A new measure of divergence with its application to multi-criteria decision making under fuzzy environment

Divergence measure is an important tool for determining the amount of discrimination between two probability distributions. Since the introduction of fuzzy sets, divergence measures between two fuzzy sets have gained attention for their applications in various fields. Exponential entropy measure has some advantages over Shannon's entropy. In this paper, we used the idea of Jensen-Shannon divergence to define a new divergence measure called 'fuzzy Jensen-exponential divergence (FJSD)' for measuring the discrimination/difference between two fuzzy sets. The measure is demonstrated to satisfy some very elegant properties, which shows its strength for applications in multi-criteria decision-making problems. Further, we develop a method to solve multicriteria decision-making problems under fuzzy phenomenon by utilizing the proposed measure and demonstrate by a numerical example.