In order to obtain batter results in ANFIS, different membership functions are used. Is there any inductive way for obtaining best membership function based on the type of data used?
Dear friend
Greetings.
To chose the membership function in ANFIS, you need to look at the distribution of the data. That is the first thing you look at.
Second, you can try some of the existing functions. Just see the results.
I hope this helps you.
Best regards
Dr.Indrajit Mandal, Ph.D.
Dear Hassan,
let me recommend you this related question:
https://www.researchgate.net/post/In_Fuzzy_Logic_Control_How_should_we_choose_Membership_Function?_tpcectx=profile_answers
It has got some relevant information which might be interesting for you.
Regards.
please check the paper in the link below.
https://www.researchgate.net/publication/266262199_Revised_General_TestGross_Point_Average_System_via_Fuzzy_Logic_Techniques
Article Revised General Test/Gross Point Average System via Fuzzy Lo...
My 15-year experience with ANFIS tells that experimentation is the best way to come up with best system performance. It is a design process. However, type of MF doesn't usually play a vital role in shaping how the system performs. Number of MF absolutely does. I always tend to try Gaussian MF first as they are represented by the least number of parameters (Only two parameters: mean and variance). This makes the number of modifiable parameters minimum if you keep everything else unchanged. The number of modifiable parameters, which is affected by type and number of MF as well as system order, determines the computational time and burden required for conversion. I hope this helps.
Good luck,
Mohamed
Yes! I can. If the sample is big enough, let m(Aj|x)=P(yj|x)/max(P(yj/x)=[P(x|yj)/P(x)]/max(P(x|yj)/P(x)). If the sample is not big enough, use a generalized Kullback-Leibler formula to optimize the membership function. Please see Article Semantic Information G Theory and Logical Bayesian Inference...
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.
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