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Mathematics
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Fuzzy Sets and Artificial Intelligence
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Fuzzy Sets and Artificial Intelligence

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 (31 December 2022) | Viewed by 14242

Special Issue Editors

Prof. Dr. José Carlos R. Alcantud

E-Mail Website
Guest Editor
BORDA Research Unit, Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, Spain
Interests: decision theory; social choice; mathematical economics; fuzzy set theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Gustavo Santos-García

E-Mail Website
Guest Editor
Facultad de Economía y Empresa and Multidisciplinary Institute of Enterprise (IME), Universidad de Salamanca, 37007 Salamanca, Spain
Interests: artificial Intelligence; soft computing; rewriting logic; computational biology; decision theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

Soft computing is a branch of Artificial Intelligence that studies the techniques used in the resolution of problems incorporating incomplete, uncertain and/or inaccurate information.

Fuzzy set theory and its generalizations have proven to be fundamental in the management of imprecise information and in reasoning under uncertainty. These theories provide theoretical and practical frameworks that have proven suitable for numerous types of modeling applications.

The purpose of this Special Issue is to gather a collection of articles on the cutting-edge advances and developments in this field of research, which includes but is not limited to topics such as: optimization, decision making, aggregation functions, natural language processing, knowledge representation, extensions and generalizations of fuzzy sets, aggregation operations, fuzzy programming, and approximate reasoning. Manuscripts on theoretical foundations, as well as applied developments and related methodologies of soft computing, in the domains of economics, medical sciences, engineering, industry, social sciences, etc., are welcome.

Prof. Dr. José Carlos R. Alcantud
Prof. Dr. Gustavo Santos-García
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

  • decision making
  • multiple-criteria decision making
  • optimization
  • uncertainty
  • linguistic variables
  • artificial intelligence
  • soft computing
  • fuzzy set theory
  • fuzzy sets and their generalizations
  • deep learning
  • neural networks
  • machine learning
  • expert systems
  • applications of fuzziness in artificial intelligence, economics, medicine, industry, etc

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Published Papers (6 papers)

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Research

10 pages, 431 KiB  
Article
Andness Directedness for t-Norms and t-Conorms
by Vicenç Torra
Mathematics 2022, 10(9), 1598; https://doi.org/10.3390/math10091598 - 8 May 2022
Cited by 2 | Viewed by 2083
Abstract
Tools for decision making need to be simple to use. In previous papers, we advocated that decision engineering needs to provide these tools, as well as a list of necessary properties that aggregation functions need to satisfy. When we model decisions using aggregation [...] Read more.
Tools for decision making need to be simple to use. In previous papers, we advocated that decision engineering needs to provide these tools, as well as a list of necessary properties that aggregation functions need to satisfy. When we model decisions using aggregation functions, andness-directedness is one of them. A crucial aspect in any decision is the degree of compromise between criteria. Given an aggregation function, andness establishes to what degree the function behaves in a conjunctive manner. That is, to what degree some criteria are mandatory. Nevertheless, from an engineering perspective, what we know is that some criteria are strongly required and we cannot ignore a bad evaluation even when other criteria are correctly evaluated. That is, given our requirements of andness, what are the aggregation functions we need to select. Andness is not only for mean-like functions, but it also applies to t-norms and t-conorms. In this paper, we study this problem and show how to select t-norms and t-conorms based on the andness level. Full article
(This article belongs to the Special Issue Fuzzy Sets and Artificial Intelligence)
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14 pages, 1311 KiB  
Article
Induction Motor DTC Performance Improvement by Inserting Fuzzy Logic Controllers and Twelve-Sector Neural Network Switching Table
by Chaymae Fahassa, Yassine Zahraoui, Mohammed Akherraz, Mohammed Kharrich, Ehab E. Elattar and Salah Kamel
Mathematics 2022, 10(9), 1357; https://doi.org/10.3390/math10091357 - 19 Apr 2022
Cited by 11 | Viewed by 1909
Abstract
Human civilization has changed forever since induction motors were invented. Induction motors are widely used and have become the most prevalent electrical componentsdue to their beneficial characteristics. Many control strategies have been developed for their performance improvement, starting from scalar to vector to [...] Read more.
Human civilization has changed forever since induction motors were invented. Induction motors are widely used and have become the most prevalent electrical componentsdue to their beneficial characteristics. Many control strategies have been developed for their performance improvement, starting from scalar to vector to direct torque control. The latter, which is a class of vector control, was proposed as an alternative to ensure separate flux and torque control while remaining completely in a stationary reference frame. This technique allows direct inverter switching and reasonable simplicity compared to other vector control techniques, and it is less sensitive to parameter variation. Yet, the use of hysteresis controllers in conventional DTC involves undesired ripples in the stator current, flux, and torque, which lead to bad performances. This paper aims to minimize the ripple level and ensure the system’s performance in terms of robustness and stability. To generate the appropriate reference control voltages, the proposed method is an improved version of DTC, which combines the power of fuzzy logic, neural networks, and an increased number of sectors. Satisfactory results were obtained by numerical simulation in MATLAB/Simulink. The proposed method was proven to be a fast dynamic decoupled control that robustly responds to external disturbance and system uncertainties. Full article
(This article belongs to the Special Issue Fuzzy Sets and Artificial Intelligence)
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30 pages, 3598 KiB  
Article
Probabilistic Linguistic Matrix Game Based on Fuzzy Envelope and Prospect Theory with Its Application
by Shuying Li and Guoping Tu
Mathematics 2022, 10(7), 1070; https://doi.org/10.3390/math10071070 - 26 Mar 2022
Cited by 4 | Viewed by 1679
Abstract
Game theory is a powerful tool in modeling strategic interaction among rational players. However, as practical problems become more complex, uncertainty inevitably appears in the game. Due to the advantages of probabilistic linguistic term sets (PLTSs) in comprehensively and flexibly portraying uncertainty, fuzziness [...] Read more.
Game theory is a powerful tool in modeling strategic interaction among rational players. However, as practical problems become more complex, uncertainty inevitably appears in the game. Due to the advantages of probabilistic linguistic term sets (PLTSs) in comprehensively and flexibly portraying uncertainty, fuzziness and hesitancy, this paper uses PLTSs to express players’ payoff values, and aims to develop an integrated method based on fuzzy envelope and prospect theory (PT) under a probabilistic linguistic environment for solving matrix games. In this method, an improved probabilistic ordered weighted averaging (POWA) operator is defined. Then, a novel trapezoidal fuzzy envelope for PLTSs is proposed and some related theorems are analyzed. Next, based on the defined cosine distance measure for PLTSs, the players’ psychological behavior in the game is considered by establishing the prospect value function. Besides, the applicability and practicability of the proposed method is verified with an example from the development strategy of Sanjiangyuan National Nature Reserve (SNNR) in China. Finally, some comparative analyses are carried out to illustrate the superiority of the proposed method. In order to improve the application of this proposed method, a decision support system (DSS) based on it is designed. Full article
(This article belongs to the Special Issue Fuzzy Sets and Artificial Intelligence)
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21 pages, 385 KiB  
Article
Pessimistic Multigranulation Roughness of a Fuzzy Set Based on Soft Binary Relations over Dual Universes and Its Application
by Jamalud Din, Muhammad Shabir and Ye Wang
Mathematics 2022, 10(4), 541; https://doi.org/10.3390/math10040541 - 9 Feb 2022
Cited by 6 | Viewed by 1362
Abstract
The rough set model for dual universes and multi granulation over dual universes is an interesting generalization of the Pawlak rough set model. In this paper, we present a pessimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual [...] Read more.
The rough set model for dual universes and multi granulation over dual universes is an interesting generalization of the Pawlak rough set model. In this paper, we present a pessimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes. Firstly, we approximate fuzzy set w.r.t aftersets and foresets of the finite number of soft binary relations. As a result, we obtained two sets of fuzzy soft sets known as the pessimistic lower approximation of a fuzzy set and the pessimistic upper approximation of a fuzzy set—the w.r.t aftersets and the w.r.t foresets. The pessimistic lower and pessimistic upper approximations of the newly proposed multigranulation rough set model are then investigated for several interesting properties. This article also addresses accuracy measures and measures of roughness. Finally, we give a decision-making algorithm as well as examples from the perspective of application. Full article
(This article belongs to the Special Issue Fuzzy Sets and Artificial Intelligence)
37 pages, 5717 KiB  
Article
Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making
by Zeeshan Ali, Tahir Mahmood and Gustavo Santos-García
Mathematics 2021, 9(21), 2730; https://doi.org/10.3390/math9212730 - 27 Oct 2021
Cited by 16 | Viewed by 2055
Abstract
In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their [...] Read more.
In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their uncertain linguistic terms to handle problematic and challenging data in factual life impasses. By using the elaborated CLDULSs, some operational laws are also settled. Furthermore, by using the power Einstein (PE) aggregation operators based on CLDULS: the complex linear Diophantine uncertain linguistic PE averaging (CLDULPEA), complex linear Diophantine uncertain linguistic PE weighted averaging (CLDULPEWA), complex linear Diophantine uncertain linguistic PE Geometric (CLDULPEG), and complex linear Diophantine uncertain linguistic PE weighted geometric (CLDULPEWG) operators, and their useful results are elaborated with the help of some remarkable cases. Additionally, by utilizing the expounded works dependent on CLDULS, I propose a multi-attribute decision-making (MADM) issue. To decide the quality of the expounded works, some mathematical models are outlined. Finally, the incomparability and relative examination of the expounded approaches with the assistance of graphical articulations are evolved. Full article
(This article belongs to the Special Issue Fuzzy Sets and Artificial Intelligence)
15 pages, 1003 KiB  
Article
Caliber and Chain Conditions in Soft Topologies
by José Carlos R. Alcantud, Tareq M. Al-shami and A. A. Azzam
Mathematics 2021, 9(19), 2349; https://doi.org/10.3390/math9192349 - 22 Sep 2021
Cited by 21 | Viewed by 2212
Abstract
In this paper, we contribute to the growing literature on soft topology. Its theoretical underpinning merges point-set or classical topology with the characteristics of soft sets (a model for the representation of uncertain knowledge initiated in 1999). We introduce two types of axioms [...] Read more.
In this paper, we contribute to the growing literature on soft topology. Its theoretical underpinning merges point-set or classical topology with the characteristics of soft sets (a model for the representation of uncertain knowledge initiated in 1999). We introduce two types of axioms that generalize suitable concepts of soft separability. They are respectively concerned with calibers and chain conditions. We investigate explicit procedures for the construction of non-trivial soft topological spaces that satisfy these new axioms. Then we explore the role of cardinality in their study, and the relationships among these and other properties. Our results bring to light a fruitful field for future research in soft topology. Full article
(This article belongs to the Special Issue Fuzzy Sets and Artificial Intelligence)
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