After training stage, your input parameters go through a function known as membership function. It classifies them into several groups which may have overlap with others (FUZZY).

Consider Z=f(X,Y), every X may set in 3 or 4 subset groups for instance. The number of subset classifications and their members are determined during training stage. By the way, membership function is a function distribute the input values (i.e. X and Y) to predict a certain equation for them. finally all of output sum together.

Good luck.

Hi,

start to work on the basics of membership functions: http://www.csee.wvu.edu/classes/cpe521/presentations/Membership.pdf

Prof. Laxmidhar Behera has given a very good fundamental video lecture on Fuzzy in Youtube. So try to see all the 4 module videos. Hope you will learn the basics from these videos and also you will get your answer soon.

https://www.youtube.com/watch?v=H9SikB7HbSU&index=13&list=PL080F1A848428C3FD

Dear all, my actual query is that how can we decide which type of membership function particularly applicable in particular problem?  

If your question is for control purposes, different types (shapes) of membership functions result in slightly different control surfaces and hence will affect the transient response of the system. For instance, if you have Gaussian membership functions, the ways rules are fired is much smoother than in Triangular membership functions. Therefore, the resulting control signal is much smoother. However, in some cases the difference may not be noticeable. You can find the MATLAB codes I have uploaded on Mathworks website on fuzzy control. The code is written for Triangular membership functions, but you can change them to any type of membership function and see the difference.

http://www.mathworks.com/matlabcentral/fileexchange/52230-optimal-fuzzy-logic-controller-using-pso

The related paper is also here:

https://www.researchgate.net/publication/280131650_Optimal_PID-type_Fuzzy_Logic_Controller_for_a_Multi-Input_Multi-Output_Active_Magnetic_Bearing_System

Hope this helps,

Article Optimal PID-type Fuzzy Logic Controller for a Multi-Input Mu...

there are different types of membership function that are used in the design of a fuzzy logic system. Each membership function has its own number of parameters. e.g, triangular membership function has three parameters, trapezoidal has four..The shapes of a membership functions for a system are usually selected by trial and error. However, the membership function type with less parameters is a good choice if need to improve the computational time of the system.

Membership functions - an Example:

Suppose there is a team of some type of members. Let it will be a fixed set of all (say n) teachers in a school [or any other "team" of both actual and "potential" members (candidates) ].

At each post (some of the posts are not [yet] fulfilled so that kind of members are "potential") there is a "qualifications requirement" and a candidate to obtain this full-time job should be able to teach all the given m courses (m = 2, 3, ... ). If a given candidate is only able teach k out of m (all equaly rated) courses he can be hired as a part time teacher for that k courses and his salary will be (or "is") k/m of the full job salary (k = 0, 1, ... m). So, in this case, he will (or he does) belong to the set of all the teachers of this school with the "membership coefficient" equal to k/m (the "membership function" assigns to all the teachers of the shool their corresponding membership coefficients ). Now, theoretizing, suppose that the number of the "courses" m in some school(s) grows (so also, propotionally, grows the "teachers" abilities k) unboundently. Thus, theoretically, we may have the situation that the parthood (membership) coefficient converges: k/m --> r, where r can be any real number from the interval [0, 1].

The values of membership functions are then defined as limits of the fractions k/m.

The situation seems to be similar to definition of probability [however this concept is quite different] as the limit [idealization] of relative frequences. Also it resembles the definition of Riemann integral as the limit of partial sums (considering a sequence of growing subdivisions of interval, say [0, 1] ). The above construction can be generalized and modified in various obvious ways.

J. F.