Special Issue "Fuzzy Sets and Soft Computing"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Set Theory".

Deadline for manuscript submissions: 31 March 2021.

Special Issue Editors

Prof. Dr. Gustavo Santos-García
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Guest Editor
Department of Economic Analysis, University of Salamanca, 37007 Salamanca, Spain
Interests: artificial Intelligence; soft computing; rewriting logic; computational biology; decision theory
Prof. Dr. José Carlos R. Alcantud
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Guest Editor
Department of Economics and Economic History, University of Salamanca, Spain
Interests: decision theory; social choice; mathematical economics; fuzzy set theory
Special Issues and Collections in MDPI journals
Dr. Enrico Marchioni
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Guest Editor
Department of Electronics and Computer Science, University of Southampton, UK
Interests: game theory; reasoning under uncertainty; mathematical logic

Special Issue Information

Dear Colleagues

John McCarthy coined the term Artificial Intelligence in the 1950s. From his point of view, AI is not about imitating human reasoning and the human way of solving problems, but about finding the essence of abstract reasoning and problem solving. At present, IA focuses on the study of intelligent agents, that is, of autonomous entities capable of perceiving their environment and which, like humans, have the capacity to act so as to optimize their objectives.

Soft computing is a branch of Artificial Intelligence that studies the techniques used in the resolution of problems that handle incomplete, uncertain, and/or inaccurate information. Fuzzy sets are fundamental in the theory of uncertainty. Fuzzy sets and soft computing provide numerous theoretical and practical tools for complex linguistic and numerical modeling applications.

The purpose of this Special Issue is to gather a collection of articles on the latest research and developments in this field of research which includes but is not limited to topics such as: automated reasoning and inference, heuristic search, natural language processing, applications in medical sciences and bioinformatics, knowledge representation, extensions and generalizations of fuzzy sets, aggregation operations, information content measures, preference modeling and multicriteria evaluation, and reasoning under uncertainty.

Prof. Dr. Gustavo Santos-García 
Prof. Dr. José Carlos R. Alcantud
Dr. Enrico Marchioni
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 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

  • Mathematical logic and mathematical foundation
  • Foundations of soft computing
  • Fuzzy set theory
  • Reasoning under uncertainty
  • Extensions and generalizations of fuzzy sets
  • Knowledge representation
  • Web-based intelligence
  • Heuristic search in soft computing
  • Soft computing applications in medical sciences and bioinformatics
  • Mathematical and computational biology

Published Papers (13 papers)

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Research

Open AccessArticle
On Unification of Methods in Theories of Fuzzy Sets, Hesitant Fuzzy Set, Fuzzy Soft Sets and Intuitionistic Fuzzy Sets
Mathematics 2021, 9(4), 447; https://doi.org/10.3390/math9040447 - 23 Feb 2021
Viewed by 122
Abstract
The main goal of this publication is to show that the basic constructions in the theories of fuzzy sets, fuzzy soft sets, fuzzy hesitant sets or intuitionistic fuzzy sets have a common background, based on the theory of monads in categories. It is [...] Read more.
The main goal of this publication is to show that the basic constructions in the theories of fuzzy sets, fuzzy soft sets, fuzzy hesitant sets or intuitionistic fuzzy sets have a common background, based on the theory of monads in categories. It is proven that ad hoc defined basic concepts in individual theories, such as concepts of power set structures in these theories, relations or approximation operators defined by these relations are only special examples of applications of the monad theory in categories. This makes it possible, on the one hand, to unify basic constructions in all these theories and, on the other hand, to verify the legitimacy of ad hoc definitions of these constructions in individual theories. This common background also makes it possible to transform these basic concepts from one theory to another. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
Open AccessArticle
Several Limit Theorems on Fuzzy Quantum Space
Mathematics 2021, 9(4), 438; https://doi.org/10.3390/math9040438 - 23 Feb 2021
Viewed by 213
Abstract
The probability theory using fuzzy random variables has applications in several scientific disciplines. These are mainly technical in scope, such as in the automotive industry and in consumer electronics, for example, in washing machines, televisions, and microwaves. The theory is gradually entering the [...] Read more.
The probability theory using fuzzy random variables has applications in several scientific disciplines. These are mainly technical in scope, such as in the automotive industry and in consumer electronics, for example, in washing machines, televisions, and microwaves. The theory is gradually entering the domain of finance where people work with incomplete data. We often find that events in the financial markets cannot be described precisely, and this is where we can use fuzzy random variables. By proving the validity of the theorem on extreme values of fuzzy quantum space in our article, we see possible applications for estimating financial risks with incomplete data. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
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Open AccessArticle
Path-Planning for Mobile Robots Using a Novel Variable-Length Differential Evolution Variant
Mathematics 2021, 9(4), 357; https://doi.org/10.3390/math9040357 - 11 Feb 2021
Viewed by 277
Abstract
Mobile robots are currently exploited in various applications to enhance efficiency and reduce risks in hard activities for humans. The high autonomy in those systems is strongly related to the path-planning task. The path-planning problem is complex and requires in its formulation the [...] Read more.
Mobile robots are currently exploited in various applications to enhance efficiency and reduce risks in hard activities for humans. The high autonomy in those systems is strongly related to the path-planning task. The path-planning problem is complex and requires in its formulation the adjustment of path elements that take the mobile robot from a start point to a target one at the lowest cost. Nevertheless, the identity or the number of the path elements to be adjusted is unknown; therefore, the human decision is necessary to determine this information reducing autonomy. Due to the above, this work conceives the path-planning as a Variable-Length-Vector optimization problem (VLV-OP) where both the number of variables (path elements) and their values must be determined. For this, a novel variant of Differential Evolution for Variable-Length-Vector optimization named VLV-DE is proposed to handle the path-planning VLV-OP for mobile robots. VLV-DE uses a population with solution vectors of different sizes adapted through a normalization procedure to allow interactions and determine the alternatives that better fit the problem. The effectiveness of this proposal is shown through the solution of the path-planning problem in complex scenarios. The results are contrasted with the well-known A* and the RRT*-Smart path-planning methods. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
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Open AccessArticle
New Product Idea Selection in the Fuzzy Front End of Innovation: A Fuzzy Best-Worst Method and Group Decision-Making Process
Mathematics 2021, 9(4), 337; https://doi.org/10.3390/math9040337 - 08 Feb 2021
Viewed by 222
Abstract
New product development (NPD) is essential to most business organizations to create new values and protect existing values for maintaining high profitability and sustainability. However, the success of NPD projects is deemed to be difficult and challenging owing to high organizational complexity, uncertain [...] Read more.
New product development (NPD) is essential to most business organizations to create new values and protect existing values for maintaining high profitability and sustainability. However, the success of NPD projects is deemed to be difficult and challenging owing to high organizational complexity, uncertain business environment, and time-critical innovation. Under the smart manufacturing paradigm, NPD is an active research area to establish effective measures through the adoption of systematic approaches so as to facilitate idea management in the fuzzy front end for the product innovation. In this paper, the domain of new product idea selection is focused on and enhanced by means of the multi-criteria decision-making (MCDM) approach, in which multiple criteria and sub-criteria can be considered in the selection process. Among a number of MCDM approaches, the fuzzy set theory and best-worst method (BWM) are integrated as the fuzzy BWM in this study to structure the new product idea selection process under a group decision-making process. The hierarchy structure for the new product idea selection is also established to consider the perspectives of finance, marketing, engineering, manufacturing, and sustainability. Overall speaking, this study contributes to the field of NPD through overcoming the new product idea selection problem, while the group decision-making process is incorporated into the fuzzy BWM. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
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Open AccessArticle
An Intuitionistic Fuzzy Set Driven Stochastic Active Contour Model with Uncertainty Analysis
Mathematics 2021, 9(4), 301; https://doi.org/10.3390/math9040301 - 03 Feb 2021
Viewed by 263
Abstract
Image segmentation is a process that densely classifies image pixels into different regions corresponding to real world objects. However, this correspondence is not always exact in images since there are many uncertainty factors, e.g., recognition hesitation, imaging equipment, condition, and atmosphere environment. To [...] Read more.
Image segmentation is a process that densely classifies image pixels into different regions corresponding to real world objects. However, this correspondence is not always exact in images since there are many uncertainty factors, e.g., recognition hesitation, imaging equipment, condition, and atmosphere environment. To achieve the segmentation result with low uncertainty and reduce the influence on the subsequent procedures, e.g., image parsing and image understanding, we propose a novel stochastic active contour model based on intuitionistic fuzzy set, in which the hesitation degree is leveraged to model the recognition uncertainty in image segmentation. The advantages of our model are as follows. (1) Supported by fuzzy partition, our model is robust against image noise and inhomogeneity. (2) Benefiting from the stochastic process, our model easily crosses saddle points of energy functional. (3) Our model realizes image segmentation with low uncertainty and co-produces the quantitative uncertainty degree to the segmentation results, which is helpful to improve reliability of intelligent image systems. The associated experiments suggested that our model could obtain competitive segmentation results compared to the relevant state-of-the-art active contour models and could provide segmentation with a pixel-wise uncertainty degree. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
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Open AccessArticle
Induced OWA Operator for Group Decision Making Dealing with Extended Comparative Linguistic Expressions with Symbolic Translation
Mathematics 2021, 9(1), 20; https://doi.org/10.3390/math9010020 - 23 Dec 2020
Cited by 1 | Viewed by 352
Abstract
Nowadays, decision making problems have increased their complexity and a single decision maker cannot handle these problems, with a more diverse and comprehensive view of them being necessary, which results in group decision making (GDM) schemes. The complexity of GDM problems is often [...] Read more.
Nowadays, decision making problems have increased their complexity and a single decision maker cannot handle these problems, with a more diverse and comprehensive view of them being necessary, which results in group decision making (GDM) schemes. The complexity of GDM problems is often due to their inherent uncertainty that is not solved just by using a group. Consequently, different methodologies has been proposed to handle it, in which, the use of the fuzzy linguistic approach stands out. Among the multiple fuzzy linguistic modeling approaches, Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT) information has been recently introduced, which enhances classical linguistic modeling that is based on single terms by providing linguistic expressions in a continuous linguistic domain. Its application to decision making is quite promising, but it is necessary to develop enough operators to accomplish aggregation processes in the decision solving scheme. So far, just a small number of aggregation operators have been defined for ELICIT information. Hence, this paper aims at providing new aggregation operators for ELICIT information by developing novel OWA based operators, such as the Induced OWA (IOWA) operator in order to avoid the OWA operator needs of reordering its arguments, because ELICIT information does not have an inherent order due to its fuzzy representation. Our proposal not only consists of extending the definition of an IOWA operator for ELICIT information with crisp weights, but it is also proposed a type-1 IOWA operator for ELICIT information in which both weights and arguments are fuzzy as well as the use of ELICIT information constructing the order inducing variable to reorder the arguments. Additionally, the use of ELICIT information in GDM demands the ability to manage majority based decisions that are better represented in the IOWA operator by linguistic quantifiers. Hence, a majority-driven GDM process for ELICIT information is proposed, which it is the first proposal for fulfilling the majority solving process for GDM while using ELICIT information. Eventually, an illustrative example and a brief comparative analysis are presented in order to show the performance of the proposal and its feasibility. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
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Open AccessArticle
A Consensus Model for Extended Comparative Linguistic Expressions with Symbolic Translation
Mathematics 2020, 8(12), 2198; https://doi.org/10.3390/math8122198 - 10 Dec 2020
Viewed by 360
Abstract
Consensus Reaching Process (CRP) is a necessary process to achieve agreed solutions in group decision making (GDM) problems. Usually, these problems are defined in uncertain contexts, in which experts do not have a full and precise knowledge about all aspects of the problem. [...] Read more.
Consensus Reaching Process (CRP) is a necessary process to achieve agreed solutions in group decision making (GDM) problems. Usually, these problems are defined in uncertain contexts, in which experts do not have a full and precise knowledge about all aspects of the problem. In real-world GDM problems under uncertainty, it is usual that experts express their preferences by using linguistic expressions. Consequently, different methodologies have modelled linguistic information, in which computing with words stands out and whose basis is the fuzzy linguistic approach and their extensions. Even though, multiple consensus approaches under fuzzy linguistic environments have been proposed in the specialized literature, there are still some areas where their performance must be improved because of several persistent drawbacks. The drawbacks include the use of single linguistic terms that are not always enough to model the uncertainty in experts’ knowledge or the oversimplification of fuzzy information during the computational processes by defuzzification processes into crisp values, which usually implies a loss of information and precision in the results and also a lack of interpretability. Therefore, to improving the effects of previous drawbacks, this paper aims at presenting a novel CRP for GDM problems dealing with Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT) for modelling experts’ linguistic preferences. Such a CRP will overcome previous limitations because ELICIT information allows both fuzzy modelling of the experts’ uncertainty including hesitancy and performs comprehensive fuzzy computations to, ultimately, obtain precise and understandable linguistic results. Additionally, the proposed CRP model is implemented and integrated into the CRP support system so-called A FRamework for the analYsis of Consensus Approaches (AFRYCA) 3.0 that facilitates the application of the proposed CRP and its comparison with previous models. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
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Open AccessArticle
Barrakuda: A Hybrid Evolutionary Algorithm for Minimum Capacitated Dominating Set Problem
Mathematics 2020, 8(11), 1858; https://doi.org/10.3390/math8111858 - 23 Oct 2020
Viewed by 523
Abstract
The minimum capacitated dominating set problem is an NP-hard variant of the well-known minimum dominating set problem in undirected graphs. This problem finds applications in the context of clustering and routing in wireless networks. Two algorithms are presented in this work. The first [...] Read more.
The minimum capacitated dominating set problem is an NP-hard variant of the well-known minimum dominating set problem in undirected graphs. This problem finds applications in the context of clustering and routing in wireless networks. Two algorithms are presented in this work. The first one is an extended version of construct, merge, solve and adapt, while the main contribution is a hybrid between a biased random key genetic algorithm and an exact approach which we labeled Barrakuda. Both algorithms are evaluated on a large set of benchmark instances from the literature. In addition, they are tested on a new, more challenging benchmark set of larger problem instances. In the context of the problem instances from the literature, the performance of our algorithms is very similar. Moreover, both algorithms clearly outperform the best approach from the literature. In contrast, Barrakuda is clearly the best-performing algorithm for the new, more challenging problem instances. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
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Open AccessArticle
An Integrated Decision Approach with Probabilistic Linguistic Information for Test Case Prioritization
Mathematics 2020, 8(11), 1857; https://doi.org/10.3390/math8111857 - 23 Oct 2020
Viewed by 439
Abstract
This paper focuses on an exciting and essential problem in software companies. The software life cycle includes testing software, which is often time-consuming, and is a critical phase in the software development process. To reduce time spent on testing and to maintain software [...] Read more.
This paper focuses on an exciting and essential problem in software companies. The software life cycle includes testing software, which is often time-consuming, and is a critical phase in the software development process. To reduce time spent on testing and to maintain software quality, the idea of a systematic selection of test cases is needed. Attracted by the claim, researchers presented test case prioritization (TCP) by applying the concepts of multi-criteria decision-making (MCDM). However, the literature on TCP suffers from the following issues: (i) difficulty in properly handling uncertainty; (ii) systematic evaluation of criteria by understanding the hesitation of experts; and (iii) rational prioritization of test cases by considering the nature of criteria. Motivated by these issues, an integrated approach is put forward that could circumvent the problem in this paper. The main aim of this research is to develop a decision model with integrated methods for TCP. The core importance of the proposed model is to (i) provide a systematic/methodical decision on TCP with a reduction in testing time and cost; (ii) help software personnel choose an apt test case from the suite for testing software; (iii) reduce human bias by mitigating intervention of personnel in the decision process. To this end, probabilistic linguistic information (PLI) is adopted as the preference structure that could flexibly handle uncertainty by associating occurrence probability to each linguistic term. Furthermore, an attitude-based entropy measure is presented for criteria weight calculation, and finally, the EDAS ranking method is extended to PLI for TCP. An empirical study of TCP in a software company is presented to certify the integrated approach’s effectiveness. The strengths and weaknesses of the introduced approach are conferred by comparing it with the relevant methods. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
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Open AccessArticle
Comparing Built-in Power Banks for a Smart Backpack Design Using an Auto-Weighting Fuzzy-Weighted-Intersection FAHP Approach
Mathematics 2020, 8(10), 1759; https://doi.org/10.3390/math8101759 - 13 Oct 2020
Cited by 1 | Viewed by 342
Abstract
Smart backpacks are a prevalent application of smart technologies, with functions such as motion recording, navigation, and energy harvesting and provision. Selecting a suitable built-in power bank is a critical task for a smart backpack design, which has rarely been investigated in the [...] Read more.
Smart backpacks are a prevalent application of smart technologies, with functions such as motion recording, navigation, and energy harvesting and provision. Selecting a suitable built-in power bank is a critical task for a smart backpack design, which has rarely been investigated in the past. To fulfill this task, an auto-weighting fuzzy-weighted-intersection fuzzy analytic hierarchy process (FAHP) approach is proposed in this study. When decision makers lack an overall consensus, the auto-weighting fuzzy-weighted-intersection FAHP approach specifies decision makers’ authority levels according to the consistency ratios of their judgments. In this way, the consensus among all decision makers can be sought. The auto-weighting fuzzy-weighted-intersection FAHP approach has been applied to compare six mobile power banks for a smart backpack design. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
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Open AccessArticle
An Improved Migrating Birds Optimization Algorithm for a Hybrid Flow Shop Scheduling within Steel Plants
Mathematics 2020, 8(10), 1661; https://doi.org/10.3390/math8101661 - 26 Sep 2020
Viewed by 442
Abstract
Steelmaking and the continuous-casting (SCC) scheduling problem is a realistic hybrid flow shop scheduling problem with continuous-casting production at the last stage. This study considers the SCC scheduling problem with diverse products, which is a vital and difficult problem in steel plants. To [...] Read more.
Steelmaking and the continuous-casting (SCC) scheduling problem is a realistic hybrid flow shop scheduling problem with continuous-casting production at the last stage. This study considers the SCC scheduling problem with diverse products, which is a vital and difficult problem in steel plants. To tackle this problem, this study first presents the mixed-integer linear programming (MILP) model to minimize the objective of makespan. Then, an improved migrating birds optimization algorithm (IMBO) is proposed to tackle this considered NP-hard problem. In the proposed IMBO, several improvements are employed to achieve the proper balance between exploration and exploitation. Specifically, a two-level decoding procedure is designed to achieve feasible solutions; the simulated annealing-based acceptance criterion is employed to ensure the diversity of the population and help the algorithm to escape from being trapped in local optima; a competitive mechanism is developed to emphasize exploitation capacity by searching around the most promising solution space. The computational experiments demonstrate that the proposed IMBO obtains competing performance and it outperforms seven other implemented algorithms in the comparative study. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
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Open AccessArticle
Arithmetics of Vectors of Fuzzy Sets
Mathematics 2020, 8(9), 1614; https://doi.org/10.3390/math8091614 - 18 Sep 2020
Viewed by 338
Abstract
The arithmetic operations of fuzzy sets are completely different from the arithmetic operations of vectors of fuzzy sets. In this paper, the arithmetic operations of vectors of fuzzy intervals are studied by using the extension principle and a form of decomposition theorem. These [...] Read more.
The arithmetic operations of fuzzy sets are completely different from the arithmetic operations of vectors of fuzzy sets. In this paper, the arithmetic operations of vectors of fuzzy intervals are studied by using the extension principle and a form of decomposition theorem. These two different methodologies lead to the different types of membership functions. We establish their equivalences under some mild conditions. On the other hand, the α-level sets of addition, difference and scalar products of vectors of fuzzy intervals are also studied, which will be useful for the different usage in applications. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
Open AccessArticle
Minkowski Weighted Score Functions of Intuitionistic Fuzzy Values
Mathematics 2020, 8(7), 1143; https://doi.org/10.3390/math8071143 - 13 Jul 2020
Cited by 1 | Viewed by 484
Abstract
In multiple attribute decision-making in an intuitionistic fuzzy environment, the decision information is sometimes given by intuitionistic fuzzy soft sets. In order to address intuitionistic fuzzy decision-making problems in a more efficient way, many scholars have produced increasingly better procedures for ranking intuitionistic [...] Read more.
In multiple attribute decision-making in an intuitionistic fuzzy environment, the decision information is sometimes given by intuitionistic fuzzy soft sets. In order to address intuitionistic fuzzy decision-making problems in a more efficient way, many scholars have produced increasingly better procedures for ranking intuitionistic fuzzy values. In this study, we further investigate the problem of ranking intuitionistic fuzzy values from a geometric point of view, and we produce related applications to decision-making. We present Minkowski score functions of intuitionistic fuzzy values, which are natural generalizations of the expectation score function and other useful score functions in the literature. The rationale for Minkowski score functions lies in the geometric intuition that a better score should be assigned to an intuitionistic fuzzy value farther from the negative ideal intuitionistic fuzzy value. To capture the subjective attitude of decision makers, we further propose the Minkowski weighted score function that incorporates an attitudinal parameter. The Minkowski score function is a special case corresponding to a neutral attitude. Some fundamental properties of Minkowski (weighted) score functions are examined in detail. With the aid of the Minkowski weighted score function and the maximizing deviation method, we design a new algorithm for solving decision-making problems based on intuitionistic fuzzy soft sets. Moreover, two numerical examples regarding risk investment and supplier selection are employed to conduct comparative analyses and to demonstrate the feasibility of the approach proposed in this article. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
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