JPH05298108A - Multi-dimensional membership function setter - Google Patents

Abstract

PURPOSE:To provide a multi-dimensional membership function setter which can easily set three-or-more dimensional membership functions without especially requiring mathematical knowledge concerning the multi-dimensional membership functions of fuzzy inference. CONSTITUTION:This device is provided with an input device 1 to designate the desired multi-dimensional membership functions and to input data required for setting the parameters of the multi-dimensional membership functions, display device 4 for displaying the multi-dimensional membership functions designated by the input device 1, and parameter conversion part 2 to convert the data inputted from the input device 1 concerning the displayed multi-dimensional membership functions to the parameters of the multi-dimensional membership functions, and the parameters of the multi-dimensional membership functions can be set by displaying lines or points of adaptivity '1' for the designated multi-dimensional membership functions.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an apparatus for setting 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, an object of the present invention is to provide a user interface for utilizing the above-mentioned multidimensional membership function, which does not particularly require mathematical knowledge of the multidimensional membership function and can be easily used in three or more dimensions. It is to provide a multi-dimensional membership function setting device that can set the membership function.

[0014]

A multidimensional membership function setting device of the present invention stores data necessary for designating a desired multidimensional membership function and setting parameters of the multidimensional membership function. An input device for inputting, a display device having a display screen for displaying a multidimensional membership function designated by the input device, and a multidimensional membership function displayed on the display screen, which is input from the input device. A multi-dimensional membership function by displaying a line or a point having a fitness of 1 of the designated multi-dimensional membership function on the display screen. It enables the parameter setting of the ship function.

According to one aspect of the present invention, a line having a goodness of fit of the multidimensional membership function or a point on the display screen on which a point is displayed is designated by the input device to specify a point having a particular goodness of fit. An apparatus is provided for setting certain parameters of the multidimensional membership function.

[0016]

According to the present invention, a desired multidimensional membership function is designated by the input device and displayed on the display screen of the display device. By using the display screen to specify the line or point having the goodness of fit 1 of the multidimensional membership function with the input device and displaying the line or point having the goodness of fit 1 on the display screen, the operator can: You can set parameters for the multidimensional membership function.

Also, the goodness of fit of the multidimensional membership function 1
By using the display screen on which lines or points are displayed to specify a point having a specific fitness, it is possible to set a predetermined parameter (for example, a parameter that determines fuzzy entropy) of the multidimensional membership function. ..

[0018]

FIG. 1 shows the configuration of a three-dimensional membership function (hereinafter abbreviated as 3DMF) setting device which is an embodiment of the present invention.

This setting device comprises an input device 1, a parameter conversion unit 2, a 3DMF storage unit 3 and a display device 4.

The input device 1 is composed of either or both of a mouse and a keyboard, or a touch screen, and is used for inputting parameters of 3DMF to be set, as described later.

The parameter conversion unit 2 has a CPU 5 for controlling the operation of the setting device and a 3D for which a parameter is desired to be set.
The MF includes an algorithm storage unit 6 that stores an algorithm for converting image data designated on the display screen into 3DMF parameters as described below.

The display device 4 comprises a device having a CRT or other display screen and is used to display the 3DMF in this embodiment. 3DM you want to display on this display device
F is designated by the input device 1 by a predetermined number. The operation procedure for displaying is included in the algorithm storage unit 5.

Next, the operation when the 3DMF setting device of the embodiment is applied to the pattern recognition based on the fuzzy theory will be described with reference to FIGS.

(1) Setting of circles (or arcs), straight lines and points when the parameters for fuzzy entropy are already set to a certain fixed value (1.1) "Arc" of goodness of fit "1" Setting operation (Fig. 2) First, use the mouse, which is one of the input devices, to specify "Circle" on the display screen, as shown in Fig. 4.
e) is clicked (step S1).

Next, as shown in FIG. 5, the center point of the circle and one point on the circumference are clicked (steps S2 and S3).
Then, using the keyboard of the input device, the starting center angle of the arc is entered (step S4), and the ending center angle of the arc is entered (step S5). Finally, click "END" again with the mouse to finish (step S
6).

In this case, the operation of the 3DMF setting device is as shown in FIG. In the following figures, n in the array parameters prm (n, 1) to prm (n, 6) is the serial number of the membership function to be set and represents the nth three-dimensional membership function.

In FIG. 3, first, the number of the functional expression of the circular arc is registered in the array prm (n, 1) (step S21), and then the horizontal axis coordinate of the center point of the circular arc is registered in the array prm (n, 2). Value, array pr
The vertical axis coordinate value of the center point is registered in m (n, 3) (step S22), and the distance (radius) between the center point and the point on the circumference is registered in the array prm (n, 4) (step S23). ).

Next, as shown in FIG. 6, the designated circle is displayed in an appropriate color (for example, green) (step S24),
Register the starting center angle of the arc in the array prm (n, 5) (step S
25), the ending center angle of the circular arc is registered in the array prm (n, 6) (step S26), and the designated circular arc is displayed in red (step S27).

(1.2) Setting operation of “straight line” of fitness “1” (FIG. 7) First, click “L” (Line) with the mouse (step S1), and then set the start point of the straight line. Click (step S2).

Next, as shown in FIG. 9, the end point of the straight line is clicked (step S3), and finally "END" is clicked to finish (step S4).

In this case, the operation of the setting device is as shown in FIG.

First, the number of the linear function formula is registered in the array prm (n, 1) (step S41), and then the array prm (n, 2) is registered.
The horizontal axis coordinate value of the midpoint of the straight line is registered in the array, and the vertical axis coordinate value of the midpoint is registered in the array prm (n, 3) (step S42).
Register the distance from the midpoint to the end point in (n, 4) (step S
43), the inclination (angle) of the straight line is registered in the array prm (n, 5) (step S44), and the designated straight line (line segment) is displayed in a color different from the circle (for example, red) (step S44). S
5).

(1.3) Setting operation of "point" of fitness "1" (Fig. 10) First, click "P" (Point) with the mouse (step S51), and then click the position of point. (Step S52), and finally "END" is clicked to finish (step S53).

In this case, the operation of the setting device is as shown in FIG.

First, the number of the functional expression of the point is registered in the array prm (n, 1) (step S61), and then the abscissa coordinate value of the point and the array prm (n, 2) in the array prm (n, 2). The vertical axis coordinate values are registered in 3) (step S62).

By repeating this operation, it is possible to actually set a curve of any shape.

(2) Operation for setting the equi-fitness line of the elliptical contour to the point of goodness-of-fit "1" with arbitrary fuzzy entropy (Fig. 12). First, "N" is set with the mouse. Click (Step S
71), and then click the position of the point (step S7)
2). Further, as shown in FIG. 14, a point on the axis parallel to the horizontal axis of the elliptical equi-fitness line of goodness of fit “0.5” is clicked with the mouse (step S73), and the goodness of fit of “0.5” is obtained. ”
Click a point on the axis parallel to the vertical axis of the elliptical iso-fitting line (step S74), and finally click "END" to finish (step S75).

In this case, the operation of the setting device is as shown in FIG.

First, the array prm (n, 1) has an arbitrary fuzzy
The number of the function formula of the entropy elliptic membership function is registered (step S81), and then the abscissa coordinate values of the points are placed in the array prm (n, 2) and the ordinate coordinate values are placed in the array prm (n, 3). Register (step S82), register a value proportional to fuzzy entropy on the axis parallel to the horizontal axis in the array prm (n, 4) (step S83), and parallel to the vertical axis in the array prm (n, 5). A value proportional to the fuzzy entropy on the axis is registered (step S84). Then, as shown in FIG. 15, an elliptic equal-fitting line with a matching degree of “0.5” is displayed in a color different from that of the circle or straight line (for example, blue) (step S8).
5).

The above embodiment is preferably used as means for setting 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.

More specifically, the base set plane of the three-dimensional membership function (coordinate plane formed by two coordinate axes other than the coordinate axis indicating the goodness of fit) is divided into a finite number of dots (points of a certain size). , The fitness of the three-dimensional membership function obtained by the coordinate value of the center point of each dot is calculated. The calculation of the goodness of fit is performed by a calculating means such as a CPU based on the stored function formula of the three-dimensional membership function and parameters. Once the goodness of fit is obtained,
A black circle with a radius proportional to the size of the goodness of fit for each dot is displayed in each dot. 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. As a specific example, FIGS. 16 and 17 show three-dimensional membership functions of the number patterns “2” and “8”, respectively.

[0042]

As described above, the present invention enables the parameter setting of the multidimensional membership function by displaying the line or the point having the goodness of fit 1 of the multidimensional membership function designated by the input device. Therefore, even an operator who does not particularly have mathematical knowledge about the multidimensional membership function can easily set and use the membership function of three or more dimensions.

[Brief description of drawings]

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

FIG. 2 is a diagram showing a setting operation of an “arc” having a fitness “1” of a three-dimensional membership function.

FIG. 3 is a diagram showing the operation of the setting device in the case of FIG.

FIG. 4 is a diagram showing a display state when a three-dimensional membership function of “circle” is specified.

FIG. 5 is a diagram showing a display state when a center point of a circle and points on the circumference are input.

FIG. 6 is a diagram showing a state in which a designated circle is displayed.

FIG. 7 is a diagram showing a setting operation of a “straight line” of the fitness “1” of the three-dimensional membership function.

FIG. 8 is a diagram showing the operation of the setting device in the case of FIG.

FIG. 9 is a diagram showing a display state when an end point is input after a start point of a straight line.

FIG. 10 is a diagram showing a setting operation of a “point” of the fitness “1” of the three-dimensional membership function.

FIG. 11 is a diagram showing an operation of the setting device in the case of FIG.

FIG. 12 is a diagram showing an operation of setting an equal fitness line of an elliptic contour for a point of fitness “1” by arbitrary fuzzy entropy.

13 is a diagram showing the operation of the setting device in the case of FIG.

FIG. 14 is a diagram showing a display state when a point on the equi-fitness line of the goodness of fit “0.5” is input.

FIG. 15 is a diagram showing a display state of an elliptic equi-fitness line with a goodness of fit of “0.5”.

FIG. 16 is a diagram showing a three-dimensional membership function of the numeral pattern “2”.

FIG. 17 is a diagram showing a three-dimensional membership function of the numeral pattern “8”.

[Explanation of symbols]

1 ... Input device, 2 ... Parameter conversion unit, 3 ... 3DMF storage unit, 4 ... Display device, 5 ... CPU, 6 ... Algorithm storage unit.

Claims (2)

[Claims] 1. Designating a desired multidimensional membership function,
An input device for inputting data necessary for setting parameters of the multidimensional membership function; a display device having a display screen for displaying the multidimensional membership function designated by the input device; A multi-dimensional membership function displayed on the display screen, and a parameter conversion unit for converting data input from the input device into parameters of the multi-dimensional membership function, and the degree of conformity of the designated multi-dimensional membership function. A multidimensional membership function setting device that enables setting of parameters of a multidimensional membership function by displaying one line or point on the display screen. 2. The multi-dimensional membership function setting device according to claim 1, wherein a point having a specific relevance is found by looking at a display screen on which lines or points having a relevance of 1 of the multi-dimensional membership function are displayed. A device for setting predetermined parameters of the multidimensional membership function by designating with an input device.