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Symmetry
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Advances in Fuzzy Convexity Theory and Its Related Topics
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Advances in Fuzzy Convexity Theory and Its Related Topics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 2987

Special Issue Editor

Dr. Bin Pang

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
Interests: fuzzy convex structure; fuzzy topology; fuzzy rough set
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Convexity is a very important mathematical property, and it exists in many research areas, such as vector space, metric space, and partially ordered sets. By abstracting the common properties of convex sets, the notion of convex structures was proposed. Since Zadeh introduced the concept of fuzzy sets, fuzzy set theory has been applied to many research areas, including both theoretical and applied aspects. In this Special Issue, we will concentrate on the advances in fuzzy convex structures and related topics, combining fuzzy set theory and many theories related to convexity theory. From the theoretical aspect, this Issue will refer to fuzzy convex structure, fuzzy convex algebra, fuzzy topology and fuzzy metric. From the applied aspect, it will concentrate on fuzzy convex optimization, fuzzy data envelope and fuzzy rough set.

Dr. Bin Pang
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. Symmetry is an international peer-reviewed open access monthly 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 2400 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 convex structure
  • fuzzy algebra
  • fuzzy topology
  • fuzzy metric
  • fuzzy rough set
  • fuzzy convex optimization

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Published Papers (3 papers)

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Research

25 pages, 1508 KiB  
Article
Intuitionistic Fuzzy Rough Aczel-Alsina Average Aggregation Operators and Their Applications in Medical Diagnoses
by Jabbar Ahmmad, Tahir Mahmood, Nayyar Mehmood, Khamika Urawong and Ronnason Chinram
Symmetry 2022, 14(12), 2537; https://doi.org/10.3390/sym14122537 - 30 Nov 2022
Cited by 24 | Viewed by 1531
Abstract
Managing ambiguous and asymmetric types of information is a very challenging task under the consideration of classical data. Furthermore, Aczel-Alsina aggregation operators are the new developments in fuzzy sets theory. However, when decision-makers need to use these structures in fuzzy rough structures, these [...] Read more.
Managing ambiguous and asymmetric types of information is a very challenging task under the consideration of classical data. Furthermore, Aczel-Alsina aggregation operators are the new developments in fuzzy sets theory. However, when decision-makers need to use these structures in fuzzy rough structures, these operators fail to deal with such types of values, as fuzzy rough structures use lower and upper approximation spaces. Thus, an encasement of an intuitionistic fuzzy set has a chance of data loss, whereas an intuitionistic fuzzy rough set can resolve the problem of data loss. Motivated by the notion of intuitionistic fuzzy rough sets and new aggregation operators i.e., intuitionistic fuzzy Aczel-Alsina operators, this paper firstly initiates some basic Aczel-Alsina operational rules for intuitionistic fuzzy rough numbers. Secondly, based on these newly defined operational rules, we have developed some new aggregation operators, such as intuitionistic fuzzy rough Aczel-Alsina weighted average (IFRAAWA), intuitionistic fuzzy rough Aczel-Alsina ordered weighted average (IFRAAOWA), and intuitionistic fuzzy rough Aczel-Alsina hybrid average (IFRAAHA) aggregation operators. Moreover, the properties of these aggregation operators have been initiated. These operators can help in evaluating awkward and asymmetric information in real-life problems. The use of aggregation operators in medical diagnosis and MADM is an efficient method that can help in healthcare and decision-making applications. To present an effective use of these developed operators in medical diagnosis and the selection of the best next-generation firewall, we have established an algorithm along with a numerical example to provide authenticity and clarity to the established work. Furthermore, a comparative analysis of the introduced work shows the superiority of the introduced approach. Full article
(This article belongs to the Special Issue Advances in Fuzzy Convexity Theory and Its Related Topics)
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22 pages, 346 KiB  
Article
Intuitionistic Fuzzy Topology Based on Intuitionistic Fuzzy Logic
by Osama R. Sayed, Ayman A. Aly and Shaoyu Zhang
Symmetry 2022, 14(8), 1613; https://doi.org/10.3390/sym14081613 - 5 Aug 2022
Cited by 1 | Viewed by 1493
Abstract
There are many symmetries in intuitionistic fuzzifying topology. In the present paper, the notion of intuitionistic fuzzifying topology as an extension of fuzzifying topology and a preliminary of the research on bi-intuitionistic fuzzy topology is introduced. A theory of intuitionistic fuzzy topology with [...] Read more.
There are many symmetries in intuitionistic fuzzifying topology. In the present paper, the notion of intuitionistic fuzzifying topology as an extension of fuzzifying topology and a preliminary of the research on bi-intuitionistic fuzzy topology is introduced. A theory of intuitionistic fuzzy topology with the semantic method of intuitionistic fuzzy logic is established. Full article
(This article belongs to the Special Issue Advances in Fuzzy Convexity Theory and Its Related Topics)
13 pages, 283 KiB  
Article
A Novel Approach to the Fuzzification of Fields
by Mingyi Zeng, Lan Wang and Fu-Gui Shi
Symmetry 2022, 14(6), 1190; https://doi.org/10.3390/sym14061190 - 9 Jun 2022
Cited by 1 | Viewed by 1359
Abstract
There are many symmetries in L-fuzzy algebras. In this paper, a novel approach to the fuzzification of a field is introduced. We define a mapping F:LX→L from the family of all the L-fuzzy sets on a [...] Read more.
There are many symmetries in L-fuzzy algebras. In this paper, a novel approach to the fuzzification of a field is introduced. We define a mapping F:LX→L from the family of all the L-fuzzy sets on a field X to L such that each L-fuzzy set is an L-fuzzy subfield to some extent. Some equivalent characterizations F(μ) are given by means of cut sets. It is proved that F is L-fuzzy convex structure on X, hence (X,F) forms an L-fuzzy convexity space. A homomorphism between fields is exactly an L-fuzzy convexity preserving mapping and an L-fuzzy convex-to-convex mapping. Finally, we discuss some operations of L-fuzzy subsets. Full article
(This article belongs to the Special Issue Advances in Fuzzy Convexity Theory and Its Related Topics)
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