A class of fuzzy subgroups of finite reflection groups

Abstract

A finite group W generated by reflections is called a finite reflection group and have been studied deeply in different important contexts such as geometry and group theory, matrix algebra and Lie Theory. In this paper we study a class of fuzzy subgroups of finite reflection groups which are called parabolic fuzzy subgroups using preferential equality. In the classical case parabolic subgroups are associated with a set of generators, each a simple reflection, indexed by elements of subsets of a fixed root system Δ. We establish a one-to-one correspondence between the class of fuzzy parabolic subgroups of W and the class of fuzzy subsets of S where S is a set of simple reflections associated with Δ.