The concept of intuitionistic fuzzy β-almost compactness and intuitionistic fuzzy β-nearly compactness in intuitionistic fuzzy topological spaces is introduced and studied. Besides giving characterizations of these spaces, we study some of their properties. Also, we investigate the behavior of intuitionistic fuzzy β-compactness, intuitionistic fuzzy β-almost compactness, and intuitionistic fuzzy β-nearly compactness under several types of intuitionistic fuzzy continuous mappings.

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On Intuitionistic Fuzzy β-Almost Compactness and β-Nearly Compactness.

Purpose – In 2000, Wang and He published an important result on the theory of intuitionistic fuzzy sets (IFSs) Indeed, they showed that every IFS may be regarded as an L‐fuzzy set for some appropriate lattice L This paper aims to show that, nevertheless, the results obtained by various authors on intuitionistic fuzzy topological spaces (IFTSs), are not redundant with others for the ordinary fuzzy senseDesign/methodology/approach – The most important definitions and results on intuitionistic fuzzy topology (IFT) one compared with the result obtained by Wang and HeFindings – That these results are not redundantResearch limitations/implications – Clearly, this paper is devoted to IFTSsPractical implications – The main applications are in the mathematical fieldOriginality/value – The originality and value of IFT are here demonstrated

On intuitionistic fuzzy topological spaces

Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued “intuitionistic” sets, “intuitionistic” fuzzy sets and topologies

Purpose – Recently, Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs). Also, this author defined the notion of neutrosophic topology on the non‐standard interval. One can expect some relation between the intuitionistic fuzzy topology (IFT) on an IFS and the neutrosophic topology. This paper aims to show that this is false.Design/methodology/approach – The possible relation between the IFT and the neutrosophic topology is studied.Findings – Relations on neutrosophic topology and IFT are found.Research limitations/implications – Clearly, this paper is confined to IFSs and NSs.Practical implications – The main applications are in the mathematical field.Originality/value – The paper shows original results on fuzzy sets and topology.

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On neutrosophic topology

We introduce the category IRel(H) consisting of intuitionistic fuzzy relational spaces on sets and we study structures of the category IRel(H) in the viewpoint of the topological universe introduced by Nel. Thus we show that IRel(H) satisfies all the conditions of a topological universe over Set except the terminal separator property and IRel(H) is cartesian closed over Set.

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Intuitionistic H-fuzzy relations

In this paper, we introduce the concept of intuitionistic fuzzy points and intuitionistic fuzzy neighborhoods. We investigate the properties of continuous, open and closed maps in the intuitionistic fuzzy topological spaces, and show that the category of Chang's fuzzy topological spaces is a bireflective full subcategory of that of intuitionistic fuzzy topological spaces.

The category of intuitionistic fuzzy topological spaces

In this paper, we introduce the notions of fuzzy -peropen (-perclosed) sets and fuzzy -percontinuous (-peropen, -perclosed) maps, and investigate some of their properties.

FUZZY ${\gamma}$-PREOPEN SETS AND FUZZY ${\gamma}$-PRECONTINUOUS MAPS

In this paper, we introduce the notions of ()-fuzzy (r, s)-preopen sets and fuzzy pairwise (r, s)-precontinuous mappings in smooth bitopological spaces and then we investigate some of their characteristic properties.

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Preopen sets in smooth bitopological spaces

We introduce and investigate the concepts of (-fuzzy -semiopen -semiclosed) sets and fuzzy pairwise -semicontinuous mappings in smooth bitopological spaces.

(T i , T j )-FUZZY α-(r.s)-SEMIOPEN SETS AND FUZZY PAIRWISE α-(r.s)-SEMICONTINUOUS MAPPINGS

In this paper we introduce a new definition of a lattice fuzzy topology which is a generalization of Lowen's fuzzy topology and show that the category of Lowen's fuzzy topological spaces is a bireflective full subcategory of the category of lattice fuzzy topological spaces.

Eun-Pyo Lee

Papers

The category of intuitionistic fuzzy topological spaces

FUZZY ${\gamma}$-PREOPEN SETS AND FUZZY ${\gamma}$-PRECONTINUOUS MAPS

Preopen sets in smooth bitopological spaces

(T i , T j )-FUZZY α-(r.s)-SEMIOPEN SETS AND FUZZY PAIRWISE α-(r.s)-SEMICONTINUOUS MAPPINGS

A generalization of a lattice fuzzy topology