Generalized Fuzzy Entropy Optimization Methods for Fuzzy Data Analysis

The fuzzy entropy is used to express the mathematical values of the fuzziness of fuzzy sets and is defined by using the concept of membership function. The maximum entropy principle attempts to choose the membership function with a finite number of the fuzzy values subject to constraints generated by given moment vector functions that have maximum entropy value. On the other hand, the minimum cross-entropy principle tells us that out of all membership functions satisfying given moment constraints, select the one that is closest to the given a priori membership function. This study is connected with new Generalized Minimum Cross Fuzzy Entropy Methods (GMinx(F)EntM) in the form of MinMinx(F)Ent and MaxMinx(F)Ent methods. The aim of this study consists of applying GMinx(F)EntM on given simulated fuzzy data. The performances of distributions (MinMinx(F)Ent)m and (MaxMinx(F)Ent)m are compared by Chi-Square, Root Mean Square Error, coefficient of determination criteria and fuzzy cross entropy measure. The obtained results show that Generalized Minimum Cross Fuzzy Entropy Optimization distributions give significant results in the data modeling for fuzzy data analysis.