On Tri-α-Open Sets in Fuzzifying Tritopological Spaces

Abstract

In this paper, we introduced and studied (1,2,3)-α-open set, (1,2,3)-α-neighborhood system, (1,2,3)-α-derived, (1,2,3)-α-closure, (1,2,3)-α-interior, (1,2,3)-α-exterior, (1,2,3)-α-boundary, (1,2,3)-α-convergence of nets, and (1,2,3)-α-convergence of filters in fuzzifying tritopological spaces.

On tri α-separation axioms in fuzzifying tri-topological spaces

“…We use the fundamentals of fuzzy logic with consonant set theoretical notations which are introduced by Ying (1991Ying ( -1993 [7][8][9] throughout this paper. Definition 1.1 [5] If ( , 1 , 2 , 3 ) is a fuzzifying tri-topological space (FTTS), (i) The family of fuzzifying (1,2,3) α-open sets in , symbolized as (1,2,3) ∈ ℑ( ( )), and defined as ∈ (1,2,3) ≔ ∀ ( ∈ → ∈ 1 ( 2 ( 3 ( )))), i.e., (1,2,3) ( ) = ∈ ( 1 ( 2 ( 3 ( ))))( ).…”