Special Issue "New Trends in Fuzzy Set Theory and Related Items"

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 30 April 2018

Special Issue Editors

Guest Editor
Dr. Javier Fernandez

Department of Automatic and Computation, Public University of Navarra, Pamplona 31006, Spain
E-Mail
Interests: aggregation functions; theoretical aspects of fuzzy sets and their extensions; image processing; classification; decision making; bio-inspired algorithms; partial differential equations
Guest Editor
Dr. Esteban Indurain

Department of Mathematics, Public University of Navarre, Campus Arrosadía, Edificio las Encinas, Pamplona 31006, Spain
Website | E-Mail
Interests: ordered structures and their numerical representability; fuzzy sets and systems; functional equations; real analysis; general topology; mathematical social choice; mathematical economics; functional analysis
Guest Editor
Prof. Dr. Humberto Bustince

Department of Automatic and Computation, Public University of Navarra, Pamplona 31006, Spain
Website | E-Mail
Interests: aggregation functions; theoretical aspects of fuzzy sets and their extensions; image processing; classification; decision making; bio-inspired algorithms; partial differential equations

Special Issue Information

Dear Colleagues,

We have the intention of launching a Special Issue of Axioms. The central topic in the Special Issue will be “fuzzy set theory”. We would provide an opportunity to showcase recent developments in the many branches of both theoretical and practical studies in Mathematics, which are related to fuzzy set theory and/or its extensions and generalizations. Among the topics that this Special Issue will address, we may consider the following non-exhaustive list:

Fuzzy sets and systems; Fuzzy Logic; Linguistic labels; Fuzzy numbers; Functional equations; Aggregation functions and operators; Extensions of fuzzy sets; Ordered structures; Fuzzy relations; Miscellaneous applications of fuzzy sets and their extensions, etc.

Needless to say, the Special Issue is open to receiving further ideas, apart from the aforementioned topics.

In the hopes that this initiative are of interest, we encourage you to submit your current research to be included in the Special Issue.

Best regards,

Dr. Javier Fernandez
Dr. Esteban Indurain
Prof. Dr. Humberto Bustince
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 papers will be 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 quarterly 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 350 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 sets
  • Fuzzy logic
  • Labels
  • Aggregation operators
  • Functional equations
  • Ordered structures
  • Numerical representability
  • General topology
  • Social choice
  • Decision making;
  • Image processing
  • Type-2 fuzzy sets
  • Extensions of fuzzy sets
  • Fuzzy relations
  • Copulas

Published Papers (4 papers)

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Research

Open AccessArticle Existence of Order-Preserving Functions for Nontotal Fuzzy Preference Relations under Decisiveness
Axioms 2017, 6(4), 29; doi:10.3390/axioms6040029
Received: 6 October 2017 / Revised: 23 October 2017 / Accepted: 26 October 2017 / Published: 28 October 2017
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Abstract
Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy
[...] Read more.
Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
Open AccessArticle Orness For Idempotent Aggregation Functions
Axioms 2017, 6(3), 25; doi:10.3390/axioms6030025
Received: 23 August 2017 / Revised: 15 September 2017 / Accepted: 17 September 2017 / Published: 20 September 2017
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Abstract
Aggregation functions are mathematical operators that merge given data in order to obtain a global value that preserves the information given by the data as much as possible. In most practical applications, this value is expected to be between the infimum and the
[...] Read more.
Aggregation functions are mathematical operators that merge given data in order to obtain a global value that preserves the information given by the data as much as possible. In most practical applications, this value is expected to be between the infimum and the supremum of the given data, which is guaranteed only when the aggregation functions are idempotent. Ordered weighted averaging (OWA) operators are particular cases of this kind of function, with the particularity that the obtained global value depends on neither the source nor the expert that provides each datum, but only on the set of values. They have been classified by means of the orness—a measurement of the proximity of an OWA operator to the OR-operator. In this paper, the concept of orness is extended to the framework of idempotent aggregation functions defined both on the real unit interval and on a complete lattice with a local finiteness condition. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
Open AccessArticle New Order on Type 2 Fuzzy Numbers
Axioms 2017, 6(3), 22; doi:10.3390/axioms6030022
Received: 5 June 2017 / Revised: 14 July 2017 / Accepted: 24 July 2017 / Published: 28 July 2017
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Abstract
Since Lotfi A. Zadeh introduced the concept of fuzzy sets in 1965, many authors have devoted their efforts to the study of these new sets, both from a theoretical and applied point of view. Fuzzy sets were later extended in order to get
[...] Read more.
Since Lotfi A. Zadeh introduced the concept of fuzzy sets in 1965, many authors have devoted their efforts to the study of these new sets, both from a theoretical and applied point of view. Fuzzy sets were later extended in order to get more adequate and flexible models of inference processes, where uncertainty, imprecision or vagueness is present. Type 2 fuzzy sets comprise one of such extensions. In this paper, we introduce and study an extension of the fuzzy numbers (type 1), the type 2 generalized fuzzy numbers and type 2 fuzzy numbers. Moreover, we also define a partial order on these sets, which extends into these sets the usual order on real numbers, which undoubtedly becomes a new option to be taken into account in the existing total preorders for ranking interval type 2 fuzzy numbers, which are a subset of type 2 generalized fuzzy numbers. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
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Open AccessArticle Assigning Numerical Scores to Linguistic Expressions
Axioms 2017, 6(3), 19; doi:10.3390/axioms6030019
Received: 7 June 2017 / Revised: 29 June 2017 / Accepted: 30 June 2017 / Published: 6 July 2017
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Abstract
In this paper, we study different methods of scoring linguistic expressions defined on a finite set, in the search for a linear order that ranks all those possible expressions. Among them, particular attention is paid to the canonical extension, and its representability through
[...] Read more.
In this paper, we study different methods of scoring linguistic expressions defined on a finite set, in the search for a linear order that ranks all those possible expressions. Among them, particular attention is paid to the canonical extension, and its representability through distances in a graph plus some suitable penalization of imprecision. The relationship between this setting and the classical problems of numerical representability of orderings, as well as extension of orderings from a set to a superset is also explored. Finally, aggregation procedures of qualitative rankings and scorings are also analyzed. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
Figures

Figure 1

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