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Mathematics
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Fuzzy Topology
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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 (31 October 2022) | Viewed by 16622

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 better 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 of use 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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Published Papers (7 papers)

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Research

10 pages, 209 KiB  
Article
Intuitionistic Fuzzy Modal Topological Structure
by Krassimir Atanassov
Mathematics 2022, 10(18), 3313; https://doi.org/10.3390/math10183313 - 13 Sep 2022
Cited by 14 | Viewed by 1406
Abstract
The concept of an Intuitionistic Fuzzy Modal Topological Structure (IFMTS) or for brevity, Intuitionistic Fuzzy Modal Topology (IFMT), is introduced. It is proved that the two standard intuitionistic fuzzy topological operators C and I, and the two standard intuitionistic fuzzy modal operators [...] Read more.
The concept of an Intuitionistic Fuzzy Modal Topological Structure (IFMTS) or for brevity, Intuitionistic Fuzzy Modal Topology (IFMT), is introduced. It is proved that the two standard intuitionistic fuzzy topological operators C and I, and the two standard intuitionistic fuzzy modal operators ☐ and ♢ generate two different IFMTs. Some basic properties of both IFMTs are discussed. Some important properties of the intuitionistic fuzzy modal and topological operators are discussed. These properties will be a basis of next research on the IFMTSs. Ideas for future development of the IFMT theory are formulated. Full article
(This article belongs to the Special Issue Fuzzy Topology)
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3 pages, 254 KiB  
Article
On Fuzzy C-Paracompact Topological Spaces
by Francisco Gallego Lupiáñez
Mathematics 2022, 10(9), 1478; https://doi.org/10.3390/math10091478 - 28 Apr 2022
Viewed by 1378
Abstract
The aim of this paper is to study fuzzy extensions of some covering properties defined by A. V. Arhangel’skii and studied by other authors. Indeed, in 2016, A. V. Arhangel’skii defined other paracompact-type properties: C-paracompactness and C2-paracompactness. Later, M. M. Saeed, [...] Read more.
The aim of this paper is to study fuzzy extensions of some covering properties defined by A. V. Arhangel’skii and studied by other authors. Indeed, in 2016, A. V. Arhangel’skii defined other paracompact-type properties: C-paracompactness and C2-paracompactness. Later, M. M. Saeed, L. Kalantan and H. Alzumi investigated these two properties. In this paper, we define fuzzy extensions of these notions and obtain results about them, and in particular, prove that these are good extensions of those defined by Arhangel’skii. Full article
(This article belongs to the Special Issue Fuzzy Topology)
12 pages, 766 KiB  
Article
Soft Semi ω-Open Sets
by Samer Al Ghour
Mathematics 2021, 9(24), 3168; https://doi.org/10.3390/math9243168 - 9 Dec 2021
Cited by 5 | Viewed by 2388
Abstract
In this paper, we introduce the class of soft semi ω-open sets of a soft topological space (X,τ,A), using soft ω-open sets. We show that the class of soft semi ω-open sets contains [...] Read more.
In this paper, we introduce the class of soft semi ω-open sets of a soft topological space (X,τ,A), using soft ω-open sets. We show that the class of soft semi ω-open sets contains both the soft topology τω and the class of soft semi-open sets. Additionally, we define soft semi ω-closed sets as the class of soft complements of soft semi ω-open sets. We present here a study of the properties of soft semi ω-open sets, especially in (X,τ,A) and (X,τω,A). In particular, we prove that the class of soft semi ω-open sets is closed under arbitrary soft union but not closed under finite soft intersections; we also study the correspondence between the soft topology of soft semi ω-open sets of a soft topological space and their generated topological spaces and vice versa. In addition to these, we introduce the soft semi ω-interior and soft semi ω-closure operators via soft semi ω-open and soft semi ω-closed sets. We prove several equations regarding these two new soft operators. In particular, we prove that these operators can be calculated using other usual soft operators in both of (X,τ,A) and (X,τω,A), and some equations focus on soft anti-locally countable soft topological spaces. Full article
(This article belongs to the Special Issue Fuzzy Topology)
11 pages, 277 KiB  
Article
Soft ωp-Open Sets and Soft ωp-Continuity in Soft Topological Spaces
by Samer Al Ghour
Mathematics 2021, 9(20), 2632; https://doi.org/10.3390/math9202632 - 19 Oct 2021
Cited by 15 | Viewed by 1869
Abstract
We define soft ωp-openness as a strong form of soft pre-openness. We prove that the class of soft ωp-open sets is closed under soft union and do not form a soft topology, in general. We prove that soft [...] Read more.
We define soft ωp-openness as a strong form of soft pre-openness. We prove that the class of soft ωp-open sets is closed under soft union and do not form a soft topology, in general. We prove that soft ωp-open sets which are countable are soft open sets, and we prove that soft pre-open sets which are soft ω-open sets are soft ωp-open sets. In addition, we give a decomposition of soft ωp-open sets in terms of soft open sets and soft ω-dense sets. Moreover, we study the correspondence between the soft topology soft ωp-open sets in a soft topological space and its generated topological spaces, and vice versa. In addition to these, we define soft ωp-continuous functions as a new class of soft mappings which lies strictly between the classes of soft continuous functions and soft pre-continuous functions. We introduce several characterizations for soft pre-continuity and soft ωp-continuity. Finally, we study several relationships related to soft ωp-continuity. Full article
(This article belongs to the Special Issue Fuzzy Topology)
14 pages, 305 KiB  
Article
Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts
by Samer Al Ghour
Mathematics 2021, 9(15), 1781; https://doi.org/10.3390/math9151781 - 28 Jul 2021
Cited by 8 | Viewed by 1633
Abstract
In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give [...] Read more.
In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give several sufficient conditions for the equivalence between soft p-open sets and each of the soft u-open sets and soft s-open sets, respectively. In addition to these, we introduce the soft u-ω-open, soft p-ω-open, and soft s-ω-open sets as three new classes of soft sets in soft bitopological spaces, which contain soft u-open sets, soft p-open sets, and soft s-open sets, respectively. Via soft u-open sets, we define two notions of Lindelöfeness in SBTSs. We discuss the relationship between these two notions, and we characterize them via other types of soft sets. We define several types of soft local countability in soft bitopological spaces. We discuss relationships between them, and via some of them, we give two results related to the discrete soft topological space. According to our new concepts, the study deals with the correspondence between soft bitopological spaces and their generated bitopological spaces. Full article
(This article belongs to the Special Issue Fuzzy Topology)
13 pages, 803 KiB  
Article
Connectedness and Local Connectedness on Infra Soft Topological Spaces
by Tareq M. Al-shami and El-Sayed A. Abo-Tabl
Mathematics 2021, 9(15), 1759; https://doi.org/10.3390/math9151759 - 26 Jul 2021
Cited by 20 | Viewed by 2315
Abstract
This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We [...] Read more.
This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We provide some descriptions for infra soft connectedness and elucidate that there is no relationship between an infra soft topological space and its parametric infra topological spaces with respect to the property of infra soft connectedness. We discuss the behaviors of infra soft connected and infra soft locally connected spaces under infra soft homeomorphism maps and a finite product of soft spaces. We complete this manuscript by defining a component of a soft point and establishing its main properties. We determine the conditions under which the number of components is finite or countable, and we discuss under what conditions the infra soft connected subsets are components. Full article
(This article belongs to the Special Issue Fuzzy Topology)
12 pages, 334 KiB  
Article
An Operational Characterization of Soft Topologies by Crisp Topologies
by José Carlos R. Alcantud
Mathematics 2021, 9(14), 1656; https://doi.org/10.3390/math9141656 - 14 Jul 2021
Cited by 19 | Viewed by 3238
Abstract
This paper contributes to the expanding literature on soft topology. We first prove that soft topologies can be characterized by crisp topologies. This takes advantage of two connected constructions that produce soft topologies from crisp topologies and vice versa. Both constructions are explicit [...] Read more.
This paper contributes to the expanding literature on soft topology. We first prove that soft topologies can be characterized by crisp topologies. This takes advantage of two connected constructions that produce soft topologies from crisp topologies and vice versa. Both constructions are explicit and amenable to mathematical manipulations. Various consequences demonstrate that our theory has far-reaching implications for the development of soft topology and its extensions. Full article
(This article belongs to the Special Issue Fuzzy Topology)
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