Abstract
We introduce the notions of totally continuous functions, totally semicontinuous functions, and semitotally continuous functions in double fuzzy topological spaces. Their characterizations and the relationship with other already known kinds of functions are introduced and discussed.
Highlights
The concept of fuzzy sets was introduced by Zadeh in his classical paper [1]
We introduce the notions of totally continuous, totally semicontinuous, and semitotally continuous functions in double fuzzy topological spaces and investigate some of their characterizations
We study the relationships between these new classes and other classes of functions in double fuzzy topological spaces
Summary
In 1968, Chang [2] used fuzzy sets to introduce the notion of fuzzy topological spaces. Coker [3, 4] defined the intuitionistic fuzzy topological spaces using intuitionistic fuzzy sets. The name “intuitionistic” did not continue due to some doubts that were thrown about the suitability of this term These doubts were quickly ended in 2005 by Gutierrez Garcıa and Rodabaugh [7]. They proved that this term is unsuitable in mathematics and applications. The notion of intuitionistic gradation of openness is given the new name “double fuzzy topological spaces.”. We introduce the notions of totally continuous, totally semicontinuous, and semitotally continuous functions in double fuzzy topological spaces and investigate some of their characterizations. We study the relationships between these new classes and other classes of functions in double fuzzy topological spaces
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