JPH06110694A - Membership function management device and execution instruction preparation device - Google Patents

Abstract

PURPOSE:To provide the membership function management device easily managing the membership function. CONSTITUTION:A membership function storage means 3 is constructed by a hierarchical structure where a characteristic of a membership function is contained by its low-order membership function. The means 3 does not store the characteristic common to the high-order membership function from among the characteristic of the low-order membership function, but it stores the membership function correction information correcting the high-order membership function. Thus, the low-order membership function is stored. A membership function acquisition means 5 acquires the membership function to be retrieved from the membership function storage means 3 when the membership function to be retrieved is inputted.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a membership function management device.

[0002]

2. Description of the Related Art Today, fuzzy arithmetic processing devices for performing fuzzy inference have been proposed. This is to perform a certain inference by calculating the fitness of the input fuzzy information based on the membership function and the rule. In a fuzzy arithmetic processing device, when it is difficult to express an arithmetic operation by a mathematical expression, an appropriate inference result can be obtained by setting an appropriate membership function and rule.

By the way, depending on the membership function, there is also a membership function related to other membership functions. Even in such a case, the programmer had to define the membership function separately in each source program. Managing such a membership function is complicated. Especially, since the program is complicated nowadays because more complicated fuzzy operations are performed, and the number of membership functions to be used is increasing dramatically, this is all the more remarkable.

Further, since a membership function is defined separately, a large amount of information is described in the source program,
There is also a problem that the source program becomes large and the memory capacity becomes large.

It is an object of the present invention to solve the above problems and to provide a membership function management device that facilitates management of membership functions.

[0006]

According to another aspect of the membership function management apparatus of the present invention, the membership function storing means has a hierarchical structure in which the membership function of a certain membership function is included in the lower membership function. By storing the membership function modification information that modifies the upper membership function without storing the common characteristics of the lower membership function with the upper membership function. , The lower membership function is stored, and the membership function acquisition means acquires the desired membership function based on the membership function modification information and the characteristics of the membership function located above the desired membership function. What to do is characterized.

In the membership function management device according to the second aspect, when a new membership function is registered in the membership function storage means, the membership function to be registered is already stored in the membership function storage means. If the membership function has the same characteristics as the existing membership function, the membership function to be registered is positioned below the remembered membership function and the membership function modification information for modifying the membership function above it is modified. Among the characteristics of the membership function to be registered, the characteristics not included in the higher membership function are stored.

According to another aspect of the membership function management apparatus of the present invention, the membership function stored in the membership function storage means comprises membership function shape information and a membership function name which is the name of the membership function shape information. The membership function name is characterized in that the lower level membership function name is stored in a hierarchical structure including the higher level membership function name.

According to the fourth aspect of the present invention, there is provided an execution instruction creating device,
The membership function storage means stores a lower-rank membership function name in a hierarchical structure including a higher-rank membership function name, and ranks higher than the characteristics of the membership function shape information corresponding to the lower-rank membership function name. The membership function shape information that corrects the membership function shape information corresponding to the higher-level membership function name is stored without storing the common characteristics with the membership function shape information corresponding to the membership function name of Due to
Membership function shape information corresponding to the lower membership function name is stored, and the membership function acquisition means is based on the membership function modification information and the characteristics of the membership function located above the desired membership function. , Acquiring membership function shape information corresponding to a desired membership function name.

[0010]

In the membership function management device according to the first aspect, the membership function storage means is constructed in a hierarchical structure such that the characteristics of a certain membership function are included in the lower membership function. Further, among the characteristics of the lower membership function, the characteristics common to the upper membership function are not stored, but the membership function modification information for modifying the upper membership function is stored, so that the lower membership Remember the function.

In this way, the upper membership function and the lower membership function can be associated with each other.
Further, the lower-rank membership function inherits the characteristics of the higher-rank membership function, which facilitates the management of the higher-rank and lower-rank membership functions.

The membership function acquisition means acquires a desired membership function based on the membership function modification information and the characteristics of the membership function located above the desired membership function. Therefore, it is possible to acquire necessary information about the desired membership function.

In the membership function management device of the present invention, when registering a new membership function in the membership function storage means, the membership function to be registered is already stored in the membership function storage means. If the membership function has the same characteristics as the stored membership function, the membership function to be registered is positioned below the stored membership function. Further, among the characteristics included in the membership function to be registered, the characteristics not included in the higher membership function are stored as the membership function modification information for modifying the higher membership function.

Therefore, when registering the membership function, it is possible to register it in a hierarchical structure and to register the characteristics not included in the higher-level membership function.

According to another aspect of the membership function management apparatus of the present invention, the membership function stored in the membership function storage means is composed of membership function shape information and a membership function name which is its name. Membership function names are stored in a hierarchical structure in which lower-rank membership function names include higher-rank membership function names.
Therefore, the membership function can be managed by the membership function name and the membership function name can be managed by the hierarchical structure.

In the execution instruction creating apparatus of claim 4,
The membership function storage means stores a lower-rank membership function name in a hierarchical structure including a higher-rank membership function name, and ranks higher than the characteristics of the membership function shape information corresponding to the lower-rank membership function name. The membership function shape information that corrects the membership function shape information corresponding to the higher-level membership function name is stored without storing the common characteristics with the membership function shape information corresponding to the membership function name of Due to
The membership function shape information corresponding to the lower-order membership function name is stored. Therefore, it is possible to manage the membership functions in the upper and lower relationships by the membership function name.

Further, the membership function acquisition means, based on the membership function modification information and the characteristics of the membership function positioned above the desired membership function,
The membership function shape information corresponding to the desired membership function name is acquired. Therefore, it is possible to acquire necessary information about the desired membership function.

[0018]

【Example】

[Execution Command Creating Device 1] An embodiment of the present invention will be described with reference to the drawings. FIG. 2 shows a functional block diagram of the execution instruction creation device 10. The execution instruction creating device 10 includes a membership function storage unit 3, a membership function acquisition unit 5, an instruction input unit 7, and an execution instruction creation unit 9.

The membership function storage means 3 stores the membership function shape information and the membership function name which is its name. In the present embodiment, the membership function is composed of the membership function shape information and the membership function name which is its name. The membership function storage unit 3 is stored in a hierarchical structure in which lower membership function names include higher membership function names.

Further, the membership function storage means 3 has a common characteristic with the membership function shape information corresponding to the upper membership function name among the characteristics of the membership function shape information corresponding to the lower membership function name. Does not store, but stores membership function modification information for modifying the membership function shape information corresponding to the higher-level membership function name. Thereby, the membership function shape information corresponding to the lower membership function name is stored. The characteristic of the membership function is the information required to represent the shape information of the membership function.

A command including a membership function name is input to the command input means 7. Membership function acquisition means 5
Acquires the corresponding membership function shape information from the membership function storage unit 3 based on the membership function name included in the command input to the command input unit 7. The execution instruction creating means 9 creates an execution instruction based on the instruction input to the instruction input means 7 and the membership function shape information given from the membership function acquisition means 5.

As described above, in the execution instruction creating apparatus 10, even if an instruction including the membership function name, that is, an instruction not including the membership function shape information is input to the instruction input means 7, the corresponding membership function shape is input. Information can be obtained and execution instructions can be created.

[Execution Command Creating Device 21] FIG. 3 shows an execution command creating device 21 in which the execution command creating device 10 is more specifically configured. The execution instruction creating device 21 includes a membership function registration unit 22, a membership function library 23 which is a membership function storage unit, a source program input unit 24 which is an instruction input unit, a preprocessor 25 which is a membership function acquisition unit, and an execution unit. A compiler 26, which is an instruction creating means, is provided.

The execution command creating device 21 is a device for creating an execution program from a source program, and further has a membership function registration unit for registering a membership function in the execution command creating device 1.

The source program includes a membership function name, but does not include membership function shape information. When compiling this source program, necessary membership function shape information is acquired from previously registered data to create an execution program.

The outline of each function of the execution instruction creating device 21 will be described. First, the case of registering a membership function will be described. When the membership function to be registered in the membership function registration unit 22 is input, the membership function library 23 stores the membership function shape information and the membership function name which is its name. At this time, the membership function library 23 stores the membership function name of the lower hierarchy in a hierarchical structure including the membership function name of the higher membership function.

Also, the membership function library 23
Does not store the characteristics common to the membership function shape information corresponding to the upper membership function name among the characteristics of the membership function shape information corresponding to the lower membership function name, and stores the upper membership function. The membership function modification information for modifying the membership function shape information corresponding to the name is stored. In this way, the membership function information is registered.

Next, the case of searching the membership function information and creating the execution program will be described.
First, the source program is the source program input unit 24.
Entered in. This source program contains the membership function name. The preprocessor 25 determines whether or not the input source program has undefined membership function shape information (hereinafter referred to as undefined information),
If there is undefined information, the membership function library 23 is searched based on the membership function name, and the membership function shape information corresponding to the membership function name is acquired. The obtained membership function shape information and the source program are given to the compiler 26 and compiled. As a result, the execution program is output.

[Regarding method of storing membership function]
Next, the structure of the membership function library 23 will be described with reference to FIGS.

In FIG. 4, the membership function name of the highest-level membership function is "takai". As the membership function of the lower level, "se _- taka
There are membership functions whose membership function names are "i" and "yama _- takai". "Se _- taka
For the membership function with the membership function name of "i", "nihonjin _- se _- takai",
There is a membership function whose membership function name is "amerikajin _- se _- takai".

Further, the membership function having the membership function name "yama _- takai" has "n"
There is a membership function with the membership function name "ihon _- yama _- takai".

As described above, in this embodiment, the lower membership function names are stored in a hierarchical structure including the upper membership function names.

Next, a method of storing the membership function shape information will be described. The membership function shape information of the membership function name "takai" generally has a shape as shown in FIG. 5B. The membership function having such a shape can be defined by the coordinates of four points (α, β, γ, δ). The definition data of the membership function shape information of FIG. 9B is shown in FIG. By specifying “x, y, z” of this definition data, “m1, m2,
m3 ”is specified. Thereby, the shape of the membership function is specified.

It should be noted that takai operator + (takai x, int y) {x.m1 = x.m1 + y; x.m2 = x.m2 + y;} and takai operator− (takai x, int y) {x.m1 = The part of x.m1-y; x.m2 = x.m2-y;} is an additional data part, and is for changing the shape of the membership function shape information. Specific description will be given later.

Next, regarding the membership function shape information of the membership function name "se _- takai",
This will be described with reference to FIGS. 6A and 6B. As shown in FIG.
There is "inherit: takai". "Inher
"it: takai" means that the membership function with the membership function name "se _- takai" is "taka
This means that the characteristics of the membership function with the membership function name "i" are inherited. That is, "se _- t
In the membership function having the membership function name “akai”, “ta” is included in the membership function shape information.
kai ”membership function definition data ({(0,0.0) ...; x.m2 =
x.m2-y;}} portion (see FIG. 5A).

Furthermore, in the membership function having the membership function name of "se _-- takai", "m3
= 220 ”. That is, "taka
This means that "m3" is specified from the definition data of the membership function having the membership function name "i". In the present specification, such specific data is referred to as correction information.

In FIG. A, the little {m1 = m1-5; m2 = m2-10} part is an additional data part.

As described above, the membership function having the membership function name "se _- takai" is "taka-takai".
The membership function definition data having the membership function name "i" and the modification information ("m3 = 220") are used to form a membership function as shown in FIG.

[0039] Referring to FIG. 7A, "nihonjin _-
se _- in the membership function of the membership function name takai ", in the same manner," se _- taka
Inherit the characteristics of the membership function with the membership function name "i". Furthermore, “m1 = 150; m2 = 17
0; ”. Therefore, "nihonjin _- s
The membership function having the membership function name "e _- takai" is a membership function as shown in FIG.

The "amerik" defined in FIG.
The membership function having the membership function name "ajin _- se _- takai" becomes the membership function shown in FIG.

[Example of Hardware Configuration] FIG. 9 shows an execution instruction creating device 51. The execution instruction creating device 51 is an example of a hardware configuration in which each function of FIG. 2 is realized by using a CPU. The execution instruction creating device 51 includes a CPU 73,
A CRT 83, a ROM 75, a RAM 77, a hard disk 79, a keyboard 78 and a bus line 60 are provided.

The ROM 75 stores a control program for the CPU 73, etc., and the CPU 73 controls each unit via the bus line 60 in accordance with this control program. The keyboard 78 is an input means for inputting a membership function to be registered and a membership function to be searched, and these pieces of information are stored in the RAM 77.

Membership functions are stored in the hard disk 79. The calculation result performed by the CPU 73 is R
It is stored in the AM 77 and is output to the CRT 83 based on the output command.

[Registration / Search of Membership Function] Next, the programs stored in the CPU 73 will be described with reference to the flowcharts of FIGS. First, the case of registering a membership function will be described.

[Registration] For example, a case of registering a membership function having a membership function name “sekai _- yama _- takai” as shown in FIG. 8 will be described. When this membership function is input to the keyboard 78 (step ST1 in FIG. 10), the CPU 73
The inputted membership function is stored in the RAM 77.
Next, it is checked whether the input membership function has a syntactical error (step ST2). If there is an error, the fact is displayed on the CRT 83, and step ST1
Return to. If there is no error, the CPU 73 attaches a pointer to the address of the higher membership function to the input membership function. In this case, as shown in FIG. 8, since there is "inherit: yama _- takai", this membership function is "yama _- ta-ai".
The characteristics of the membership function with the membership function name "kai" are inherited. Therefore, "yama _- taka
A pointer to the address of the membership function with the membership function name "i" is added.

Next, the CPU 73 stores the pointer and the correction information in the hard disk 79 (step ST4). In this case, as the correction information, “m1 = 20
00; m2 = 8000; m3 = 9000 "is stored. In this way, the membership function is registered.

[Retrieval] Next, a case of retrieving membership function shape information and creating an execution program will be described with reference to FIG. Here, FIG.
It is assumed that the membership function as shown in FIG. When the source program is input to the keyboard 78 (step ST11 in FIG. 10), the CPU 73
Stores this source program in the RAM 77. Next, it is determined whether or not the input source program has undefined membership function shape information (hereinafter referred to as undefined information) (step ST12).

For example, as the undefined information, "nihon
It is assumed that there is a membership function name "jin _- se _- takai". In this case, the CPU 73 searches the hard disk 79 for a membership function with this membership function name (step ST13). Further, the membership function shape information of the membership function is acquired (step ST14). In this case, "nihonjin
_- se - definition data membership function shape information of the membership function name takai "(see FIG. 7A), R
Store in AM77.

Next, the CPU 73 synthesizes the membership function shape information stored in the RAM 77 (step S).
T15). In this case, since only the membership function having the membership function name “nihonjin _- se _- takai” is stored in the RAM 77,
There is no change before and after synthesis. The membership function after composition is shown in FIG. 12A.

Returning to FIG. 11, the CPU 73 determines whether the definition data has an "inherit" portion (step ST16). In this case, "inherit: se
_- so takai "that there is, returns to step ST13,
A membership function having a membership function name of "se _- takai" is searched, and further, membership function shape information of the membership function is acquired (step ST
14). In this case, the definition data (see FIG. 6A) of the membership function shape information of the membership function name “se _- takai” is stored in the RAM 77.

Next, the CPU 73 synthesizes the membership function shape information stored in the RAM 77 (step S).
T15). Specifically, "nihonjin _- se _- ta
A membership function having a membership function name of "kai" and a membership function having a membership function name of "se _- takai" are synthesized. The membership function of the membership function name after composition is shown in FIG. 12B. In this way, the values of m1, m2 and m3 are determined.

Returning to FIG. 11, the CPU 73 determines whether or not the definition data has an "inherit" portion (step ST16). In this case, "inherit: ta
Since there is "kai", the process returns to step ST13 and "ta"
The membership function with the membership function name "kai" is searched, and the membership function shape information of the membership function is acquired (step ST14).

In this case, the definition data (see FIG. 5C) of the membership function shape information of the membership function name "takai" is stored in the RAM 77.

Next, the CPU 73 synthesizes the membership function shape information stored in the RAM 77 (step S).
T15). Specifically, "nihonjin _- se _- ta
The membership function with the membership function name "kai" and the membership function with the membership function name "takai" are combined. FIG. 13 shows the membership function of the membership function name after composition.

Returning to FIG. 11, the CPU 73 determines whether or not the definition data has an "inherit" portion (step ST16). In this case, since there is no "inherit" portion, the process proceeds to step ST17.

In this way, when the acquired definition data of the membership function shape information has an "inherit" portion, the definition data of the membership function shape information of the higher-order membership function is searched next to
It is possible to acquire definition data of undefined membership function shape information.

Next, the CPU 73 compiles the input source program using the obtained definition data of the membership function shape information (step ST1).
7). The CPU 73 stores the compiled execution program in the hard disk 79. In this way, an execution program can be created from a source program containing undefined information.

When there is no undefined information in step ST12, the source program may be compiled as it is.

[Additional Data] Next, the additional data will be described with reference to FIG. The additional data is for changing the shape of the membership function shape information. For example, a membership function with a membership function name of "yama _- takai" is shown in FIG. 14A.
It is assumed that the definition data is as shown in. Where "to
A membership function having a membership function name "temo _- yama _- takai" is defined as shown in FIG. As a result, the definition data as shown in FIG.

More specifically, as shown in FIG. 9B, the membership function having the membership function name "totemo _- yama _- takai" is "yama _- t".
The data “+1000” is added to the membership function with the membership function name “akai”. Here, as shown in FIG. 5A, in the membership function having the membership function name "takai", "+"
The arithmetic process is defined to add a number after “+” to “m1, m2”. Therefore, "m1,
“1000” is added to “m2”, and “m1 = 2000, m2
= 2500 ". The same applies to the arithmetic processing " _- ".

As described above, in this embodiment, since the additional membership data can be used to define another membership function from the basic membership function, the membership function can be easily defined.

Note that the following additional data little {m1 = m1-5; m2 = m2-10} is similarly converted from the basic membership function to
Another membership function can be defined.

[Other Application Examples] In this embodiment, the trapezoidal membership function shape information has been described. However, when the membership function shape information is triangular, the representative value and the width of the base are used. Can be represented. If the representative value is a triangular membership function, the coordinates of its vertices may be used as the representative value.

Even if the membership function shape information is other than a trapezoidal shape or a triangular shape, it may be stored as follows. For example, a bell-shaped case can be represented by a Gaussian distribution, and an arbitrary curve such as a spline or an Nth-order curve can be represented by each coordinate point and its interpolation function.

In the present embodiment, the keyboard 78 or the mouse 81 is used for data input and correction.
However, any device that can input a numerical value may be used, and a light pen, a digitizer, or the like may be used.

Further, in the above embodiment, the present invention is configured as an execution instruction creating apparatus, but as shown in FIG.
It may be configured as a membership function management device.

In this embodiment, the lower membership function names are stored in a hierarchical structure including the upper membership function names. However, without being limited to this, the lower membership function may be stored so as to include the characteristics of the upper membership function.

[0068]

According to the membership function management device of the present invention, the membership function storage means has a hierarchical structure in which the characteristics of a certain membership function are included in the lower membership functions. There is. Further, among the characteristics of the lower membership function, the characteristics common to the upper membership function are not stored, but the membership function modification information for modifying the upper membership function is stored, so that the lower membership Remember the function.

In this way, the upper membership function and the lower membership function can be associated with each other.
Further, the lower-rank membership function inherits the characteristics of the higher-rank membership function, which facilitates the management of the higher-rank and lower-rank membership functions.

Further, the membership function acquisition means acquires the desired membership function based on the membership function modification information and the characteristics of the membership function located above the desired membership function. Therefore,
The necessary information about the desired membership function can be obtained. That is, it is possible to provide a membership function management device that facilitates management of membership functions.

In the membership function management device of the second aspect, when a new membership function is registered in the membership function storage means, the membership function to be registered is already stored in the membership function storage means. If the membership function has the same characteristics as the stored membership function, the membership function to be registered is positioned below the stored membership function. Further, among the characteristics included in the membership function to be registered, the characteristics not included in the higher membership function are stored as the membership function modification information for modifying the higher membership function.

Therefore, when registering the membership function, it is possible to register it in a hierarchical structure and to register the characteristics that are not included in the higher-level membership function.
That is, it is possible to provide a membership function management device that facilitates management of membership functions.

According to another aspect of the membership function management apparatus of the present invention, the membership function stored in the membership function storage means comprises membership function shape information and a membership function name which is the name of the membership function shape information. Membership function names are stored in a hierarchical structure in which lower-rank membership function names include higher-rank membership function names.
Therefore, the membership function can be managed by the membership function name and the membership function name can be managed by the hierarchical structure. That is, it is possible to provide a membership function management device that facilitates management of membership functions.

In the execution instruction creating device of claim 4,
The membership function storage means stores a lower-rank membership function name in a hierarchical structure including a higher-rank membership function name, and ranks higher than the characteristics of the membership function shape information corresponding to the lower-rank membership function name. The membership function shape information that corrects the membership function shape information corresponding to the higher-level membership function name is stored without storing the common characteristics with the membership function shape information corresponding to the membership function name of Due to
The membership function shape information corresponding to the lower-order membership function name is stored. Therefore, it is possible to manage the membership functions in the upper and lower relationships by the membership function name.

Further, the membership function acquisition means, based on the membership function modification information and the characteristic of the membership function located above the desired membership function,
The membership function shape information corresponding to the desired membership function name is acquired. Therefore, it is possible to acquire necessary information about the desired membership function. That is, it is possible to provide an execution instruction creating device that facilitates management of membership functions.

[Brief description of drawings]

FIG. 1 is a functional block diagram of a membership function management device 1.

FIG. 2 is a functional block diagram of an execution instruction creation device 10.

FIG. 3 is a diagram showing an execution instruction creation device 21.

FIG. 4 is a diagram showing a structure of a membership function library 23.

FIG. 5 is a diagram showing definition data of a membership function.

FIG. 6 is a diagram showing definition data of a membership function.

FIG. 7 is a diagram showing definition data of a membership function.

FIG. 8 is a diagram showing definition data of a membership function.

FIG. 9 is a diagram showing a hardware configuration in which the instruction form changing device 10 is realized by a CPU.

FIG. 10 is a flowchart for registering a membership function.

FIG. 11 is a flowchart in the case of retrieving membership function shape information and creating an execution program.

FIG. 12 is a diagram showing a membership function of a membership function name after composition.

FIG. 13 is a diagram showing a membership function of a membership function name after composition.

FIG. 14 is a diagram for explaining additional data.

[Explanation of symbols]

 3 ... Membership function storage means 5 ... Membership function acquisition means 7 ... Command input means 9 ... Execution command creation means

Claims (4)

[Claims] 1. Membership function storage means for storing a membership function, membership function acquisition means for acquiring a membership function to be searched from the membership function storage means when a membership function to be searched is input, In the membership function management device, the membership function storage means is configured in a hierarchical structure in which the membership function of a certain membership function is included in the membership function of the lower level. Among the characteristics of the membership function, the characteristics common to the upper membership function are not stored, but the lower membership function is stored by storing the membership function correction information that corrects the upper membership function. The membership function acquisition means is configured to obtain the membership function modification information and desired membership information. Based on the characteristics of the membership function is located in the number of higher-level, membership function management apparatus characterized by, to obtain the desired membership function. 2. The membership function management device according to claim 1, wherein when a new membership function is registered in the membership function storage means, the membership function to be registered is:
If it has the same characteristics as the membership function already stored in the membership function storage means, the membership function to be registered is positioned below the stored membership function, and the membership function above it is stored. Membership function management, characterized by storing, as membership function modification information, the characteristics of the membership function to be registered that are not included in the higher-level membership function. apparatus. 3. The membership function management device according to claim 1, wherein the membership function stored in the membership function storage means comprises membership function shape information and a membership function name which is its name. The membership function name is stored in a hierarchical structure in which lower membership function names include upper membership function names. 4. Membership function shape information and membership function storage means for storing membership function name which is the name thereof, instruction input means for inputting an instruction including the membership function name, and instruction input means. A membership function acquisition means for acquiring corresponding membership function shape information from the membership function storage means based on the membership function name included in the instruction, and an instruction input to the instruction input means and a membership function acquisition means. And a membership function storing means for creating an execution instruction based on the membership function shape information, wherein the membership function storage means has a lower membership function name and a higher membership function name. A member that is stored in a hierarchical structure that includes the name and that corresponds to the lower-level membership function name. The membership function shape information corresponding to the upper membership function name is corrected without storing the characteristics common to the membership function shape information corresponding to the higher membership function name among the characteristics of the ship function shape information. By storing the membership function modification information, the membership function shape information corresponding to the lower membership function name is stored, and the membership function acquisition means stores the membership function modification information and the desired membership function upper layer. Acquiring the membership function shape information corresponding to the desired membership function name based on the characteristics of the membership function located at.