Anti Fuzzy HX Ring and Its Level Sub HX Ring

Abstract

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