invention.

FIG. 2 is a circuit diagram showing an embodiment of the present invention.

FIG. 3 is an explanatory diagram showing steps of simplified fuzzy inference.

FIG. 4 is an explanatory diagram showing a conventional method of obtaining a center-of-gravity value.

FIG. 5 is an explanatory diagram showing a problem of a conventional method of obtaining a center of gravity value.

FIG. 6 is an explanatory diagram showing a method of obtaining a centroid value of the present invention.

FIG. 7 is an explanatory diagram showing the effect of the method of obtaining the centroid value of the present invention.

[Explanation of symbols]

1 inference grade calculation block, 2 maximum value calculation block, 3 bias value generation block, 4 bias addition block, 5 weighted addition block, 6 simple addition block, 7 division block

Claims (1)

[Claims] 1. In a defuzzification apparatus in which the consequent part of an inference rule is represented by a singleton, a means for applying a bias value of an arbitrary size to each inference output grade and a means for applying each inference output grade after applying the bias value. A defuzzification apparatus comprising: means for calculating a centroid value.