Constructing membership function based on fuzzy shannon entropy and human's interval estimation

This paper develops a new constructing approach of an appropriate membership function to integrate a given probability density function and fuzzy Shannon entropy extending the statistical theory into the heuristic method based on the human cognitive behavior and subjectivity. The proposed approach is formulated as a more general mathematical programming problem than previous approaches due to using a general S-curve function and the fuzzy Shannon entropy. Then, performing deterministic equivalent transformations to the initial problem, the optimal condition of parameters is obtained. Furthermore, in order to show the appropriate membership function using the proposed approach, some probability density functions are provided as numerical examples.