• BIPOLAR FUZZY HX GROUP AND ITS LEVEL SUB HX GROUPS

R. Muthura*, M. Sridharan

Abstract


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


Keywords


HX group, fuzzy set, fuzzy subgroup, anti fuzzy subgroup, fuzzy HX group, anti fuzzy HX group, bipolar fuzzy set, bipolar fuzzy HX group, bipolar anti fuzzy HX group, level subset, level sub HX group.

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