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Recent Advances on Fuzzy Topology
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Recent Advances on Fuzzy Topology

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: closed (30 November 2024) | Viewed by 7626

Special Issue Editor

Dr. Francisco Gallego Lupiaňez

E-Mail Website
Guest Editor
Department of Mathematics, Universidad Complutense, Ciudad Universitaria, 28040 Madrid, Spain
Interests: topology; covering properties; paracompactness; fuzzy sets; intuitionistic fuzzy sets
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Zadeh's fuzzy sets provide a more accurate representation of reality than the classical mathematical representation based on two-valued logic. Fuzzy sets have been applied in various branches of mathematics, including topology.

This Special Issue will be devoted to original research papers (and well-written reviews) in the field of fuzzy topology. We hope that this Special Issue will be valuable to specialists in this topic.

We invite authors to submit papers that will stimulate the continuing efforts to provide new results on fuzzy topological spaces in the sense of Chang, Lowen, and Michalek. We also welcome papers on intuitionistic fuzzy topological spaces and neutrosophic topological spaces.

Dr. Francisco Gallego Lupiaňez
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • good extensions
  • fuzzy topological spaces
  • intuitionistic fuzzy topological spaces
  • neutrosophic topology.

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (6 papers)

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Research

8 pages, 319 KiB  
Article
Fixed-Point Theorems for Fuzzy Mappings
by Allan Edley Ramos de Andrade and Vinícius Francisco Wasques
Mathematics 2024, 12(14), 2165; https://doi.org/10.3390/math12142165 - 10 Jul 2024
Viewed by 921
Abstract
Since the 1970s and 1980s, significant contributions have been made by Weiss, Butnariu, Heilpern, Chitra, Subrahmanyam, and others, extending fixed-point theorems to fuzzy mappings and topological spaces. This paper provides two generalizations of two important fixed-point theorems, one provided by Butnariu and the [...] Read more.
Since the 1970s and 1980s, significant contributions have been made by Weiss, Butnariu, Heilpern, Chitra, Subrahmanyam, and others, extending fixed-point theorems to fuzzy mappings and topological spaces. This paper provides two generalizations of two important fixed-point theorems, one provided by Butnariu and the other provided by Chitra. The first generalization ensures that, under certain conditions, an acyclic fuzzy mapping has a fixed point. The second result ensures the existence of a point in the intersection of two or more fuzzy mappings considering contractible finite dimensional ANR spaces, which is a generalization of the statement provided by Chitra. Full article
(This article belongs to the Special Issue Recent Advances on Fuzzy Topology)
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15 pages, 326 KiB  
Article
Stronger Forms of Fuzzy Pre-Separation and Regularity Axioms via Fuzzy Topology
by Salem Saleh, Tareq M. Al-shami, A. A. Azzam and M. Hosny
Mathematics 2023, 11(23), 4801; https://doi.org/10.3390/math11234801 - 28 Nov 2023
Cited by 2 | Viewed by 991
Abstract
It is common knowledge that fuzzy topology contributes to developing techniques to address real-life applications in various areas like information systems and optimal choices. The building blocks of fuzzy topology are fuzzy open sets, but other extended families of fuzzy open sets, like [...] Read more.
It is common knowledge that fuzzy topology contributes to developing techniques to address real-life applications in various areas like information systems and optimal choices. The building blocks of fuzzy topology are fuzzy open sets, but other extended families of fuzzy open sets, like fuzzy pre-open sets, can contribute to the growth of fuzzy topology. In the present work, we create some classifications of fuzzy topologies which enable us to obtain several desirable features and relationships. At first, we introduce and analyze stronger forms of fuzzy pre-separation and regularity properties in fuzzy topology called fuzzy pre-Ti,i=0,12,1,2,3,4, fuzzy pre-symmetric, and fuzzy pre-Ri,i=0,1,2,3 by utilizing the concepts of fuzzy pre-open sets and quasi-coincident relation. We investigate more novel properties of these classes and uncover their unique characteristics. By presenting a wide array of related theorems and interconnections, we structure a comprehensive framework for understanding these classes and interrelationships with other separation axioms in this setting. Moreover, the relations between these classes and those in some induced topological structures are examined. Additionally, we explore the hereditary and harmonic properties of these classes. Full article
(This article belongs to the Special Issue Recent Advances on Fuzzy Topology)
15 pages, 811 KiB  
Article
Soft ω-θ-Continuous and Soft Weakly θω-Continuous Mappings
by Samer Al Ghour and Hanan Al-Saadi
Mathematics 2023, 11(19), 4092; https://doi.org/10.3390/math11194092 - 27 Sep 2023
Cited by 3 | Viewed by 805
Abstract
Soft ω-θ-continuity and soft weak-θω-continuity as two new concepts of continuity are presented and investigated. The investigation of the links between these forms of soft mappings and their general topological relatives is given. With the help of [...] Read more.
Soft ω-θ-continuity and soft weak-θω-continuity as two new concepts of continuity are presented and investigated. The investigation of the links between these forms of soft mappings and their general topological relatives is given. With the help of examples, it is investigated that soft ω-θ-continuity lies strictly between soft θ-continuity and soft weak-continuity, while soft weak-θω-continuity lies strictly between soft continuity (i.e., soft θω-continuity) and soft weak-continuity. A number of conditions for the equivalence between soft ω-θ-continuity and soft weak continuity (i.e., soft ω-θ-continuity and soft θ-continuity, soft weak-θω-continuity and soft weak-continuity, soft weak-θω-continuity and soft continuity) are obtained. Additionally, soft θ-closure and soft θω-closure operators are used to characterize our new types of soft mappings. Full article
(This article belongs to the Special Issue Recent Advances on Fuzzy Topology)
17 pages, 336 KiB  
Article
Soft Slight Omega-Continuity and Soft Ultra-Separation Axioms
by Samer Al Ghour and Hanan Al-Saadi
Mathematics 2023, 11(15), 3334; https://doi.org/10.3390/math11153334 - 29 Jul 2023
Cited by 2 | Viewed by 987
Abstract
The notions of continuity and separation axioms have significance in topological spaces. As a result, there has been a substantial amount of research on continuity and separation axioms, leading to the creation of several modifications of these axioms. In this paper, the concepts [...] Read more.
The notions of continuity and separation axioms have significance in topological spaces. As a result, there has been a substantial amount of research on continuity and separation axioms, leading to the creation of several modifications of these axioms. In this paper, the concepts of soft slight ω-continuity, soft ultra-Hausdorff, soft ultra-regular, and soft ultra-normal are initiated and investigated. Their characterizations and main features are determined. Also, the links between them and some other relevant concepts are obtained with the help of examples. Moreover, the equivalency between these notions and other related concepts is given under some necessary conditions. In addition, the inverse image of the introduced types of soft separation axioms under soft slight continuity and soft slight ω-continuity is studied, and their reciprocal relationships with respect to their parametric topological spaces are investigated. Full article
(This article belongs to the Special Issue Recent Advances on Fuzzy Topology)
11 pages, 271 KiB  
Article
A New Approach to Soft Continuity
by Sandeep Kaur, Tareq M. Al-shami, Alkan Özkan and M. Hosny
Mathematics 2023, 11(14), 3164; https://doi.org/10.3390/math11143164 - 19 Jul 2023
Cited by 6 | Viewed by 1059
Abstract
The concept of continuity in topological spaces has a very important place. For this reason, a great deal of work has been done on continuity, and many generalizations of continuity have been obtained. In this work, we seek to find a new approach [...] Read more.
The concept of continuity in topological spaces has a very important place. For this reason, a great deal of work has been done on continuity, and many generalizations of continuity have been obtained. In this work, we seek to find a new approach to the study of soft continuity in soft topological spaces in connection with an induced mapping based on soft sets. By defining the *-image of a soft set, we define an induced soft mapping and present its related properties. To elaborate on the obtained results and relationships, we furnish a number of illustrative examples. Full article
(This article belongs to the Special Issue Recent Advances on Fuzzy Topology)
16 pages, 351 KiB  
Article
A Novel Framework for Generalizations of Soft Open Sets and Its Applications via Soft Topologies
by Tareq M. Al-shami, Abdelwaheb Mhemdi and Radwan Abu-Gdairi
Mathematics 2023, 11(4), 840; https://doi.org/10.3390/math11040840 - 7 Feb 2023
Cited by 31 | Viewed by 1641
Abstract
Soft topological spaces (STSs) have received a lot of attention recently, and numerous soft topological ideas have been created from differing viewpoints. Herein, we put forth a new class of generalizations of soft open sets called “weakly soft semi-open subsets” following an approach [...] Read more.
Soft topological spaces (STSs) have received a lot of attention recently, and numerous soft topological ideas have been created from differing viewpoints. Herein, we put forth a new class of generalizations of soft open sets called “weakly soft semi-open subsets” following an approach inspired by the components of a soft set. This approach opens the door to reformulating the existing soft topological concepts and examining their behaviors. First, we deliberate the main structural properties of this class and detect its relationships with the previous generalizations with the assistance of suitable counterexamples. In addition, we probe some features that are obtained under some specific stipulations and elucidate the properties of the forgoing generalizations that are missing in this class. Next, we initiate the interior and closure operators with respect to the classes of weakly soft semi-open and weakly soft semi-closed subsets and look at some of their fundamental characteristics. Ultimately, we pursue the concept of weakly soft semi-continuity and furnish some of its descriptions. By a counterexample, we elaborate that some characterizations of soft continuous functions are invalid for weakly soft semi-continuous functions. Full article
(This article belongs to the Special Issue Recent Advances on Fuzzy Topology)
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