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Mathematics
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Analytical and Algebraic Aspects of Decision Making
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Analytical and Algebraic Aspects of Decision Making

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: closed (30 June 2021) | Viewed by 4012

Special Issue Editor

Prof. Dr. Martin Kalina

E-Mail Website
Guest Editor
Department of Mathematics and Descriptive Geometry, Faculty of Informatics and Information Technologies, Slovak University of Technology, Bratislava, Slovakia
Interests: construction of fuzzy connectives capacities (monotone measures); integrals with respect to capacities; aggregation functions; fuzzy preference relations; similarity measures

Special Issue Information

Dear Colleagues,

The scope of the issue is decision-making in A broader sense. This covers constructing and studying algebraic and analytical properties of fuzzy connectives (fuzzy implications, uninorms, OWA operators), studying aggregation functions applicable in decision-making problems, and integrals with respect to capacities. The issue aims to show progress in decision-making theory and also some applications of this theory.

Uninorms, OWA operators, and also various types of integrals with respect to capacities are presently a research area that attracts the interest of many researchers. Within the last 5 years, there have been more than 100 papers published on uninorms, about 500 papers on Choquet integral, and so on.

Potential authors are encouraged to submit their recent results as well as relevant reviews. All papers will be peer-reviewed.

Prof. Dr. Martin Kalina
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. 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

  • Uninorm
  • Fuzzy implication
  • Choquet integral
  • Capacity
  • Aggregation function
  • Fuzzy preference relation

Published Papers (2 papers)

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Research

16 pages, 262 KiB  
Article
Level Operators over Intuitionistic Fuzzy Index Matrices
by Krassimir Atanassov, Peter Vassilev and Olympia Roeva
Mathematics 2021, 9(4), 366; https://doi.org/10.3390/math9040366 - 11 Feb 2021
Cited by 7 | Viewed by 1727
Abstract
The index matrix (IM) is an extension of the ordinary matrix with indexed rows and columns. Over IMs’ standard matrix operations are defined and a lot of other ones that do not exist in the standard case. Intuitionistic fuzzy IMs (IFIMs) are modification [...] Read more.
The index matrix (IM) is an extension of the ordinary matrix with indexed rows and columns. Over IMs’ standard matrix operations are defined and a lot of other ones that do not exist in the standard case. Intuitionistic fuzzy IMs (IFIMs) are modification of the IMs, when their elements are intuitionistic fuzzy pairs (IFPs). Extended IFIMs are IFIMs whose indices of the rows and columns are evaluated by IFPs. Different operations, relations and operators over IFIMs, and some specific ones, are defined for EIFIMs. In the paper, twelve new level operators are defined for EIFIMs and in the partial case, over IFIMs. The proposed level operators fall into two groups: operators that change the values of the EIFIM elements and operators that change the IFPs associated to the indices of the rows and columns. The basic properties of the operators are studied. Full article
(This article belongs to the Special Issue Analytical and Algebraic Aspects of Decision Making)
16 pages, 337 KiB  
Article
On Admissible Orders on the Set of Discrete Fuzzy Numbers for Application in Decision Making Problems
by Juan Vicente Riera, Sebastia Massanet, Humberto Bustince and Javier Fernandez
Mathematics 2021, 9(1), 95; https://doi.org/10.3390/math9010095 - 04 Jan 2021
Cited by 5 | Viewed by 1786
Abstract
The study of orders is a constantly evolving topic, not only for its interest from a theoretical point of view, but also for its possible applications. Recently, one of the hot lines of research has been the construction of admissible orders in different [...] Read more.
The study of orders is a constantly evolving topic, not only for its interest from a theoretical point of view, but also for its possible applications. Recently, one of the hot lines of research has been the construction of admissible orders in different frameworks. Following this direction, this paper presents a new representation theorem in the field of discrete fuzzy numbers that enables the construction of two families of admissible orders in the set of discrete fuzzy numbers whose support is a closed interval of a finite chain, leading to the first admissible orders introduced in this framework. Full article
(This article belongs to the Special Issue Analytical and Algebraic Aspects of Decision Making)
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