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In this paper, we define a new algebraic structure of an induced fuzzy k-ideal 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 fuzzy HX k-ideals of a HX ring. We also establish the relation between fuzzy HX ideals and fuzzy HX k-ideals of a HX ring . Characterizations of level subsets of a fuzzy HX k-ideal of a HX ring are given. We also discussed the relation between a given fuzzy HX k-ideals of a HX ring and its level HX k-ideals and investigate the conditions under which a given HX ring has a properly inclusive chain of HX k-ideals. In particular, we formulate how to structure a fuzzy HX k-ideal of a HX ring by a given chain of HX k-ideals.

Induced Fuzzy K-Ideal and Its Level K-Ideals on a HX Ring