Bridging the Gap Between Probabilistic and Fuzzy Entropy

The real-world decision making often involves a comparison of uncertain systems or alternatives based on fuzzy evaluations. The concept of fuzzy entropy is quite useful in such situations. However, fuzzy entropy and the conventional probabilistic entropy differ in their semantics. This article critically examines the existing fuzzy entropy functions and redefine them to bring them closer to the probabilistic entropy. More specifically, new variants of the extant Luca and Termini, and Pal and Pal fuzzy entropy functions are proposed. The proposed fuzzy entropy functions are extended for the probabilistic-fuzzy uncertainty, commonly observed in the real world. A real application is included to demonstrate the usefulness of the proposed entropy functions in decision making applications.