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Mathematics
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Fuzzy Convex Structures and Some Related Topics
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Fuzzy Convex Structures and Some Related Topics

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 September 2024 | Viewed by 6399

Special Issue Editors

Prof. Dr. Fu-Gui Shi

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China
Interests: fuzzy convex structures; fuzzy topology; fuzzy matroid; fuzzy algebra
Dr. Bin Pang

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China
Interests: fuzzy convex structures; fuzzy topology; fuzzy convergence; fuzzy rough set

Special Issue Information

Dear Colleagues,

Since Zadeh introduced the concept of fuzzy sets, fuzzy set theory has been applied to many research areas, including both of theoretical and applied aspects. In this issue, we will focus on the theory of fuzzy convex structures and its related topics, which combines fuzzy set theory and many theories that are related to convexity theory. From the theoretical aspect, this issue will be referred to fuzzy convex structure, fuzzy topological structure, fuzzy matroid and fuzzy algebra. From the applied aspect, it will concentrate on fuzzy convex optimization, fuzzy game, fuzzy data envelope and fuzzy rough set.

Prof. Dr. Fu-Gui Shi
Dr. Bin Pang
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 convex structures
  • fuzzy topology
  • fuzzy metric
  • fuzzy algebra
  • fuzzy order
  • fuzzy matroid
  • fuzzy game
  • fuzzy graphs
  • fuzzy rough set
  • fuzzy clustering
  • fuzzy data envelope

Published Papers (5 papers)

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Research

20 pages, 324 KiB  
Article
Analysis of Fuzzy Vector Spaces as an Algebraic Framework for Flag Codes
by Carlos Bejines, Manuel Ojeda-Hernández and Domingo López-Rodríguez
Mathematics 2024, 12(3), 498; https://0-doi-org.brum.beds.ac.uk/10.3390/math12030498 - 5 Feb 2024
Viewed by 668
Abstract
Flag codes are a recent network coding strategy based on linear algebra. Fuzzy vector subspaces extend the notions of classical linear algebra. They can be seen as abstractions of flags to the point that several fuzzy vector subspaces can be identified to the [...] Read more.
Flag codes are a recent network coding strategy based on linear algebra. Fuzzy vector subspaces extend the notions of classical linear algebra. They can be seen as abstractions of flags to the point that several fuzzy vector subspaces can be identified to the same flag, which naturally induces an equivalence relation on the set of fuzzy vector subspaces. The main contributions of this work are the methodological abstraction of flags and flag codes in terms of fuzzy vector subspaces, as well as the generalisation of three distinct equivalence relations that originated from the fuzzy subgroup theory and study of their connection with flag codes, computing the number of equivalence classes in the discrete case, which represent the number of essentially distinct flags, and a comprehensive analysis of such relations and the properties of the corresponding quotient sets. Full article
(This article belongs to the Special Issue Fuzzy Convex Structures and Some Related Topics)
20 pages, 378 KiB  
Article
The Metrization Problem in [0,1]-Topology
by Peng Chen
Mathematics 2023, 11(21), 4430; https://0-doi-org.brum.beds.ac.uk/10.3390/math11214430 - 26 Oct 2023
Viewed by 762
Abstract
This paper discusses the classification of fuzzy metrics based on their continuity conditions, dividing them into Erceg, Deng, Shi, and Chen metrics. It explores the relationships between these types of fuzzy metrics, concluding that a Deng metric in [0,1] [...] Read more.
This paper discusses the classification of fuzzy metrics based on their continuity conditions, dividing them into Erceg, Deng, Shi, and Chen metrics. It explores the relationships between these types of fuzzy metrics, concluding that a Deng metric in [0,1]-topology must also be Erceg, Chen, and Shi metrics. This paper also proves that the product of countably many Deng pseudo-metric spaces remains a Deng pseudo-metric space, and demonstrates some σ-locally finite properties of Deng metric space. Additionally, this paper constructs two interrelated mappings based on normal space and concludes that, if a [0,1]-topological space is T1 and regular, and its topology has a σ-locally finite base, then it is Deng-metrizable, and thus Erceg-, Shi-, and Chen-metrizable as well. Full article
(This article belongs to the Special Issue Fuzzy Convex Structures and Some Related Topics)
15 pages, 302 KiB  
Article
L-Quasi (Pseudo)-Metric in L-Fuzzy Set Theory
by Peng Chen, Bin Meng and Xiaohui Ba
Mathematics 2023, 11(14), 3152; https://0-doi-org.brum.beds.ac.uk/10.3390/math11143152 - 18 Jul 2023
Cited by 1 | Viewed by 693
Abstract
The aim of this paper is to focus on the metrization question in L-fuzzy sets. Firstly, we put forward an L-quasi (pseudo)-metric on the completely distributive lattice LX by comparing some existing lattice-valued metrics with the classical metric and show [...] Read more.
The aim of this paper is to focus on the metrization question in L-fuzzy sets. Firstly, we put forward an L-quasi (pseudo)-metric on the completely distributive lattice LX by comparing some existing lattice-valued metrics with the classical metric and show a series of its related properties. Secondly, we present two topologies: ψp and ζp, generated by an L-quasi-metric p with different spherical mappings, and prove ψp=ζp′ if p is further an L-pseudo-metric on LX. Thirdly, we characterize an equivalent form of L-pseudo-metric in terms of a class of mapping clusters and acquire several satisfactory results. Finally, based on this kind of L-metric, we assert that, on LX, a Yang–Shi metric topology is Q−CI, but an Erceg metric topology is not always so. Full article
(This article belongs to the Special Issue Fuzzy Convex Structures and Some Related Topics)
18 pages, 572 KiB  
Article
The Research on Consistency Checking and Improvement of Probabilistic Linguistic Preference Relation Based on Similarity Measure and Minimum Adjustment Model
by Huimin Xiao, Shouwen Wu and Chunsheng Cui
Mathematics 2022, 10(9), 1369; https://0-doi-org.brum.beds.ac.uk/10.3390/math10091369 - 20 Apr 2022
Cited by 5 | Viewed by 1490
Abstract
In the process of decision making, the probabilistic linguistic term set (PLTS) is a useful tool to express the evaluation information provided by decision makers (DMs). On the basis of PLTS, the probabilistic linguistic preference relation (PLPR) has been proposed, which can well [...] Read more.
In the process of decision making, the probabilistic linguistic term set (PLTS) is a useful tool to express the evaluation information provided by decision makers (DMs). On the basis of PLTS, the probabilistic linguistic preference relation (PLPR) has been proposed, which can well describe the uncertainty of preferences when experts conduct pairwise comparison between any two alternatives. The consistency analysis is an essential process to check whether the preferences are reasonable and logical. For the consistency checking and improvement of PLPR, some methods have been developed to conduct the work. However, the previous methods seldom consider whether the information of original preferences is distorted after the adjustment of inconsistency preferences, and the adjustment processes are complicated in much of the literature. To overcome the defects of existing methods, we developed a novel PLPR consistency analysis model, and this paper mainly contains two sections. On the one hand, a new consistency index and the consistency checking method are proposed based on similarity measure, respectively. On the other hand, based on the idea of minimum adjustment, we constructed an optimization model to improve the consistency level and develop the process of decision making on the basis of consistency analysis. A numerical example about talent recruitment is given to verify the feasibility of the proposed method. We have a comparative analysis with Zhang’s method from many aspects including the decision results, consistency checking and improvement, as well as adjusted preferences, adjustment costs and consistence threshold. At length, the conclusion of this research is that the proposed consistency analysis model is superior to the previous method on the determination of adjustment parameter, as well as the adjustment cost and the retention of original preferences. To show the effectiveness and superiority, we have a comparative analysis with other approaches. At length, the conclusion of this study is drawn. Full article
(This article belongs to the Special Issue Fuzzy Convex Structures and Some Related Topics)
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17 pages, 987 KiB  
Article
(L,M)-Fuzzy k-Pseudo Metric Space
by Yu Zhong, Xin Wu, Alexander Šostak and Fu-Gui Shi
Mathematics 2022, 10(7), 1151; https://0-doi-org.brum.beds.ac.uk/10.3390/math10071151 - 2 Apr 2022
Cited by 1 | Viewed by 1471
Abstract
Recently, the notion of a classical k-metric, which make the triangle inequality to a more general axiom: d(x,z)≤k(d(x,y)+d(y,z)), has [...] Read more.
Recently, the notion of a classical k-metric, which make the triangle inequality to a more general axiom: d(x,z)≤k(d(x,y)+d(y,z)), has been presented and is applied in many fields. In this paper, the definitions of an (L,M)-fuzzy k-pseudo metric and an (L,M)-fuzzy k-remote neighborhood ball system are introduced. It is proved that the category of (L,M)-fuzzy k-pseudo metric spaces is isomorphic to the category of (L,M)-fuzzy k-remote neighborhood ball spaces. Besides, (L,M)-fuzzy topological structures induced by an (L,M)-fuzzy k-pseudo metric are presented and their properties are investigated. Finally, the concept of a nest of pointwise k-pseudo metrics is proposed and it is shown that there is a one-to-one correspondence between (L,M)-fuzzy k-pseudo metrics and nests of pointwise k-pseudo metrics. Full article
(This article belongs to the Special Issue Fuzzy Convex Structures and Some Related Topics)
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