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Mathematics
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Fuzzy Sets and Fuzzy Systems
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Fuzzy Sets and Fuzzy Systems

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: 31 August 2024 | Viewed by 6420

Special Issue Editors

Dr. Dipak Kumar Jana

E-Mail Website
Guest Editor
School of Applied Science & Humanities, Haldia Institute of Technology, Haldia 721657, West Bengal, India
Interests: operations research; fuzzy; inventory; uncertain theory; biomathematics; transportation; fuzzy set; rough set; optimal control; fuzzy inference
Prof. Dr. Petr Dostál

E-Mail Website
Guest Editor
Faculty of Business and Management, Brno University of Technology, 60190 Brno, Czech
Interests: fuzzy logic; artificial neural networks

Special Issue Information

Dear Colleagues,

Over time, the concepts of cost, time, delivery, space, quality, durability, and price began to gain more significance in the emerging trends of information technology when it comes to solving managerial decision-making problems in supply chain models, transportation issues, inventory control issues, etc. Additionally, in uncertain situations, competition is becoming more difficult by the day. For instance, a number of diverse aspects, such as the cost of manufacturing, one's degree of income, and others, frequently influence consumer demand. In these situations, the demand is either still unmet or remarkably hard to meet in the real-world market. Due to their numeric membership functions, fuzzy sets cannot always represent this uncertainty explicitly. However, it has been discovered that type two random fuzzy, bifuzzy, and fuzzy random sets are more suited to account for intrinsic uncertainty. These various fuzzy systems are able to manage greater degrees of ambiguity in increasingly difficult real-world issues. However, it is crucial to employ optimization techniques in order to obtain the ideal design as diverse fuzzy systems grow more complicated to conceive.

We invite both academics and industrial engineering, as well as management professionals, to submit original high-quality articles to this Special Issue addressing novel ideas in the following areas: green supply chains, inventory control issues, transportation issues, and novel information for topics from both theoretical and practical perspectives in fuzzy, random fuzzy, bifuzzy, type two fuzzy, and random environments.

  1. Fuzzy set theory and applications;
  2. Bifuzzy, fuzzy random theory and applications;
  3. Type two fuzzy and engineering applications;
  4. Possibility, necessity, and credibility measures;
  5. Fuzzy differential equations, modeling, and simulation;
  6. Bifuzzy, random fuzzy, fuzzy rough, and rough expectations;
  7. PID, FLC controllers, soft computing, and fuzzy logic;
  8. Application areas in operations research, ANNs, WSNs, and artificial intelligence;
  9. Design of nonlinear controllers;
  10. Type two fuzzy controllers;
  11. Intuitionistic fuzzy logic;
  12. All real-life applications.

Dr. Dipak Kumar Jana
Prof. Dr. Petr Dostál
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

  • fuzzy set
  • type two fuzzy
  • optimization
  • computational economics
  • soft computing
  • fuzzy expert systems
  • ANN
  • RSM

Published Papers (5 papers)

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Research

18 pages, 373 KiB  
Article
The Operational Laws of Symmetric Triangular Z-Numbers
by Hui Li, Xuefei Liao, Zhen Li, Lei Pan, Meng Yuan and Ke Qin
Mathematics 2024, 12(10), 1443; https://doi.org/10.3390/math12101443 - 8 May 2024
Viewed by 270
Abstract
To model fuzzy numbers with the confidence degree and better account for information uncertainty, Zadeh came up with the notion of Z-numbers, which can effectively combine the objective information of things with subjective human interpretation of perceptive information, thereby improving the human comprehension [...] Read more.
To model fuzzy numbers with the confidence degree and better account for information uncertainty, Zadeh came up with the notion of Z-numbers, which can effectively combine the objective information of things with subjective human interpretation of perceptive information, thereby improving the human comprehension of natural language. Although many numbers are in fact Z-numbers, their higher computational complexity often prevents their recognition as such. In order to reduce computational complexity, this paper reviews the development and research direction of Z-numbers and deduces the operational rules for symmetric triangular Z-numbers. We first transform them into classical fuzzy numbers. Using linear programming, the extension principle of Zadeh, the convolution formula, and fuzzy number algorithms, we determine the operational rules for the basic operations of symmetric triangular Z-numbers, which are number-multiplication, addition, subtraction, multiplication, power, and division. Our operational rules reduce the complexity of calculation, improve computational efficiency, and effectively reduce the information difference while being applicable to other complex operations. This paper innovatively combines Z-numbers with classical fuzzy numbers in Z-number operations, and as such represents a continuation and innovation of the research on the operational laws of Z-numbers. Full article
(This article belongs to the Special Issue Fuzzy Sets and Fuzzy Systems)
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14 pages, 242 KiB  
Article
Ideals and Homomorphism Theorems of Fuzzy Associative Algebras
by Xiaoman Yang and Xin Zhou
Mathematics 2024, 12(8), 1125; https://doi.org/10.3390/math12081125 - 9 Apr 2024
Viewed by 448
Abstract
Based on the definitions of fuzzy associative algebras and fuzzy ideals, it is proven that the intersections of fuzzy subalgebras are fuzzy subalgebras, and the intersections of fuzzy ideals are fuzzy ideals. Moreover, we prove that the kernels of fuzzy homomorphisms are fuzzy [...] Read more.
Based on the definitions of fuzzy associative algebras and fuzzy ideals, it is proven that the intersections of fuzzy subalgebras are fuzzy subalgebras, and the intersections of fuzzy ideals are fuzzy ideals. Moreover, we prove that the kernels of fuzzy homomorphisms are fuzzy ideals. Using fuzzy ideals, the quotient structures of fuzzy associative algebras are constructed, their corresponding properties are discussed, and their homomorphism theorems are proven. Full article
(This article belongs to the Special Issue Fuzzy Sets and Fuzzy Systems)
12 pages, 307 KiB  
Article
On Nash Equilibria in a Finite Game for Fuzzy Sets of Strategies
by Svajone Bekesiene and Serhii Mashchenko
Mathematics 2023, 11(22), 4619; https://doi.org/10.3390/math11224619 - 11 Nov 2023
Cited by 2 | Viewed by 652
Abstract
The present paper investigates a finite game with fuzzy sets of player strategies. It is proven that Nash equilibria constitute a type-2 fuzzy set defined on the universal set of strategy profiles. Furthermore, the corresponding type-2 membership function is provided. This paper demonstrates [...] Read more.
The present paper investigates a finite game with fuzzy sets of player strategies. It is proven that Nash equilibria constitute a type-2 fuzzy set defined on the universal set of strategy profiles. Furthermore, the corresponding type-2 membership function is provided. This paper demonstrates that the Nash equilibria type-2 fuzzy set of the game can be decomposed based on the secondary membership grades into a finite collection of crisp sets. Each of these crisp sets represents the Nash equilibria set of the corresponding game with crisp sets of player strategies. A characteristic feature of the proposed decomposition approach is its independence from the chosen method for calculating the Nash equilibria in crisp subgames. Some properties of game equilibria T2FSs are studied. These sets correspond to specific partitions or cuts of the original fuzzy sets of player strategies. An illustrative example is also included for clarity. Full article
(This article belongs to the Special Issue Fuzzy Sets and Fuzzy Systems)
15 pages, 4529 KiB  
Article
A Cloud-Based Software Defect Prediction System Using Data and Decision-Level Machine Learning Fusion
by Shabib Aftab, Sagheer Abbas, Taher M. Ghazal, Munir Ahmad, Hussam Al Hamadi, Chan Yeob Yeun and Muhammad Adnan Khan
Mathematics 2023, 11(3), 632; https://doi.org/10.3390/math11030632 - 26 Jan 2023
Cited by 3 | Viewed by 1984
Abstract
This research contributes an intelligent cloud-based software defect prediction system using data and decision-level machine learning fusion techniques. The proposed system detects the defective modules using a two-step prediction method. In the first step, the prediction is performed using three supervised machine learning [...] Read more.
This research contributes an intelligent cloud-based software defect prediction system using data and decision-level machine learning fusion techniques. The proposed system detects the defective modules using a two-step prediction method. In the first step, the prediction is performed using three supervised machine learning techniques, including naïve Bayes, artificial neural network, and decision tree. These classification techniques are iteratively tuned until the maximum accuracy is achieved. In the second step, the final prediction is performed by fusing the accuracy of the used classifiers with a fuzzy logic-based system. The proposed fuzzy logic technique integrates the predictive accuracy of the used classifiers using eight if–then fuzzy rules in order to achieve a higher performance. In the study, to implement the proposed fusion-based defect prediction system, five datasets were fused, which were collected from the NASA repository, including CM1, MW1, PC1, PC3, and PC4. It was observed that the proposed intelligent system achieved a 91.05% accuracy for the fused dataset and outperformed other defect prediction techniques, including base classifiers and state-of-the-art ensemble techniques. Full article
(This article belongs to the Special Issue Fuzzy Sets and Fuzzy Systems)
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36 pages, 4333 KiB  
Article
A Sustainable Green Supply Chain Model with Carbon Emissions for Defective Items under Learning in a Fuzzy Environment
by Basim S. O. Alsaedi, Osama Abdulaziz Alamri, Mahesh Kumar Jayaswal and Mandeep Mittal
Mathematics 2023, 11(2), 301; https://doi.org/10.3390/math11020301 - 6 Jan 2023
Cited by 10 | Viewed by 2041
Abstract
Assuming the significance of sustainability, it is considered necessary to ensure the conservation of our natural resources, in addition to minimizing waste. To promote significant sustainable effects, factors including production, transportation, energy usage, product control management, etc., act as the chief supports of [...] Read more.
Assuming the significance of sustainability, it is considered necessary to ensure the conservation of our natural resources, in addition to minimizing waste. To promote significant sustainable effects, factors including production, transportation, energy usage, product control management, etc., act as the chief supports of any modern supply chain model. The buyer performs the firsthand inspection and returns any defective items received from the customer to the vendor in a process that is known as first-level inspection. The vendor uses the policy of recovery product management to obtain greater profit. A concluding inspection is accomplished at the vendor’s end in order to distinguish the returned item as belonging to one of four specific categories, namely re-workable, reusable, recyclable, and disposable, a process that is known as second-level inspection. Then, it is observed that some defective items are suitable for a secondary market, while some are reusable, and some can be disassembled to shape new derived products, and leftovers can be scrapped at the disposal cost. This ensures that we can meet our target to promote a cleaner drive with a lower percentage of carbon emissions, reducing the adverse effects of landfills. The activity of both players in this model is presented briefly in the flowchart shown in the abstract. Thus, our aim of product restoration is to promote best practices while maintaining economic value, with the ultimate goal of removing the surrounding waste with minimum financial costs. In this regard, it is assumed that the demand rate is precise in nature. The learning effect and fuzzy environment are also considered in the present model. The proposed model studies the impacts of learning and carbon emissions on an integrated green supply chain model for defective items in fuzzy environment and shortage conditions. We optimized the integrated total fuzzy profit with respect to the order quantity and shortages. We described the vendor’s strategy and buyer’s strategy through flowcharts for the proposed integrated supply chain model, and here, in the flowchart, R-R-R stands for re-workable, reusable, and recyclable. The demand rate was treated as a triangular fuzzy number. In this paper, a numerical example, sensitivity analysis, limitations, future scope, and conclusion are presented for the validation of the proposed model. Full article
(This article belongs to the Special Issue Fuzzy Sets and Fuzzy Systems)
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