JPH05303495A - Display device for multi-dimensional membership function - Google Patents

Abstract

PURPOSE:To provide a multi-dimensional membership function(MF) setting device capable of accurately and easily checking the outline of a fuzzy area determined by a multi-dimensional MF more than three-dimensions without specially requiring mathematical knowledge relating to the MF of fuzzy logic. CONSTITUTION:The device is provided with an input means 1 for designating a required multi-dimensional MF, a display means 6 for displaying the designated MF and plural processing means 2 to 5 for calculating the adaptation of a previously determined point in a coordinate space constituted of coordinate axes other than coordinate axes indicating the adaptation of the multi- dimensional MF based upon the function equation and parameter of the designated MF and executing processing operation for displaying the outline of a fuzzy area determined by the designated MF and the magnitude of the adaptation of the previously determined point.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a device for displaying a three-dimensional or other multi-dimensional membership function used in the technical field of information processing or control based on fuzzy theory.

[0002]

2. Description of the Related Art A membership function M (x) based on a conventional fuzzy theory is expressed in a two-dimensional plane having a coordinate (coordinate axis) as an input variable x and a fitness (belonging) t for a fuzzy set. Therefore, two or more input variables x ₁ , x ₂ , ...
When a fuzzy operation is performed on the input variables, a membership function defined for each input variable (hereinafter referred to as a conventional membership function) is used to calculate the fitness t ₁ , t ₂ ,.
... is calculated, and the degree of conformity in which all the input variables are evaluated is calculated by combining them.

For example, in the case of two input variables x and y,
Conventional membership function M _x for variable _x and variable y
A conventional membership function M _y is defined for each and a fitness t is given for each input variable. An example of the membership function is an isosceles triangle that is often used in fuzzy control. Then, according to the fuzzy inference method, the membership functions M _x , M of the antecedent part of the fuzzy rule of the “if-then” format for the values of the input variables x, y
_The goodness of fit t _x , t _y is obtained from _y, and a combination operation (usually a min operation) is performed to obtain a goodness of fit in which both the input variables x and y are evaluated.

Here, considering a space having two or more input variables and goodness of fit as coordinate axes, the membership function corresponding to M _{x, y} obtained as a result of the above-described composition operation is in each space in the space. It becomes a figure (for example, a quadrangular pyramid) formed by combining conventional membership functions for input variables.
Then, the cross-sectional shape (equal fitness line shape) when the membership function corresponding to this M _{x, y} is cut at a certain goodness of fit is the fuzzy set (or fuzzy region) given by M _{x, y} . Interpreted as the shape of the border. However, in the conventional method, the boundary shape of the fuzzy region is limited to a certain specific shape depending on the synthesis operation. For example, in the input variable space (two-dimensional plane) defined by two input variables, the boundary shape of the fuzzy area is always represented by a rectangle.

However, the fact that the boundary shape is always constant means that the shape of the fuzzy set in the input variable space is limited, and as a result, the multi-input system that performs the fuzzy arithmetic processing is Limited to those that deal only with fuzzy sets of boundary shapes.

On the other hand, in various control fields, the correlation between two variables is expressed in the form of a distribution chart in which each variable is plotted on the abscissa and the ordinate and the input value of each variable is plotted on the coordinates. Although there are many cases, it is very difficult to judge the tendency of the distribution (the direction of linearity and the inclination) by the conventional statistical method, but humans can easily judge the tendency. It is considered that this is because the judgment is made by using a curved shape such as an ellipse as a clue, rather than a linear shape such as a rectangle. Fuzzy theory is also used to realize such a judgment by a machine. ..

Therefore, it is desired to be able to set a fuzzy set having a boundary of an arbitrary shape (for example, an ellipse) within an input variable space defined by two or more input variables. In order to realize this with the conventional method, the area formed by the boundary of the above-mentioned constant shape is finely divided for each input variable, and the conventional membership function is given to each area.
It can be set approximately by giving an appropriate value to the consequent part of an en "style rule.

[0008]

However, in the above-mentioned area division method, it is difficult to grasp the shape of the divided area, which requires a lot of membership functions and fuzzy rules, and it is only an approximation. If there are two or more regions of arbitrary shape and they overlap each other, problems such as extremely complicated processing occur.

A method of combining a large number of functions to form a fitness plane of the membership function in a multidimensional space as a result has also been proposed. According to this method, it is necessary to determine a large number of parameters. Therefore, there is a problem in that setting is troublesome and a large amount of memory is required for calculation.

For these reasons, it has been impossible to set a fuzzy set having an arbitrary boundary shape in the conventional fuzzy information processing.

Therefore, in order to realize the setting of a fuzzy set having an arbitrary boundary shape as described above, the present inventor uses a multidimensional space having coordinate axes of a plurality of input variables and a fuzzy set. A multidimensional membership function formed by an equi-fitness surface or an equi-fitness surface of an arbitrarily defined shape (eg, ellipse, parabola or rhombus) at any position of Proposed setting (Japanese Patent Application No. 2-243355 and 2)
-243356). According to these inventions, when values for a plurality of input variables are input, the fitness can be calculated and output by the membership function set in the multidimensional space. Furthermore, by using a single membership function arbitrarily selected for a plurality of input variables, a fuzzy set having a boundary of the selected shape is set in the input variable space composed of two or more input variables. At the same time, the movement can be easily performed only by appropriately changing the parameters of the selected membership function.

However, as a means for setting the membership function, conventionally, there is a setting and display device (graphic editor) for the membership function of two dimensions (fitness and one fuzzy variable), but there is more than three dimensions. There is no one for multidimensional membership functions. Therefore, a mathematical expression expressing a membership function of three dimensions or more is written using a programming language. In this case, the parameters corresponding to the contour of the multidimensional membership function to be set must be known, so that mathematical knowledge is required and setting mistakes are likely to occur.

Therefore, it is desired to display the contour of the multi-dimensional membership function to be set, that is, the contour of the fuzzy area determined by the multi-dimensional membership function. Since there is nothing that can display the above membership function, it is conceivable to substitute a tool (software) for writing a mathematical formula and displaying a three-dimensional solid diagram. However, according to this method, there is a problem in that it is difficult to grasp the contour of the fuzzy area determined by the membership function having a three-dimensional, that is, three-dimensional shape.

Therefore, an object of the present invention is to provide a user interface for utilizing the above-mentioned multidimensional membership function without requiring any particular mathematical knowledge about the multidimensional membership function. It is an object of the present invention to provide a multidimensional membership function display device capable of accurately and easily confirming the contour of a fuzzy region determined by the dimension membership function.

[0015]

The multi-dimensional membership function setting device of the present invention comprises an input means for inputting data necessary for designating a desired multi-dimensional membership function, and the input means. Display means for displaying the multidimensional membership function, and coordinates formed by coordinate axes other than the coordinate axes indicating the conformity of the multidimensional membership function based on the specified function expression and parameters of the multidimensional membership function. To calculate the fitness of a predetermined point in the space and display the contour of the fuzzy area determined by the designated multidimensional membership function and the magnitude of the fitness of the predetermined point on the display means. And processing means for performing the processing operation of.

In the multidimensional membership function setting device of the present invention, the above-mentioned predetermined points are displayed as a circle having a constant radius, and a black circle having a radius proportional to the magnitude of the goodness of fit is displayed in the circle. Is preferably displayed.

[0017]

In the present invention, when the desired multidimensional membership function is designated by the input means, the processing means
The contour of the fuzzy area determined by the function formula and parameters of the specified multidimensional membership function, and the predetermined points in the coordinate space formed by the coordinate axes other than the coordinate axes indicating the goodness of fit of the multidimensional membership function. The suitability is obtained and displayed on the display means. Therefore, the operator can accurately and easily grasp the contour of the fuzzy region determined by the multidimensional membership function of three or more dimensions.

Further, by displaying a predetermined point as a circle having a constant radius and displaying a black circle having a radius proportional to the magnitude of the degree of conformity within the circle, the higher the degree of conformity becomes, the darker it becomes. , The lower the degree of conformity, the whiter it is displayed. Therefore, the features of the three-dimensional membership function expressing a planar pattern can be easily visually recognized.

[0019]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 shows the configuration of a three-dimensional membership function (hereinafter abbreviated as 3DMF) display device which is an embodiment of the present invention.

This setting device includes an algorithm storage unit 2 storing a procedure (algorithm) for displaying the input means 1 and 3DMF on a screen, and a 3DMF function formula storage unit 3 in which functional formulas of 3DMF are stored (registered) in advance. A 3DMF parameter storage unit 4 that stores (registers) 3DMF parameters in advance, a CPU 5, and a display unit 6 are provided.

The input means 1 comprises one or both of a mouse and a keyboard, or a touch screen, and is used for inputting a number designating the 3DMF to be displayed, as described later. Further, it is also used as an input means when the parameters of 3DMF are stored in advance.

The 3DMF function formula storage unit 3 and the 3DMF parameter storage unit 4 respectively store the 3DMF function formulas and parameters as information necessary for the CPU 5 to execute a display operation described later.

In particular, the 3DMF parameter is stored in the 3DMF parameter storage unit 4 by the operation procedure shown in FIG. In the figure, the array parameter prm (n,
N in 1) to prm (n, 6) is the serial number of the 3DMF to be set, and represents the nth 3DMF.

FIG. 2 shows a parameter setting operation of the 3DMF representing an "arc" having a matching degree of "1". First, the array pr
The number of the (input) circular arc functional expression is registered in m (n, 1) (step S11), and then the abscissa coordinate value of the center point of the circular arc and the array prm (n are registered in the array prm (n, 2). , 3), the vertical axis coordinate value of the center point is registered (step S12), and the distance (radius) between the center point and the point on the circumference is registered in the array prm (n, 4) (step S13). Next, the designated circle is displayed in an appropriate color (for example, green) (step S14), the starting center angle of the arc is registered in the array prm (n, 5) (step S15), and the array prm is set.
Register the ending center angle of the arc in (n, 6) (step S1
6) Display the designated arc in red (step S1)
7).

With the above-mentioned storage units 2, 3, 4 and the CPU 5,
It constitutes processing means for performing processing operations for display as described below.

The display means 6 comprises a display device having a CRT or other display screen, and the input device 1 is provided on the display screen.
An image relating to the 3DMF designated by or the characteristic of the designated 3DMF can be displayed.

Next, the display operation by the 3DMF display device of the embodiment will be described.

As shown in FIG. 3, first, when the serial number n of the 3DMF to be displayed is input from the input means 1 (step S21), the CPU 5 reads the array prm (n, 1) from the 3DMF parameter storage unit 4, prm (n, 2), ..., Prm (n, 6) is read (step S22), and the 3DMF function formula corresponding to the number registered in prm (n, 1) is read (step S23). ..

Next, the dot numbers i and j which are the objects of the fitness calculation are designated (step S24). Here, as shown in FIG. 4, the “dot” is a finite set plane of the three-dimensional membership function (in this case, a coordinate plane formed by two x and y coordinate axes other than the coordinate axes representing the goodness of fit). It is a point of a fixed size divided into pieces (X _d × Y _d ), and the number of each dot is i (= 1, 2, 3, 3) in the x-axis direction.
..., X _d ) and j (= 1, 2, 3, ..., Y in the y-axis direction)
It is represented by _d ).

Referring again to FIG. 3, the coordinate value of the center point of the dot designated by the number as described above is obtained (step S
25). When dot numbers are assigned as shown in FIG. 4, the coordinate value (x, y) of the dot center point is expressed by the following equation.

X = i-0.5 (1) y = Y _d -j + 0.5 (2) Next, the above coordinate values (x, y) and the array prm are set to 3DMF.
It is applied to a functional expression to calculate the goodness of fit (step S2).
6). When the goodness of fit is obtained, the circle indicating the dot is displayed according to the dot arrangement on the display screen, and a black circle with a radius proportional to the size of the goodness of fit of each dot is placed in each dot (center).
(Step S27). As a result, a place with a high degree of conformity is displayed in black, and a place with a low degree of conformity is displayed in white.

Since the above-described processing from dot designation to display (steps S24 to S27) is performed for all dots, the completion of processing of all dots is checked for each dot display processing (step S28), and "Yes". The operation ends when.

FIG. 5 shows a three-dimensional membership function of the numeral pattern "8" as a specific example of the above display. In this case, “8” is a shape in which two upper and lower circles are combined, and the 3DMF set for each circle is displayed.

For example, for the circle under "8", prm
The 3DMF functional expression represented by the following expression is read by the number (n, 1).

[0035]

[Equation 1]

In the example of FIG. 5, prm (n, 2) = 6, prm (n, 3) =
6, and prm (n, 4) = 4.5 , a x and a _y are constant values (a _x
= 2, a _y = 2), prm (n, 5) and prm (n,
6) is not used.

The above embodiment is preferably used as means for displaying a three-dimensional membership function in a fuzzy pattern recognition device for recognizing a pattern such as a character or a number by using the three-dimensional membership function. it can.

[0038]

As described above, according to the present invention, since the outline of the fuzzy region determined by the multidimensional membership function of three or more dimensions is displayed by a simple input operation, the present invention relates to the multidimensional membership function. Even an operator who has no particular mathematical knowledge can easily grasp the characteristics of the membership function of three dimensions or more and use it for pattern recognition or the like.

[Brief description of drawings]

FIG. 1 is a diagram showing a configuration of a three-dimensional membership function display device according to an embodiment of the present invention.

FIG. 2 is a diagram showing a setting operation procedure of a three-dimensional membership function.

FIG. 3 is a diagram showing a display operation of the embodiment.

FIG. 4 is a diagram showing a relationship between a dot number to be a target of fitness calculation and an x, y coordinate plane.

FIG. 5 is a diagram showing a display example of a three-dimensional membership function of a numeric pattern “8”.

[Explanation of Codes] 1 ... Input means, 2 ... Algorithm storage unit, 3 ... 3DMF
Function formula storage unit, 4 ... 3DMF parameter storage unit, 5 ... C
PU, 6 ... Display means.

Claims (2)

[Claims] 1. Input means for inputting information necessary for designating a desired multidimensional membership function; display means for displaying the multidimensional membership function designated by the input means; Based on the function expression and parameters of the multidimensional membership function, the goodness of fit of a predetermined point in the coordinate space formed by coordinate axes other than the coordinate axes showing the goodness of fit of the multidimensional membership function is calculated, and the specified And a processing means for performing a processing operation for displaying on the display means the contour of the fuzzy region determined by the multidimensional membership function and the magnitude of the fitness of the predetermined point. Multidimensional membership function display. 2. The display screen displays the predetermined points as a circle having a constant radius, and a black circle having a radius proportional to the magnitude of the goodness of fit is displayed in the circle. The multi-dimensional membership function display device according to claim 1.