Author : Birojit Das 1
Date of Publication :27th February 2018
Abstract: B. C. Tripathy and S. Debnath [B. C. Tripathy, S. Debnath, -Open Sets and -Continuous Mappings in Fuzzy Bitopological Spaces, J. of Intelligence and Fuzzy Systems, 24, 631-635 (2013)] first introduced the concept of fuzzy -open set in a fuzzy bitopological space to show that the collection of all these sets forms a fuzzy topology and also studied fuzzy pairwise - continuity. In this present treatise, we redefine this set as fuzzy -open set with the help of fuzzy preopen set to show that it is completely independent from fuzzy open set. Moreover, we introduce fuzzy -generalized closed set as a generalization of fuzzy closed set and then we establish various properties and characterizations along with interrelationship among them. Also, we show an important result which states that though every fuzzy closed set is a fuzzy generalized closed set and fuzzy -generalized closed set but fuzzy generalized closed set and fuzzy -generalized closed set are totally independent of each other. Furthermore, we introduce the notion of fuzzy continuous function, continuous function, fuzzy -continuous function and - continuous function in a fuzzy bitopological space and study those functions with various properties and interrelationships. Lastly, we define a new type of closure operator and prove certain results based on this conception.
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