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 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.

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 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

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.

scholarly journals Measurement of Countable Compactness and Lindelöf Property in RL -Fuzzy Topological Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiongwei Zhang ◽  
Ibtesam Alshammari ◽  
A. Ghareeb
Keyword(s):  
Distributive Lattice ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Implication Operator ◽  
Completely Distributive ◽  
Countable Compactness ◽  
Definition Of ◽  
Fuzzy Topological Spaces ◽  
Completely Distributive Lattice ◽  
Special Case

Based on the concepts of pseudocomplement of L -subsets and the implication operator where L is a completely distributive lattice with order-reversing involution, the definition of countable RL -fuzzy compactness degree and the Lindelöf property degree of an L -subset in RL -fuzzy topology are introduced and characterized. Since L -fuzzy topology in the sense of Kubiak and Šostak is a special case of RL -fuzzy topology, the degrees of RL -fuzzy compactness and the Lindelöf property are generalizations of the corresponding degrees in L -fuzzy topology.

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 MIXED SEMI-PRE FUZZY TOPOLOGICAL SPACES

2019 ◽  
pp. 5-10
Author(s):  
Diganta Jyoti Sarma ◽  
Binod Chandra Tripathy
Keyword(s):  
Topological Spaces ◽  
Fuzzy Topology ◽  
Fuzzy Point ◽  
Fuzzy Topological Spaces

In this article we construct a fuzzy topology on a non-empty set X called mixed semi-pre fuzzy topology from two given fuzzy topological spaces on X with the help of fuzzy semi-prequasi-neighborhood of a fuzzy point.

scholarly journals More on Fuzzy Topological Spaces on Fuzzy Space

2021 ◽  
Vol 8 ◽  
pp. 21-26
Author(s):  
Abd Ulazeez Alkouri ◽  
Mohammad Hazaimeh ◽  
Ibrahim Jawarneh
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Separation Axioms ◽  
Fuzzy Space ◽  
Different Types ◽  
Fuzzy Topological Space ◽  
Isolated Points ◽  
Fuzzy Topological Spaces ◽  
Fuzzy Subsets

The fuzzy topological space was introduced by Dip in 1999 depending on the notion of fuzzy spaces. Dip’s approach helps to rectify the deviation in some definitions of fuzzy subsets in fuzzy topological spaces. In this paper, further definitions, and theorems on fuzzy topological space fill the lack in Dip’s article. Different types of fuzzy topological space on fuzzy space are presented such as co-finite, co-countable, right and left ray, and usual fuzzy topology. Furthermore, boundary, exterior, and isolated points of fuzzy sets are investigated and illustrated based on fuzzy spaces. Finally, separation axioms are studied on fuzzy spaces

scholarly journals Connectedness concept in intuitionistic fuzzy topological spaces

2021 ◽  
Vol 27 (1) ◽  
pp. 72-82
Author(s):  
Md. Aman Mahbub ◽  
◽  
Md. Sahadat Hossain ◽  
M. Altab Hossain ◽  
◽  
...  
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The purpose of this paper is to establish the connectedness in intuitionistic fuzzy topological space. In this paper we give six notions of separatedness, connectedness and total connectedness and one notion of T1-space in intuitionistic fuzzy topological space. Also, we find a relation between classical topology and intuitionistic fuzzy topology. Further, we show that connectedness in intuitionistic fuzzy topological spaces are productive and we demonstrate some of its features.

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