• LOWER ANTI Q-FUZZY GROUP AND ITS LOWER LEVEL SUBGROUPS

Abstract

In this paper, we define the algebraic structures of a lower anti Q-fuzzy subgroup and some related properties are investigated. We establish the relation between upper Q-fuzzy group and lower anti Q-fuzzy group of a group. The purpose of this study is to implement the fuzzy set theory and group theory in upper Q-fuzzy groups and lower anti Q-fuzzy groups. Characterizations of lower level subsets of a lower anti Q-fuzzy group of a group are given. We also discussed the relation between a given a lower anti Q-fuzzy group and its lower level sub groups and investigate the conditions under which a given group has a properly inclusive chain of sub groups. In particular, we formulate how to structure a lower anti Q-fuzzy group by a given chain of sub groups.