### On Characterization of Some Fuzzy Subsets of Fuzzy Ideal Topological Spaces and Decomposition of Fuzzy Continuity

#### Abstract

In this paper, fuzzy AI-set, fuzzy BI-set, fuzzy CI-set,

fuzzy I-locally closed set of fuzzy ideal topological spaces are studied and characterized and several results and implications are obtained. We introduced fuzzy strongly b-I-open set. Fuzzy strongly α-I-open set was introduced by A. Selvakumar et al. in 2009 and fuzzy strongly pre-I-open set was introduced by Bin Chen in 2011. We characterized fuzzy strongly α-I-open set in terms fuzzy strongly pre-

I-open set and fuzzy strongly b-I-open set and ultimately we obtained a new characterization of fuzzy open set. The aim of this paper is to obtain a new decomposition of fuzzy continuity. With the help of such characterizations we obtained several generalizations of fuzzy continuous functions and finally we obtained a new decomposition of

fuzzy continuity in terms of fuzzy strongly α-I-open set and fuzzy AIset. The notions and results given in this paper may lead to some interesting analytical study and research in the arena of Physical Sciences and Mathematical Sciences.

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