Abstract
The purpose of this paper is to prove a Tychonoff theorem in the so‐called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some characterizations concerning fuzzy compactness. Lastly we give a Tychonoff‐like theorem.
Highlights
After the introduction of the concept of fuzzy sets by Zadeh [8] several researches were conducted on the generalizations of the notion of fuzzy set
A TYCHONOFF THEOREM IN INTUITIONISTIC FUZZY TOPOLOGICAL. In this case the pair (X, τ) is called an intuitionistic fuzzy topological space (IFTS) and any intuitionistic fuzzy set (IFS) in τ is known as an intuitionistic fuzzy open set (IFOS) in X
Any fuzzy topological space (X, τ0) in the sense of Chang is obviously an IFTS whenever we identify a fuzzy set A in X whose membership function is μA with its counterpart x, μA(x), 1 − μA(x) : x ∈ X
Summary
After the introduction of the concept of fuzzy sets by Zadeh [8] several researches were conducted on the generalizations of the notion of fuzzy set. An intuitionistic fuzzy topology (IFT) on a nonempty set X is a family τ of IFSs in X satisfying the following axioms: (T1) 0∼, 1∼ ∈ τ, (T2) G1 ∩ G2 ∈ τ for any G1, G2 ∈ τ, (T3) ∪Gi ∈ τ, for any arbitrary family {Gi : i ∈ τ} ⊆ τ.
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