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Fuzzy Logic and Soft Computing – Dedicated to the Centenary...
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Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017)

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 2021) | Viewed by 28864

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Prof. Dr. Ioan Dzitac

E-Mail Website
Guest Editor
Aurel Vlaicu University of Arad and Agora University of Oradea, Romania
Interests: fuzzy logic; fuzzy spaces; fuzzy programming; fuzzy decision-making; soft computing
Prof. Dr. Sorin Nadaban

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Arad, Romania
Interests: fuzzy logic; fuzzy functional analysis; fuzzy spaces; fuzzy decision-making
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In 1965, Lotfi A. Zadeh published “Fuzzy Sets”, his pioneering and controversial paper, which has now reached over 115,000 citations. Zadeh’s papers have together been cited over 248,000 times (Google Scholar).

Starting from the ideas presented in that paper, Zadeh later founded the Fuzzy Logic Theory, which proved to have useful applications from consumer to industrial intelligent products.

In accordance with Zadeh’s definition, soft computing (SC) consists of computational techniques in computer science, machine learning, and some engineering disciplines to study, model, and analyze very complex reality, for which more traditional methods have been either unusable or inefficient.

SC uses soft techniques, contrasting it with classical artificial intelligence hard computing (HC) techniques, and includes fuzzy logic, neural computing, evolutionary computation, machine learning, and probabilistic reasoning.

HC is bound by a computer science (CS) concept called NP-complete, which means that there is a direct connection between the size of a problem and the amount of resources needed to solve that called the “grand challenge problem”. SC helps to surmount NP-complete problems by using inexact methods to give useful but inexact answers to intractable problems.

SC became a formal CS area of study in the early 1990s. Earlier computational approaches could model and precisely analyze only relatively simple systems. More complex systems arising in biology, medicine, the humanities, management sciences, and similar fields often remained intractable to HC. It should be pointed out that the simplicity and complexity of systems are relative, and many conventional mathematical models have been both challenging and very productive.

SC techniques resemble biological processes more closely than traditional techniques, which are largely based on formal logical systems, such as Boolean logic, or rely heavily on computer-aided numerical analysis (such as finite element analysis).

SC techniques are intended to complement HC techniques. Unlike HC schemes, which strive for exactness and full truth, SC techniques exploit the given tolerance of imprecision, partial truth, and uncertainty for a particular problem. Inductive reasoning plays a larger role in SC than in HC. SC and HC can be used together in certain fusion techniques.

SC can deal with ambiguous or noisy data and is tolerant of imprecision, uncertainty, partial truth, and approximation. In effect, the role model for SC is the human mind. Artificial intelligence and computational intelligence based on SC provide the background for the development of smart management systems and decisions in the case of ill-posed problems.

We are pleased to invite you and your collaborators to submit several papers for the Special Issue “Fuzzy Logic and Soft Computing”, which is dedicated to the centenary of the birth of Lotfi A. Zadeh (1921–2017).

Prof. Dr. Ioan Dzitac
Prof. Dr. Sorin Nadaban
Guest Editors

The Guest Editor Prof. Dzitac passed away on 6 February 2021. We thank him for his contributions to this special issue. Co-Guest Editor Prof. Nadaban is managing the special issue with the Editorial office and suggests retaining Prof. Dzitac's information on the special issue homepage.

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 mathematics
  • soft computing
  • fuzzy logic
  • fuzzy sets theory
  • neuro-fuzzy applications

Published Papers (15 papers)

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Editorial

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3 pages, 156 KiB  
Editorial
Fuzzy Logic and Soft Computing—Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921–2017)
by Sorin Nădăban
Mathematics 2022, 10(17), 3216; https://doi.org/10.3390/math10173216 - 05 Sep 2022
Cited by 3 | Viewed by 920
Abstract
In 1965, Lotfi A. Zadeh published “Fuzzy Sets”, his pioneering and controversialpaper, which has now reached over 115,000 citations [...] Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))

Research

Jump to: Editorial, Review

10 pages, 275 KiB  
Article
Applications of the Fractional Calculus in Fuzzy Differential Subordinations and Superordinations
by Alina Alb Lupaş
Mathematics 2021, 9(20), 2601; https://doi.org/10.3390/math9202601 - 15 Oct 2021
Cited by 14 | Viewed by 1049
Abstract
The fractional integral of confluent hypergeometric function is used in this paper for obtaining new applications using concepts from the theory of fuzzy differential subordination and superordination. The aim of the paper is to present new fuzzy differential subordinations and superordinations for which [...] Read more.
The fractional integral of confluent hypergeometric function is used in this paper for obtaining new applications using concepts from the theory of fuzzy differential subordination and superordination. The aim of the paper is to present new fuzzy differential subordinations and superordinations for which the fuzzy best dominant and fuzzy best subordinant are given, respectively. The original theorems proved in the paper generate interesting corollaries for particular choices of functions acting as fuzzy best dominant and fuzzy best subordinant. Another contribution contained in this paper is the nice sandwich-type theorem combining the results given in two theorems proved here using the two theories of fuzzy differential subordination and fuzzy differential superordination. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
22 pages, 379 KiB  
Article
Multigranulation Roughness of Intuitionistic Fuzzy Sets by Soft Relations and Their Applications in Decision Making
by Muhammad Zishan Anwar, Shahida Bashir, Muhammad Shabir and Majed G. Alharbi
Mathematics 2021, 9(20), 2587; https://doi.org/10.3390/math9202587 - 15 Oct 2021
Cited by 10 | Viewed by 1344
Abstract
Multigranulation rough set (MGRS) based on soft relations is a very useful technique to describe the objectives of problem solving. This MGRS over two universes provides the combination of multiple granulation knowledge in a multigranulation space. This paper extends the concept of fuzzy [...] Read more.
Multigranulation rough set (MGRS) based on soft relations is a very useful technique to describe the objectives of problem solving. This MGRS over two universes provides the combination of multiple granulation knowledge in a multigranulation space. This paper extends the concept of fuzzy set Shabir and Jamal in terms of an intuitionistic fuzzy set (IFS) based on multi-soft binary relations. This paper presents the multigranulation roughness of an IFS based on two soft relations over two universes with respect to the aftersets and foresets. As a result, two sets of IF soft sets with respect to the aftersets and foresets are obtained. These resulting sets are called lower approximations and upper approximations with respect to the aftersets and with respect to the foresets. Some properties of this model are studied. In a similar way, we approximate an IFS based on multi-soft relations and discuss their some algebraic properties. Finally, a decision-making algorithm has been presented with a suitable example. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
13 pages, 291 KiB  
Article
Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator
by Georgia Irina Oros
Mathematics 2021, 9(20), 2539; https://doi.org/10.3390/math9202539 - 10 Oct 2021
Cited by 12 | Viewed by 1272
Abstract
This paper is related to notions adapted from fuzzy set theory to the field of complex analysis, namely fuzzy differential subordinations. Using the ideas specific to geometric function theory from the field of complex analysis, fuzzy differential subordination results are obtained using a [...] Read more.
This paper is related to notions adapted from fuzzy set theory to the field of complex analysis, namely fuzzy differential subordinations. Using the ideas specific to geometric function theory from the field of complex analysis, fuzzy differential subordination results are obtained using a new integral operator introduced in this paper using the well-known confluent hypergeometric function, also known as the Kummer hypergeometric function. The new hypergeometric integral operator is defined by choosing particular parameters, having as inspiration the operator studied by Miller, Mocanu and Reade in 1978. Theorems are stated and proved, which give corollary conditions such that the newly-defined integral operator is starlike, convex and close-to-convex, respectively. The example given at the end of the paper proves the applicability of the obtained results. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
19 pages, 11361 KiB  
Article
A Fuzzy Inference System for Management Control Tools
by Carolina Nicolas, Javiera Müller and Francisco-Javier Arroyo-Cañada
Mathematics 2021, 9(17), 2145; https://doi.org/10.3390/math9172145 - 02 Sep 2021
Cited by 2 | Viewed by 2557
Abstract
Despite the importance of the role of small and medium enterprises (SMEs) in developing and growing economies, little is known regarding the use of management control tools in them. In management control in SMEs, a holistic system needs to be modeled to enable [...] Read more.
Despite the importance of the role of small and medium enterprises (SMEs) in developing and growing economies, little is known regarding the use of management control tools in them. In management control in SMEs, a holistic system needs to be modeled to enable a careful study of how each lever (belief systems, boundary systems, interactive control systems, and diagnostic control systems) affects the organizational performance of SMEs. In this article, a fuzzy logic approach is proposed for the decision-making system in management control in small and medium enterprises. C. Mamdani fuzzy inference system (MFIS) was applied as a decision-making technique to explore the influence of the use of management control tools on the organizational performance of SMEs. Perceptions data analysis is obtained through empirical research. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
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15 pages, 711 KiB  
Article
Marks: A New Interval Tool for Uncertainty, Vagueness and Indiscernibility
by Miguel A. Sainz, Remei Calm, Lambert Jorba, Ivan Contreras and Josep Vehi
Mathematics 2021, 9(17), 2116; https://doi.org/10.3390/math9172116 - 01 Sep 2021
Cited by 1 | Viewed by 1336
Abstract
The system of marks created by Dr. Ernest Gardenyes and Dr. Lambert Jorba was first published as a doctoral thesis in 2003 and then as a chapter in the book Modal Interval Analysis in 2014. Marks are presented as a tool to deal [...] Read more.
The system of marks created by Dr. Ernest Gardenyes and Dr. Lambert Jorba was first published as a doctoral thesis in 2003 and then as a chapter in the book Modal Interval Analysis in 2014. Marks are presented as a tool to deal with uncertainties in physical quantities from measurements or calculations. When working with iterative processes, the slow convergence or the high number of simulation steps means that measurement errors and successive calculation errors can lead to a lack of significance in the results. In the system of marks, the validity of any computation results is explicit in their calculation. Thus, the mark acts as a safeguard, warning of such situations. Despite the obvious contribution that marks can make in the simulation, identification, and control of dynamical systems, some improvements are necessary for their practical application. This paper aims to present these improvements. In particular, a new, more efficient characterization of the difference operator and a new implementation of the marks library is presented. Examples in dynamical systems simulation, fault detection and control are also included to exemplify the practical use of the marks. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
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18 pages, 317 KiB  
Article
Regular and Intra-Regular Semigroups in Terms of m-Polar Fuzzy Environment
by Shahida Bashir, Sundas Shahzadi, Ahmad N. Al-Kenani and Muhammad Shabir
Mathematics 2021, 9(17), 2031; https://doi.org/10.3390/math9172031 - 24 Aug 2021
Cited by 6 | Viewed by 1462
Abstract
The central objective of the proposed work in this research is to introduce the innovative concept of an m-polar fuzzy set (m-PFS) in semigroups, that is, the expansion of bipolar fuzzy set (BFS). Our main focus in this study is [...] Read more.
The central objective of the proposed work in this research is to introduce the innovative concept of an m-polar fuzzy set (m-PFS) in semigroups, that is, the expansion of bipolar fuzzy set (BFS). Our main focus in this study is the generalization of some important results of BFSs to the results of m-PFSs. This paper provides some important results related to m-polar fuzzy subsemigroups (m-PFSSs), m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs), m-polar fuzzy quasi-ideals (m-PFQIs) and m-polar fuzzy interior ideals (m-PFIIs) in semigroups. This research paper shows that every m-PFBI of semigroups is the m-PFGBI of semigroups, but the converse may not be true. Furthermore this paper deals with several important properties of m-PFIs and characterizes regular and intra-regular semigroups by the properties of m-PFIs and m-PFBIs. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
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12 pages, 285 KiB  
Article
New Applications of Sălăgean and Ruscheweyh Operators for Obtaining Fuzzy Differential Subordinations
by Alina Alb Lupaş and Georgia Irina Oros
Mathematics 2021, 9(16), 2000; https://doi.org/10.3390/math9162000 - 21 Aug 2021
Cited by 23 | Viewed by 1995
Abstract
The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, the part dealing with geometric function theory. Several fuzzy differential subordinations are established regarding the operator Lαm, given by [...] Read more.
The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, the part dealing with geometric function theory. Several fuzzy differential subordinations are established regarding the operator Lαm, given by Lαm:An→An, Lαmf(z)=(1−α)Rmf(z)+αSmf(z), where An={f∈H(U),f(z)=z+an+1zn+1+…,z∈U} is the subclass of normalized holomorphic functions and the operators Rmf(z) and Smf(z) are Ruscheweyh and Sălăgean differential operator, respectively. Using the operator Lαm, a certain fuzzy class of analytic functions denoted by SLFmδ,α is defined in the open unit disc. Interesting results related to this class are obtained using the concept of fuzzy differential subordination. Examples are also given for pointing out applications of the theoretical results contained in the original theorems and corollaries. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
14 pages, 790 KiB  
Article
L-Fuzzy Sub-Effect Algebras
by Yan-Yan Dong and Fu-Gui Shi
Mathematics 2021, 9(14), 1596; https://doi.org/10.3390/math9141596 - 07 Jul 2021
Cited by 1 | Viewed by 1257
Abstract
In this paper, the notions of L-fuzzy subalgebra degree and L-subalgebras on an effect algebra are introduced and some characterizations are given. We use four kinds of cut sets of L-subsets to characterize the L-fuzzy subalgebra degree. We induce [...] Read more.
In this paper, the notions of L-fuzzy subalgebra degree and L-subalgebras on an effect algebra are introduced and some characterizations are given. We use four kinds of cut sets of L-subsets to characterize the L-fuzzy subalgebra degree. We induce an L-fuzzy convexity by the L-fuzzy subalgebra degree, and we prove that a morphism between two effect algebras is an L-fuzzy convexity preserving mapping and a monomorphism is an L-fuzzy convex-to-convex mapping. Finally, it is proved that the set of all L-subalgebras on an effect algebra can form an L-convexity, and its L-convex hull formula is given. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
19 pages, 835 KiB  
Article
Application of Induced Preorderings in Score Function-Based Method for Solving Decision-Making with Interval-Valued Fuzzy Soft Information
by Mabruka Ali, Adem Kiliçman and Azadeh Zahedi Khameneh
Mathematics 2021, 9(13), 1575; https://doi.org/10.3390/math9131575 - 04 Jul 2021
Cited by 2 | Viewed by 1695
Abstract
Ranking interval-valued fuzzy soft sets is an increasingly important research issue in decision making, and provides support for decision makers in order to select the optimal alternative under an uncertain environment. Currently, there are three interval-valued fuzzy soft set-based decision-making algorithms in the [...] Read more.
Ranking interval-valued fuzzy soft sets is an increasingly important research issue in decision making, and provides support for decision makers in order to select the optimal alternative under an uncertain environment. Currently, there are three interval-valued fuzzy soft set-based decision-making algorithms in the literature. However, these algorithms are not able to overcome the issue of comparable alternatives and, in fact, might be ignored due to the lack of a comprehensive priority approach. In order to provide a partial solution to this problem, we present a group decision-making solution which is based on a preference relationship of interval-valued fuzzy soft information. Further, corresponding to each parameter, two crisp topological spaces, namely, lower topology and upper topology, are introduced based on the interval-valued fuzzy soft topology. Then, using the preorder relation on a topological space, a score function-based ranking system is also defined to design an adjustable multi-steps algorithm. Finally, some illustrative examples are given to compare the effectiveness of the present approach with some existing methods. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
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15 pages, 320 KiB  
Article
Interval Ranges of Fuzzy Sets Induced by Arithmetic Operations Using Gradual Numbers
by Qingsong Mao and Huan Huang
Mathematics 2021, 9(12), 1351; https://doi.org/10.3390/math9121351 - 11 Jun 2021
Cited by 1 | Viewed by 1716
Abstract
Wu introduced the interval range of fuzzy sets. Based on this, he defined a kind of arithmetic of fuzzy sets using a gradual number and gradual sets. From the point of view of soft computing, this definition provides a new way of handling [...] Read more.
Wu introduced the interval range of fuzzy sets. Based on this, he defined a kind of arithmetic of fuzzy sets using a gradual number and gradual sets. From the point of view of soft computing, this definition provides a new way of handling the arithmetic operations of fuzzy sets. The interval range is an important characterization of a fuzzy set. The interval range is also useful for analyses and applications of arithmetic. In this paper, we present general conclusions on crucial problems related to interval ranges of fuzzy sets induced by this arithmetic. These conclusions indicate that the corresponding conclusions in previous works should be modified: firstly, we give properties of the arithmetic and the composites of finite arithmetic. Then, we discuss the relationship between the domain of a gradual set and the range of its induced fuzzy set, and the relationship between the domain of a gradual set and the interval range of its induced fuzzy set. Based on the above results, we present the relationship between the intersection of the interval ranges of a group of fuzzy sets and the interval ranges of their resulting fuzzy sets obtained by compositions of finite arithmetic. Furthermore, we construct examples to show that even under conditions stronger than in previous work, there are still various possibilities in the relationship between the intersection of interval ranges of a group of fuzzy sets and the ranges of their resulted fuzzy sets, and there are still various possibilities in the relationship between the intersection of the interval ranges of a group of fuzzy sets and the interval ranges of their resulting fuzzy sets. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
13 pages, 788 KiB  
Article
M-Hazy Vector Spaces over M-Hazy Field
by Faisal Mehmood and Fu-Gui Shi
Mathematics 2021, 9(10), 1118; https://doi.org/10.3390/math9101118 - 14 May 2021
Cited by 2 | Viewed by 1637
Abstract
The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces over M [...] Read more.
The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces over M-hazy field. Some fundamental properties of M-hazy field, M-hazy vector spaces, and M-hazy subspaces are studied, and some important results are also proved. Furthermore, the linear transformation of M-hazy vector spaces is studied and their important results are also proved. Finally, it is shown that M-fuzzifying convex spaces are induced by an M-hazy subspace of M-hazy vector space. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
9 pages, 270 KiB  
Article
Fuzzy Inner Product Space: Literature Review and a New Approach
by Lorena Popa and Lavinia Sida
Mathematics 2021, 9(7), 765; https://doi.org/10.3390/math9070765 - 01 Apr 2021
Cited by 4 | Viewed by 2299
Abstract
The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy [...] Read more.
The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))

Review

Jump to: Editorial, Research

11 pages, 369 KiB  
Review
Soft Computing for Decision-Making in Fuzzy Environments: A Tribute to Professor Ioan Dzitac
by Simona Dzitac and Sorin Nădăban
Mathematics 2021, 9(14), 1701; https://doi.org/10.3390/math9141701 - 20 Jul 2021
Cited by 16 | Viewed by 3080
Abstract
This paper is dedicated to Professor Ioan Dzitac (1953–2021). Therefore, his life has been briefly presented as well as a comprehensive overview of his major contributions in the domain of soft computing methods in a fuzzy environment. This paper is part of a [...] Read more.
This paper is dedicated to Professor Ioan Dzitac (1953–2021). Therefore, his life has been briefly presented as well as a comprehensive overview of his major contributions in the domain of soft computing methods in a fuzzy environment. This paper is part of a special reverential volume, dedicated to the Centenary of the Birth of Lotfi A. Zadeh, whom Ioan Dzitac considered to be is his mentor, and to whom he showed his gratitude many times and in innumerable ways, including by being the Guest Editor of this Special Issue. Professor Ioan Dzitac had many important achievements throughout his career: he was co-founder and Editor-in-Chief of an ISI Expanded quoted journal, International Journal of Computers Communications & Control; together with L.A. Zadeh, D. Tufis and F.G. Filip he edited the volume “From Natural Language to Soft Computing: New Paradigms in Artificial Intelligence”; his scientific interest focused on different sub-fields: fuzzy logic applications, soft computing in a fuzzy environment, artificial intelligence, learning platform, distributed systems in internet. He had the most important contributions in soft computing in a fuzzy environment. Some of them will be presented in this paper. Finally, some future trends are discussed. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
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16 pages, 857 KiB  
Review
Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers
by Bogdana Stanojević, Milan Stanojević and Sorin Nădăban
Mathematics 2021, 9(11), 1272; https://doi.org/10.3390/math9111272 - 01 Jun 2021
Cited by 8 | Viewed by 2370
Abstract
Optimization problems in the fuzzy environment are widely studied in the literature. We restrict our attention to mathematical programming problems with coefficients and/or decision variables expressed by fuzzy numbers. Since the review of the recent literature on mathematical programming in the fuzzy environment [...] Read more.
Optimization problems in the fuzzy environment are widely studied in the literature. We restrict our attention to mathematical programming problems with coefficients and/or decision variables expressed by fuzzy numbers. Since the review of the recent literature on mathematical programming in the fuzzy environment shows that the extension principle is widely present through the fuzzy arithmetic but much less involved in the foundations of the solution concepts, we believe that efforts to rehabilitate the idea of following the extension principle when deriving relevant fuzzy descriptions to optimal solutions are highly needed. This paper identifies the current position and role of the extension principle in solving mathematical programming problems that involve fuzzy numbers in their models, highlighting the indispensability of the extension principle in approaching this class of problems. After presenting the basic ideas in fuzzy optimization, underlying the advantages and disadvantages of different solution approaches, we review the main methodologies yielding solutions that elude the extension principle, and then compare them to those that follow it. We also suggest research directions focusing on using the extension principle in all stages of the optimization process. Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
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