Weak and strong forms of fuzzy \(\alpha\)-open (closed) sets and its applications

2018 ◽  
Vol 9 (2) ◽  
Author(s):  
Hakeem Ahmed Ali ◽  
Alanod M. Sibih
Keyword(s):  
Topological Spaces ◽  
Connected Space ◽  
Basic Properties ◽  
Closed Sets ◽  
Continuous Mappings ◽  
New Concepts ◽  
Fuzzy Topological Spaces ◽  
Closed Mappings

In this paper, we generalize the concept of infra-\(\alpha\)-open (closed) and supra-\(\alpha\)-open (closed) sets to fuzzy topological spaces and basic properties of these new concepts have been introduced. Some applications on fuzzy (supra-) infra-\(\alpha\)-open (closed) sets, likely, fuzzy (supra-) infra-\(\alpha\)-continuous mappings, fuzzy (supra-) infra-\(\alpha\)-open (closed) mappings, fuzzy supra-\(\alpha\)- irresolute mapping and fuzzy supra-\(\alpha\)-connected space are introduced. The relations and converse relations between these new concepts and others kinds of fuzzy open sets and fuzzy continuous mappings are discussed. Special results about these new concepts are investigated and studied.

Characterization of Fuzzy δg*-Closed Sets in Fuzzy Topological Spaces

2016 ◽  
Vol 5 (2) ◽  
pp. 1-12
Author(s):  
Anahid Kamali ◽  
Hamid Reza Moradi
Keyword(s):  
Topological Space ◽  
Fuzzy Sets ◽  
Topological Spaces ◽  
Basic Properties ◽  
Closed Sets ◽  
Research Article ◽  
Classical Paper ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The purpose of this research article is to explain the meaning of g-closed sets in fuzzy topological spaces, which is more understandable to the readers and we find some of its basic properties. The concept of fuzzy sets was introduced by Zadeh in his classical paper (1965). Thereafter many investigations have been carried out, in the general theoretical field and also in different applied areas, based on this concept. The idea of fuzzy topological space was introduced by Chang (1968). The idea is more or less a generalization of ordinary topological spaces. Different aspects of such spaces have been developed, by several investigators. This paper is also devoted to the development of the theory of fuzzy topological spaces.

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

GENERALIZED FUZZY Z CLOSED SETS IN DOUBLE FUZZY TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (4) ◽  
pp. 2161-2166
Author(s):  
S. D. Sathaananthan ◽  
A. Vadivel ◽  
S. Tamilselvan ◽  
G. Saravanakumar
Keyword(s):  
Topological Spaces ◽  
Closed Sets ◽  
Fuzzy Topological Spaces

A View on Fuzzy Minimal Open Sets and Fuzzy Maximal Open Sets

2015 ◽  
Vol 7 (1) ◽  
pp. 62-73 ◽  
Author(s):  
Hamid Reza Moradi
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Basic Properties ◽  
New Class ◽  
Properties And Characterization ◽  
Open Set ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Characterization Theorems

A nonzero fuzzy open set () of a fuzzy topological space is said to be fuzzy minimal open (resp. fuzzy maximal open) set if any fuzzy open set which is contained (resp. contains) in is either or itself (resp. either or itself). In this note, a new class of sets called fuzzy minimal open sets and fuzzy maximal open sets in fuzzy topological spaces are introduced and studied which are subclasses of open sets. Some basic properties and characterization theorems are also to be investigated.

Neutrosophic Nano Ideal Topological Structures

2018 ◽  
Author(s):  
Parimala Mani ◽  
Karthika M ◽  
jafari S ◽  
Smarandache F ◽  
Ramalingam Udhayakumar
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Structures ◽  
Basic Properties ◽  
Closed Sets ◽  
Structural Space ◽  
New Type

Neutrosophic nano topology and Nano ideal topological spaces induced the authors to propose this new concept. The aim of this paper is to introduce a new type of structural space called neutrosophic nano ideal topological spaces and investigate the relation between neutrosophic nano topological space and neutrosophic nano ideal topological spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.

scholarly journals Generalizedψρ-Operations on Fuzzy Topological Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
A. M. Zahran ◽  
A. I. El-Maghrabi
Keyword(s):  
Topological Spaces ◽  
Closed Sets ◽  
Fuzzy Topological Spaces

The aim of this work is to introduceψ-operations on fuzzy topological spaces and to use them to study fuzzy generalizedψρ-closed sets and fuzzy generalizedψρ-open sets. Also, we introduce some characterizations and properties for these concepts. Finally we show that certain results of several publications on the concepts of weakness and strength of fuzzy generalized closed sets are considered as corollaries of the results of this research.

scholarly journals Continuity in fuzzy bitopological ordered spaces

2021 ◽  
Vol 40 (3) ◽  
pp. 681-696
Author(s):  
Runu Dhar
Keyword(s):  
Basic Properties ◽  
Properties And Characterization ◽  
Continuous Mappings ◽  
Characterization Theorems ◽  
Closed Mappings

The aim of the present paper is to introduce and study different forms of continuity in fuzzy bitopological ordered spaces. The concepts of different mappings such as pairwise fuzzy I -continuous mappings, pairwise fuzzy D -continuous mappings, pairwise fuzzy B -continuous mappings, pairwise fuzzy I -open mappings, pairwise fuzzy D -open mappings, pairwise fuzzy B -open mappings, pairwise fuzzy I -closed mappings, pairwise fuzzy D -closed mappings and pairwise fuzzy B -closed mappings have been introduced. Some of the basic properties and characterization theorems of these mappings have been investigated.

scholarly journals On induced map f# in fuzzy set theory and its applications to fuzzy continuity

2021 ◽  
Author(s):  
Sandeep Kaur ◽  
Nitakshi Goyal
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Closure Operator ◽  
Topological Spaces ◽  
Continuous Mappings ◽  
New Vision ◽  
Saturated Sets ◽  
Interior Operator ◽  
Fuzzy Topological Spaces

Abstract In this paper, we introduce # image of a fuzzy set which gives a induced map f # corresponding to any function f : X → Y , where X and Y are crisp sets. With this, we present a new vision of studying fuzzy continuous mappings in fuzzy topological spaces where fuzzy continuity explains the term of closeness in the mathematical models. We also define the concept of fuzzy saturated sets which helps us to prove some new characterizations of fuzzy continuous mappings in terms of interior operator rather than closure operator.

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