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Mathematics
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Novel Approaches in Fuzzy Sets and Metric Spaces
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Novel Approaches in Fuzzy Sets and Metric Spaces

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: 30 November 2024 | Viewed by 3632

Special Issue Editors

Prof. Dr. Vishal Gupta

E-Mail Website
Guest Editor
Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana 133207, Haryana, India
Interests: fuzzy set theory; fuzzy mappings; fixed point theory; topology; differential and integral equations
Dr. Pooja Dhawan

E-Mail Website
Guest Editor
Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana 133207, Haryana, India
Interests: fuzzy set theory; fuzzy mappings; fixed point theory; topology; differential and integral equations

Special Issue Information

Dear Colleagues,

The Special Issue aims to cumulate novel advancements in the field of fuzzy sets and related metric spaces. The concept of fuzzy set theory was originally introduced by Zadeh (1965) and it has been developed by a huge circle of researchers over the last two decades. This theory has turned out to be one of the most efficient decision aid techniques providing the ability to deal with uncertainty and vagueness. Till today, several papers are published in prominent journals along with various fuzzy set applications in the fields of mathematics, decision making, information technology, automatic control and artificial intelligence and much more because of its flexibility and tolerance in dealing with imprecise data.

The purpose of this Special Issue is to further investigate modern trends of fuzzy metric spaces in new frontiers that promote a comprehensive and state-of-the-art understanding of fuzzy metric theory-based extensions and relevant applications.

Prof. Dr. Vishal Gupta
Dr. Pooja Dhawan
Guest Editors

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

  • fuzzy set
  • fuzzy mappings
  • fuzzy metric space
  • metric space
  • contractions

Published Papers (4 papers)

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Research

11 pages, 251 KiB  
Article
Fixed Point Results in Modified Intuitionistic Fuzzy Soft Metric Spaces with Application
by Vishal Gupta, Aanchal Gondhi and Rahul Shukla
Mathematics 2024, 12(8), 1154; https://doi.org/10.3390/math12081154 - 11 Apr 2024
Viewed by 352
Abstract
This paper establishes a new type of space, modified intuitionistic fuzzy soft metric space (MIFSMS). Basic properties and topological structures are defined in the setting of this new notion with valid examples. Moreover, we have given some new results along with suitable examples [...] Read more.
This paper establishes a new type of space, modified intuitionistic fuzzy soft metric space (MIFSMS). Basic properties and topological structures are defined in the setting of this new notion with valid examples. Moreover, we have given some new results along with suitable examples to show their validity. An application for finding the solution of an integral equation is also given by utilizing our newly developed results. Full article
(This article belongs to the Special Issue Novel Approaches in Fuzzy Sets and Metric Spaces)
16 pages, 3274 KiB  
Article
Metric Relations in the Fuzzy Right Triangle
by Ronald Manríquez
Mathematics 2023, 11(19), 4056; https://doi.org/10.3390/math11194056 - 25 Sep 2023
Viewed by 593
Abstract
The study of fuzzy geometry and its different components has grown in recent years, establishing the formal foundations for its development. This paper is devoted to addressing some metric relations in the fuzzy right triangle; in particular, a version of the Pythagorean theorem [...] Read more.
The study of fuzzy geometry and its different components has grown in recent years, establishing the formal foundations for its development. This paper is devoted to addressing some metric relations in the fuzzy right triangle; in particular, a version of the Pythagorean theorem and geometric mean theorem are provided in analytical fuzzy geometry. The main results show, under certain conditions of the fuzzy vertices, a subset relation between the fuzzy distances associated with the fuzzy right triangle, which is very similar to the classical statements of the Pythagorean theorem and the geometric mean in Euclidean geometry. Full article
(This article belongs to the Special Issue Novel Approaches in Fuzzy Sets and Metric Spaces)
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15 pages, 434 KiB  
Article
Intuitionistic Fuzzy Metric-like Spaces and Fixed-Point Results
by Şuara Onbaşıoğlu and Banu Pazar Varol
Mathematics 2023, 11(8), 1902; https://doi.org/10.3390/math11081902 - 17 Apr 2023
Cited by 1 | Viewed by 1371
Abstract
The objective of this paper is to describe the concept of intuitionistic fuzzy metric-like spaces. This space is an extension of metric-like spaces and fuzzy metric spaces, and intuitionistic fuzzy metric spaces. We discuss convergence sequences, contractive mapping and some fixed-point theorems in [...] Read more.
The objective of this paper is to describe the concept of intuitionistic fuzzy metric-like spaces. This space is an extension of metric-like spaces and fuzzy metric spaces, and intuitionistic fuzzy metric spaces. We discuss convergence sequences, contractive mapping and some fixed-point theorems in intuitionistic fuzzy metric-like space. We also give explanations, examples and counterexamples to validate the superiority of these results. Our results provide a substantial extension of several important results from fuzzy metric-like spaces. Full article
(This article belongs to the Special Issue Novel Approaches in Fuzzy Sets and Metric Spaces)
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17 pages, 325 KiB  
Article
An Infinite System of Fractional Sturm–Liouville Operator with Measure of Noncompactness Technique in Banach Space
by Ahmed Salem, Hunida Malaikah and Eid Sayed Kamel
Mathematics 2023, 11(6), 1444; https://doi.org/10.3390/math11061444 - 16 Mar 2023
Cited by 1 | Viewed by 794
Abstract
In the current contribution, an appropriate quantity connected to the space of all convergent sequences is provided and shown to be a measure of noncompactness in a Banach space. Through the application of the fixed point theorems of Darbo and Meir–Keeler, this amount [...] Read more.
In the current contribution, an appropriate quantity connected to the space of all convergent sequences is provided and shown to be a measure of noncompactness in a Banach space. Through the application of the fixed point theorems of Darbo and Meir–Keeler, this amount is used to discuss whether a solution to an infinite system of fractional Sturm–Liouville operators exists. We offer a numerical example as an application of the key finding in the study. Full article
(This article belongs to the Special Issue Novel Approaches in Fuzzy Sets and Metric Spaces)
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