A New Introduction to Fuzzy Group Algebra

Abstract

In this paper, the concept of fuzzy group algebra is introduced using a finite group G and a fuzzy group  on G. we had proved certain basic properties of fuzzy group algebra, including its behaviour as a fuzzy algebra and as  a fuzzy G - module. The work is a continuation of the concept of semi simplicity of fuzzy G - modules and its properties including relationships with complete reducibility and injectiviness, which was already defined by the authors. The intersections and - cuts of fuzzy group algebra are also analyzed.