Hi Mr. Imran,

Interesting still open research issue because of the influence of the membership function on the behavior of the fuzzy system. In a few words, you may start for simple membership function trapezoid-shape (triangular) and singletons. If you are thinking in further learning procedures that requires gradient you may use gaussian type. You may find some guidelines in:

R. E. Haber, R. Haber, A. Alique, and S. Ros, "Application of knowledge-based systems for supervision and control of machining processes," Handbook of software engineering and knowledge engineering, vol. 2, pp. 673-710, 2002.

BR,

Rodolfo

Thank you Professor Rodolfo E.Haber. The paper is very useful in this regard.

Dear Mr. Imran ,

I think the question is too general as membership function is a hard elementary problem in the fuzzy set framework. It is SUBJECTIVE and APPLICATION-DEPENDENT problem. Therefore, there are no general criteria. For example, for user-centric applications such as the applications of fuzzy rule base systems (FRBSs), their interpretability is required, including the interpretability of fuzzy partitions, called the low-interpretability of FRBSs, that forms the so-called frames of cognition of their respective linguistic variables. There have been many studies of the low-interpretability in which many criteria (constraints) have been proposed. You can easily to find such studies on internet using some specific key-words.

For the applications which are required to interact with human user, the presence of linguistic words is necessary, the fuzzy sets to be designed must be associated with words, you should determine words fro every variable first for your application, noting that fuzzy theories are aimed to simulate human capabilities in handling words. They may form the so-called Linguistic Frames of Cognition (LFoCs). The meaning of the words of a determined LFoC for your application may suggest you to construct the fuzzy sets of their respective words. However, the effectiveness of your method to solve an application problems is crucial. So, adjusting or turning your fuzzy sets constructed for the LFoCs is necessary.

In the latter case, one way to construct fuzzy sets of the words of your determined LFoCs is to produce the desired fuzzy sets from just the semantics of the words of LFoCs. However, in this case, the word semantics must formally be defined and the word-domains of linguistic variables must be formalized to become (semantic) order-based structures, called hedge algebras, as linguistic hedges of every variable play algebraic unary operators. Note that hedges play a significant role to generate the words and their semantics of a (linguistic) variable in natural languages of human beings. The algebraic approach to the semantic structures of word-domains of variables is very specific and you can find its materials in my account of ReseachGate. It provides a formalism to connect words with their designed computational semantics, including their fuzzy set based semantics, in which the fuzziness parameters of their linguistic variables, comprising few fuzziness parameters of atomic (primary) words and of hedges of their variables, play a crucial role. That is, the given numeric values of these parameters of a variable do, in general, determine the computational semantics of the all words of the variable.