Monotonicity is a major property of entropy measures. In this paper, we focus on measures for intuitionistic fuzzy sets and interval-valued sets. We consider their polar representation which provides an easy interpretation monotonicity several introduced in the literature. Moreover, enables us to propose two new kinds such entropies, that offer more understandable way explain differences entrop...

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches. 

The central objective of the proposed work in this research is to introduce innovative concept an m-polar fuzzy set (m-PFS) semigroups, that is, expansion bipolar (BFS). Our main focus study generalization some important results BFSs m-PFSs. This paper provides related subsemigroups (m-PFSSs), ideals (m-PFIs), generalized bi-ideals (m-PFGBIs), (m-PFBIs), quasi-ideals (m-PFQIs) and interior (m-P...

Since its original formulation, the theory of fuzzy sets has spawned a number of extensions where the role of membership values in the real unit interval $[0, 1]$ is handed over to more complex mathematical entities. Amongst the many existing extensions, two similar ones, the fuzzy multisets and the hesitant fuzzy sets, rely on collections of several distinct values to represent fuzzy membershi...