Abstract
In this paper we have studied separation axiomsTi,i=0,1,2in an intuitionistic fuzzy topological space introduced by Coker. We also show the existence of functorsℬ:IF-Top→BF-Topand𝒟:BF-Top→IF-Topand observe that𝒟is left adjoint toℬ.
Highlights
Fuzzy sets were introduced by Zadeh [1] in 1965 as follows: a fuzzy set A in a nonempty set X is a mapping from X to the unit interval [0, 1], and A(x) is interpreted as the degree of membership of x in A
Atanassov [2] generalized this concept and introduced intuitionistic fuzzy sets which take into account both the degrees of membership and of nonmembership subject to the condition that their sum does not exceed 1
Coker [3] subsequently initiated a study of intuitionistic fuzzy topological spaces
Summary
Fuzzy sets were introduced by Zadeh [1] in 1965 as follows: a fuzzy set A in a nonempty set X is a mapping from X to the unit interval [0, 1], and A(x) is interpreted as the degree of membership of x in A. Replacing fuzzy sets by intuitionistic fuzzy sets in Chang’s definition of a fuzzy topological space, we get the following. An intuitionistic fuzzy topology (IFT, in short) on a nonempty set X is a family τ of IFSs in X satisfying the following axioms: (1) 0∼, 1∼ ∈ τ, (2) G1 ∩ G2 ∈ τ, for all Gi ∈ τ, i = 1, 2, (3) ∪Gi ∈ τ for any arbitrary family {Gi ∈ τ : i ∈ J}.
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