Compactness in L-fuzzy topological spaces; countability in L-fuzzy topology fuzzy sets and systems 67 (1994) 329–336; 71 (1995)241–249

1996 ◽  
Vol 84 (1) ◽  
pp. 117 ◽  
Author(s):  
S.R.T. Kudri
Keyword(s):  
Fuzzy Sets ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Fuzzy Topological Spaces

Suitable interval-valued intuitionistic fuzzy topological spaces

2021 ◽  
pp. 1-11
Author(s):  
O.R. Sayed ◽  
N.H. Sayed ◽  
Gui-Xiu Chen
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Set Operations ◽  
The Family ◽  
Fuzzy Topological Spaces ◽  
Interval Valued

In the present paper, a characterization of the intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy sets and their set-operations are given. By making use of these characterizations, the relationships between the interval-valued intuitionistic fuzzy topology and four fuzzy topologies associated to it are studied. For this reason, some subclasses of the family of interval-valued intuitionistic fuzzy topologies on a set which we call pre-suitable and suitable are introduced. Furthermore, the concepts of homeomorphism functions and compactness in the framework of interval-valued intuitionistic fuzzy topological spaces are introduced and studied.

On Multi-Fuzzy Rough Sets, Relations, and Topology

2019 ◽  
Vol 8 (1) ◽  
pp. 101-119
Author(s):  
Gayathri Varma ◽  
Sunil Jacob John
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Primitive Concept ◽  
Closed Sets ◽  
Fuzzy Topological Spaces

This article describes how rough set theory has an innate topological structure characterized by the partitions. The approximation operators in rough set theory can be viewed as the topological operators namely interior and closure operators. Thus, topology plays a role in the theory of rough sets. This article makes an effort towards considering closed sets a primitive concept in defining multi-fuzzy topological spaces. It discusses the characterization of multi-fuzzy topology using closed multi-fuzzy sets. A set of axioms is proposed that characterizes the closure and interior of multi-fuzzy sets. It is proved that the set of all lower approximation of multi-fuzzy sets under a reflexive and transitive multi-fuzzy relation forms a multi-fuzzy topology.

scholarly journals A Tychonoff theorem in intuitionistic fuzzy topological spaces

2004 ◽  
Vol 2004 (70) ◽  
pp. 3829-3837
Author(s):  
Doğan Çoker ◽  
A. Haydar Eş ◽  
Necla Turanli
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Tychonoff Theorem

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.

Almost compact fuzzy sets in fuzzy topological spaces

1990 ◽  
Vol 38 (3) ◽  
pp. 389-396 ◽  
Author(s):  
M.N. Mukherjee ◽  
S.P. Sinha
Keyword(s):  
Fuzzy Sets ◽  
Topological Spaces ◽  
Fuzzy Topological Spaces

Intuitionistic Fuzzy γ-Continuity

2009 ◽  
Vol 52 (4) ◽  
pp. 544-554 ◽  
Author(s):  
I. M. Hanafy
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Topological Spaces ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Spaces

AbstractThis paper introduces the concepts of fuzzy γ-open sets and fuzzy γ-continuity in intuitionistic fuzzy topological spaces. After defining the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy γ-open sets and intuitionistic fuzzy γ-continuity and other results related topological concepts.

scholarly journals A Study of Frontier and Semifrontier in Intuitionistic Fuzzy Topological Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Athar Kharal
Keyword(s):  
Open Problem ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Classical Form ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Spaces

Notions of frontier and semifrontier in intuitionistic fuzzy topology have been studied and several of their properties, characterizations, and examples established. Many counter-examples have been presented to point divergences between the IF topology and its classical form. The paper also presents an open problem and one of its weaker forms.

scholarly journals Fuzzyθ-closure operator on fuzzy topological spaces

1991 ◽  
Vol 14 (2) ◽  
pp. 309-314 ◽  
Author(s):  
M. N. Mukherjee ◽  
S. P. Sinha
Keyword(s):  
Topological Space ◽  
Fuzzy Sets ◽  
Closure Operator ◽  
Topological Spaces ◽  
Separation Axioms ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The paper contains a study of fuzzyθ-closure operator,θ-closures of fuzzy sets in a fuzzy topological space are characterized and some of their properties along with their relation with fuzzyδ-closures are investigated. As applications of these concepts, certain functions as well as some spaces satisfying certain fuzzy separation axioms are characterized in terms of fuzzyθ-closures andδ-closures.

scholarly journals Fuzzy Inverse Compactness

2008 ◽  
Vol 2008 ◽  
pp. 1-9
Author(s):  
Halis Aygün ◽  
A. Arzu Bural ◽  
S. R. T. Kudri
Keyword(s):  
Fuzzy Sets ◽  
Topological Spaces ◽  
Countable Compactness ◽  
Fuzzy Topological Spaces

We introduce definitions of fuzzy inverse compactness, fuzzy inverse countable compactness, and fuzzy inverse Lindelöfness on arbitrary -fuzzy sets in -fuzzy topological spaces. We prove that the proposed definitions are good extensions of the corresponding concepts in ordinary topology and obtain different characterizations of fuzzy inverse compactness.

scholarly journals Weakly induced modifications ofI-fuzzy topologies

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Yueli Yue ◽  
Jinming Fang
Keyword(s):  
Full Subcategory ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Fuzzy Topological Spaces

The aim of this paper is to study weakly inducedI-fuzzy topological spaces and weakly induced modifications ofI-fuzzy topologies. We give two kinds of weakly inducedI-fuzzy topologies for eachI-fuzzy topology and prove thatI-WIFTOP is a reflective and coreflective full subcategory ofI-FTOP. We also discuss some relationships between several categories.

scholarly journals Separation Axioms in Mixed Fuzzy Topological Spaces

1970 ◽  
Vol 32 (2) ◽  
Author(s):  
MH Rashid ◽  
DM Ali
Keyword(s):  
Fuzzy Set ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Separation Axioms ◽  
Fuzzy Topological Spaces ◽  
Academy Of Sciences

We deal with fuzzy topology. In this paper, we introduce the concept of mixed fuzzy topology which is constructed from two fuzzy topologies on the same fuzzy set X and study several features of this mixed fuzzy topology. Keywords: Fuzzy Topological Spaces, Mixed fuzzy topology doi: 10.3329/jbas.v32i2.2433 Journal of Bangladesh Academy of Sciences Vol.32(2) 2008 142-150

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