Fuzzy topology on fuzzy sets and tolerance topology

Fuzzy Bitopological Ideals Spaces

“…A fuzzy set  in fts is said to be quasi-coincident [3] with a fuzzy set  , denoted by  q , if there exists x  X such that  (x) + (x) > 1. A fuzzy set  in a fts (X, ) is called a q-nbd [1,3] of a fuzzy point x  iff there exists a fuzzy open set  such that x  q    we will denoted the set of all q-nbd of x  in (X, ) by N (X, ). A nonempty collection of fuzzy sets L of a set X is called fuzzy ideal [5] …”

“…A fuzzy point in X with support x  X and value  (0 <   1) is denoted by x  [1]. A fuzzy point x  is said to be contained in a fuzzy set  in I X iff    and this will be denoted by x    [ 3 ] .For a fuzzy set  in a fbts (X, , and  c will respectively denote closure, interior and complement of .…”

Continuity of Fuzzy Proper Functions on Sostak's I-Fuzzy Topological Spaces

“…Regarding functions in fuzzy setting, the fuzzy proper function and its continuity on Chang topological spaces are first introduced by Chakraborty and Ahsanulla [2]. Chaudhuri and Das [4] proved the equivalent statements of continuity of fuzzy proper function in the context of Chang topology.…”

FUZZY ωO-OPEN SETS

“…Fuzzy topological spaces were first introduced by [1,2]. Let (X, T) be a fuzzy topological space (simply, Fts).…”