Combination of Hamming Distance and Entropy Measure of Picture Fuzzy Sets: Case Study of COVID-19 Medicine Selection

Abstract

The picture fuzzy set (PFS) is a general form of the fuzzy and intuitionistic fuzzy set for solving real-world problems. Entropy and distance measures play significant measures in solving problems involving fuzzy environments. In multi-criteria decision-making (MCDM) problems, entropy is used to determine the weights of each criterion. Distance measures are used to rank alternatives using fuzzy picture sets. In this paper, we consider relationship between Hamming distance and entropy measures on picture fuzzy sets (PFS) and apply them to solving MCDM problems. Firstly, some distance of picture fuzzy sets are constructed by using the axioms. Secondly, a method to build the entropy measure of the picture fuzzy sets is defined as new Hamming distance measure. Finally, the distance measures apply to solve the MCDM problems. To illustrate the Hamming distance measure, this method is used to construct an entropy based on distance measures of PFS for selection of COVID-19 medicine.