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Axioms
Special Issues
Fuzzy Set Theory and Applications
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Fuzzy Set Theory and Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Logic".

Deadline for manuscript submissions: closed (31 May 2020) | Viewed by 13080

Special Issue Editors

Prof. Dr. Radko Mesiar

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, Radlinskeho 11, 81005 Bratislava, Slovakia
Interests: non-additive measure and integral theory; uncertainty modelling; fuzzy sets and fuzzy logic; multicriteria decision support; copulas; triangular norms; aggregation operators and related operators; intelligent computing
Special Issues, Collections and Topics in MDPI journals
Dr. Martin Štěpnička

E-Mail Website
Guest Editor
1. Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 701 03 Ostrava, Czech Republic
2. IT4Innovations National Supercomputing Center, Technical University of Ostrava, 708 00 Ostrava, Czech Republic
Interests: fuzzy modeling; fuzzy rules; fuzzy inference systems; fuzzy relations; fuzzy relational equations
Special Issues, Collections and Topics in MDPI journals
Dr. Martin Papčo

E-Mail Website
Guest Editor
1. Catholic University in Ružomberok, Hrabovská cesta 1, 034 01 Ružomberok, Slovak Republic
2. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovak Republic
Interests: uncertainty modeling; categorical aspects of fuzzy set theory; probabilistic topics related to fuzzy set theory

Special Issue Information

Dear Colleagues,

We cordially invite you to submit your articles to the Special Issue of Axioms entitled Fuzzy Set Theory and Applications. The title of the Special Issue does not only reflect the topicality of the Special Issue itself, but it also provides a direct link to the 15th International Conference on Fuzzy Set Theory and Applications, FSTA 2020 (www.fsta.sk) held in Liptovský Ján, Slovakia, 26–31 January 2020. The FSTA conferences have a long tradition in gathering many researchers focusing on mathematical theories related to fuzzy set theory as well as their applications, and the main idea of the event is to provide a forum for exchanging ideas. The publication outputs of the event are then usually provided in one or more Special Issues of selected journals with post-conference publications. This Special Issue is one of such typical post-conference Special Issues; however, it is also absolutely open to submissions from authors who are interested in the topic even if they have not participated at the FSTA event at all.

We encourage any researchers with novel results in fuzzy set theory and its applications to prepare the publication outputs in the Axioms format and to submit to our Special Issue.

Prof. Dr. Radko Mesiar
Dr. Martin Štěpnička
Dr. Martin Papčo
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. Axioms 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

  • Approximate reasoning
  • Clustering, classification, and pattern recognition
  • Intelligent data analysis and data-mining
  • Theoretical foundations of fuzzy logic and fuzzy set theory
  • Algebraic topics related to fuzzy set theory
  • Categorical and topological aspects of fuzzy set theory
  • Aggregation and pre-aggregation
  • Theory and applications of decision-making

Published Papers (6 papers)

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Research

8 pages, 252 KiB  
Article
Conditional Intuitionistic Fuzzy Mean Value
by Katarína Čunderlíková
Axioms 2021, 10(2), 97; https://doi.org/10.3390/axioms10020097 - 21 May 2021
Cited by 1 | Viewed by 1502
Abstract
The conditional mean value has applications in regression analysis and in financial mathematics, because they are used in it. We can find papers from recent years that use the conditional mean value in fuzzy cases. As the intuitionstic fuzzy sets are an extension [...] Read more.
The conditional mean value has applications in regression analysis and in financial mathematics, because they are used in it. We can find papers from recent years that use the conditional mean value in fuzzy cases. As the intuitionstic fuzzy sets are an extension of fuzzy sets, we will try to define a conditional mean value for the intuitionistic fuzzy case. The conditional mean value in crisp intuitionistic fuzzy events was first studied by V. Valenčáková in 2009. She used Gödel connectives. Her approach can only be used for special cases of intuitionistic fuzzy events, therefore, we want to define a conditional mean value for all elements of a family of intuitionistic fuzzy events. In this paper, we define the conditional mean value for intuitionistic fuzzy events using Lukasiewicz connectives. We use a Kolmogorov approach and the notions from a classical probability theory for construction. B. Riečan formulated a conditional intuitionistic fuzzy probability for intuitionistic fuzzy events using an intuitionistic fuzzy state in 2012. In classical cases, there exists a connection between the conditional probability and the conditional mean value, therefore we show a connection between the conditional intuitionistic fuzzy probability induced by the intuitionistic fuzzy state and the conditional intuitionistic fuzzy mean value. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Applications)
18 pages, 360 KiB  
Article
Gradation of Fuzzy Preconcept Lattices
by Alexander Šostak, Ingrīda Uļjane and Māris Krastiņš
Axioms 2021, 10(1), 41; https://doi.org/10.3390/axioms10010041 - 22 Mar 2021
Cited by 8 | Viewed by 1758
Abstract
Noticing certain limitations of concept lattices in the fuzzy context, especially in view of their practical applications, in this paper, we propose a more general approach based on what we call graded fuzzy preconcept lattices. We believe that this approach is more adequate [...] Read more.
Noticing certain limitations of concept lattices in the fuzzy context, especially in view of their practical applications, in this paper, we propose a more general approach based on what we call graded fuzzy preconcept lattices. We believe that this approach is more adequate for dealing with fuzzy information then the one based on fuzzy concept lattices. We consider two possible gradation methods of fuzzy preconcept lattice—an inner one, called D-gradation and an outer one, called M-gradation, study their properties, and illustrate by a series of examples, in particular, of practical nature. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Applications)
11 pages, 282 KiB  
Article
Hybrid Ideals of BCK/BCI-Algebras
by Kyung-Tae Kang, Seok-Zun Song, Eun Hwan Roh and Young Bae Jun
Axioms 2020, 9(3), 85; https://doi.org/10.3390/axioms9030085 - 23 Jul 2020
Cited by 5 | Viewed by 2059
Abstract
The notion of hybrid ideals in B C K / B C I -algebras is introduced, and related properties are investigated. Characterizations of hybrid ideals are discussed. Relations between hybrid ideals and hybrid subalgebras are considered. Characterizations of hybrid ideals are considered. Based [...] Read more.
The notion of hybrid ideals in B C K / B C I -algebras is introduced, and related properties are investigated. Characterizations of hybrid ideals are discussed. Relations between hybrid ideals and hybrid subalgebras are considered. Characterizations of hybrid ideals are considered. Based on a hybrid structure, properties of special sets are investigated, and conditions for the special sets to be ideals are displayed. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Applications)
20 pages, 360 KiB  
Article
On t-Conorm Based Fuzzy (Pseudo)metrics
by Olga Grigorenko, Juan Jose Miñana, Alexander Šostak and Oscar Valero
Axioms 2020, 9(3), 78; https://doi.org/10.3390/axioms9030078 - 08 Jul 2020
Cited by 8 | Viewed by 2129
Abstract
We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseudo)metrics and compare [...] Read more.
We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseudo)metrics and compare them with “classic” fuzzy (pseudo)metrics. A method for construction CB-fuzzy (pseudo)metrics from ordinary metrics is elaborated and topology induced by CB-fuzzy (pseudo)metrics is studied. We establish interrelations between CB-fuzzy metrics and modulars, and in the process of this study, a particular role of Hamacher t-(co)norm in the theory of (CB)-fuzzy metrics is revealed. Finally, an intuitionistic version of a CB-fuzzy metric is introduced and applied in order to emphasize the roles of t-norms and a t-conorm in this context. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Applications)
17 pages, 256 KiB  
Article
Functors among Relational Variants of Categories Related to L-Fuzzy Partitions, L-Fuzzy Pretopological Spaces and L-Fuzzy Closure Spaces
by Jiří Močkoř
Axioms 2020, 9(2), 63; https://doi.org/10.3390/axioms9020063 - 02 Jun 2020
Cited by 6 | Viewed by 1999
Abstract
Various types of topological and closure operators are significantly used in fuzzy theory and applications. Although they are different operators, in some cases it is possible to transform an operator of one type into another. This in turn makes it possible to transform [...] Read more.
Various types of topological and closure operators are significantly used in fuzzy theory and applications. Although they are different operators, in some cases it is possible to transform an operator of one type into another. This in turn makes it possible to transform results relating to an operator of one type into results relating to another operator. In the paper relationships among 15 categories of modifications of topological L-valued operators, including Čech closure or interior L-valued operators, L-fuzzy pretopological and L-fuzzy co-pretopological operators, L-valued fuzzy relations, upper and lower F-transforms and spaces with fuzzy partitions are investigated. The common feature of these categories is that their morphisms are various L-fuzzy relations and not only maps. We prove the existence of 23 functors among these categories, which represent transformation processes of one operator into another operator, and we show how these transformation processes can be mutually combined. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Applications)
13 pages, 272 KiB  
Article
Integral Representation of Coherent Lower Previsions by Super-Additive Integrals
by Serena Doria, Radko Mesiar and Adam Šeliga
Axioms 2020, 9(2), 43; https://doi.org/10.3390/axioms9020043 - 23 Apr 2020
Cited by 8 | Viewed by 2302
Abstract
Coherent lower previsions generalize the expected values and they are defined on the class of all real random variables on a finite non-empty set. Well known construction of coherent lower previsions by means of lower probabilities, or by means of super-modular capacities-based Choquet [...] Read more.
Coherent lower previsions generalize the expected values and they are defined on the class of all real random variables on a finite non-empty set. Well known construction of coherent lower previsions by means of lower probabilities, or by means of super-modular capacities-based Choquet integrals, do not cover this important class of functionals on real random variables. In this paper, a new approach to the construction of coherent lower previsions acting on a finite space is proposed, exemplified and studied. It is based on special decomposition integrals recently introduced by Even and Lehrer, in our case the considered decomposition systems being single collections and thus called collection integrals. In special case when these integrals, defined for non-negative random variables only, are shift-invariant, we extend them to the class of all real random variables, thus obtaining so called super-additive integrals. Our proposed construction can be seen then as a normalized super-additive integral. We discuss and exemplify several particular cases, for example, when collections determine a coherent lower prevision for any monotone set function. For some particular collections, only particular set functions can be considered for our construction. Conjugated coherent upper previsions are also considered. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Applications)
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