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Various Generalizations of Fuzzy Sets and Their Applications in Engineering...
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Various Generalizations of Fuzzy Sets and Their Applications in Engineering and Management

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 January 2025 | Viewed by 3576

Special Issue Editor

Dr. Jeevaraj Selvaraj

E-Mail Website
Guest Editor
Department of Applied Sciences (Mathematics), Atal Bihari Vajpayee Indian Institute of Information Technology and Management, Gwalior 474015, India
Interests: fuzzy mathematics; soft computing; fuzzy decision making; fuzzy information system; fuzzy and intuitionistic fuzzy approximation; similarity measures; aggregation operators

Special Issue Information

Dear Colleagues,

Real-life problems involving incomplete and inadequate information cannot be modelled well using classical (crisp) sets. To better model real-life problems, fuzzy sets were introduced in the literature. Further, many generalizations of fuzzy sets have been developed to solve real-life engineering problems. Fuzzy sets and their generalizations have wide applications in the field of image processing, information retrieval, data mining, etc. As we know, real-life data collection with respect to a specific management problem involves imprecise and incomplete information. Hence, we also plan to discuss various decision-making methods used to potentially solve such problems. Most appropriate and realistic decisions are possible when we model a problem using fuzzy sets and their generalizations. The main aim of this Special Issue is to study the various generalizations of fuzzy sets mathematically. Additionally, we aim to host discussions on the wide range of applications of these generalizations in solving real-life engineering and management problems. This Special issue provides a platform for researchers worldwide to discuss their present and unpublished work in the fields of engineering and management. In this Special Issue, original research articles and reviews are welcome. Research areas may include (but not limited to) the following:

  • Ranking of fuzzy and intuitionistic fuzzy numbers
  • Aggregation operators on various classes of fuzzy sets and their generalizations
  • Similarity measures on various generalizations of fuzzy sets
  • Distance measure-based similarity measures
  • Information retrieval applications
  • Image processing applications
  • Fermatean fuzzy sets and their applications in decision-making.

Dr. Jeevaraj Selvaraj
Guest Editor

Manuscript Submission Information

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Keywords

  • intuitionistic fuzzy sets
  • trapezoidal intuitionistic fuzzy number
  • Fermatean fuzzy sets
  • hesitant fuzzy sets
  • multi-criteria decision making
  • similarity measure
  • aggregation operators
  • image processing
  • fuzzy and intuitionistic fuzzy clustering
  • fuzzy applications in operations research
  • divergence measure

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Published Papers (4 papers)

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Research

21 pages, 326 KiB  
Article
Einstein Exponential Operational Laws Based on Fractional Orthotriple Fuzzy Sets and Their Applications in Decision Making Problems
by Muhammad Qiyas, Darjan Karabasevic, Neelam Khan and Srdjan Maričić
Mathematics 2024, 12(20), 3216; https://doi.org/10.3390/math12203216 - 14 Oct 2024
Viewed by 618
Abstract
The fractional orthotriple fuzzy set (FOFS) model is a recently created extension of fuzzy sets (FS) for coping with ambiguity in DM. The purpose of this study is to define new exponential and Einstein exponential operational (EO) laws for fractional orthotriple fuzzy sets [...] Read more.
The fractional orthotriple fuzzy set (FOFS) model is a recently created extension of fuzzy sets (FS) for coping with ambiguity in DM. The purpose of this study is to define new exponential and Einstein exponential operational (EO) laws for fractional orthotriple fuzzy sets and the aggregation procedures that accompany them. We present the operational laws for exponential and Einstein exponential FOFSs which have crisp numbers as base values and fractional orthotriple fuzzy numbers as exponents (weights). The proposed operations’ qualities and characteristics are then explored. Based on the defined operation laws regulations, various new FOFS aggregation operators, named as fractional orthotriple fuzzy weighted exponential averaging (FOFWEA), fractional orthotriple fuzzy ordered weighted exponential averaging (FOFOWEA), fractional orthotriple fuzzy hybrid weighted averaging (FOFHWEA), fractional orthotriple fuzzy Einstein weighted exponential averaging (FOFEWEA), fractional orthotriple fuzzy Einstein ordered weighted exponential averaging (FOFEOWEA), and fractional orthotriple fuzzy Einstein hybrid weighted exponential averaging (FOFEHWEA) operators are presented. A decision-making algorithm based on the newly defined aggregation operators is proposed and applied to a multicriteria group decision-making (MCGDM) problem related to bank security. Finally, we compare our proposed method with other existing methods. Full article
(This article belongs to the Special Issue Various Generalizations of Fuzzy Sets and Their Applications in Engineering and Management)
15 pages, 269 KiB  
Article
Fuzzy Assessment Mechanisms under Multi-Objective Considerations
by Yu-Hsien Liao
Mathematics 2024, 12(19), 3074; https://doi.org/10.3390/math12193074 - 30 Sep 2024
Viewed by 360
Abstract
In many operational environments, it is essential to conduct comprehensive minimal assessments of the effects arising from various operational causes, with the goal of achieving effective outcomes. For instance, the aim might be to meet basic production targets in the shortest time possible, [...] Read more.
In many operational environments, it is essential to conduct comprehensive minimal assessments of the effects arising from various operational causes, with the goal of achieving effective outcomes. For instance, the aim might be to meet basic production targets in the shortest time possible, using the least cost and minimal labor. Given that actual operational behaviors are often vague and unpredictable, this study proposes a mechanism to assess the minimal effects generated by various operational causes under multi-objective and fuzzy behavior considerations. By considering the relative significance of operational causes or its behaviors under different environments, several weighted extensions are further developed. The mathematical correctness and practical applicability of these assessment mechanisms are analyzed by using an axiomatic characterization. Full article
(This article belongs to the Special Issue Various Generalizations of Fuzzy Sets and Their Applications in Engineering and Management)
19 pages, 346 KiB  
Article
A Few Similarity Measures on the Class of Trapezoidal-Valued Intuitionistic Fuzzy Numbers and Their Applications in Decision Analysis
by Jeevaraj Selvaraj and Melfi Alrasheedi
Mathematics 2024, 12(9), 1311; https://doi.org/10.3390/math12091311 - 25 Apr 2024
Cited by 1 | Viewed by 838
Abstract
Similarity measures on trapezoidal-valued intuitionistic fuzzy numbers (TrVIFNs) are functions that measure the closeness between two TrVIFNs, which has a lot of applications in the area of pattern recognition, clustering, decision-making, etc. Researchers around the world are proposing various similarity measures on the [...] Read more.
Similarity measures on trapezoidal-valued intuitionistic fuzzy numbers (TrVIFNs) are functions that measure the closeness between two TrVIFNs, which has a lot of applications in the area of pattern recognition, clustering, decision-making, etc. Researchers around the world are proposing various similarity measures on the generalizations of fuzzy sets. However, many such measures do not satisfy the condition that “the similarity between two fuzzy numbers is equal to 1 implies that both the fuzzy numbers are equal” and this gives a pathway for the researchers to introduce different similarity measures on various classes of fuzzy sets. Also, all of them try to find out the similarity by using a single function, and in the present study, we try to propose a combined similarity measure principle by using four functions (four similarity measures). Thus, the main aim of this work is to introduce a few sets of similarity measures on the class of TrVIFNs and propose a combined similarity measure principle on TrVIFNs based on the proposed similarity measures. To do this, in this paper, firstly, we propose four distance-based similarity measures on TrVIFNs using score functions on TrVIFNs and study their mathematical properties by establishing various propositions, theorems, and illustrations, which is achieved by using numerical examples. Secondly, we propose the idea of a combined similarity measure principle by using the four proposed similarity measures sequentially, which is a first in the literature. Thirdly, we compare our combined similarity measure principle with a few important similarity measures introduced on various classes of fuzzy numbers, which shows the need for and efficacy of the proposed similarity measures over the existing methods. Fourthly, we discuss the trapezoidal-valued intuitionistic fuzzy TOPSIS (TrVIF-TOPSIS) method, which uses the proposed combined similarity measure principle for solving a multi-criteria decision-making (MCDM) problem. Then, we discuss the applicability of the proposed modified TrVIF-TOPSIS method by solving a model problem. Finally, we discuss the sensitivity analysis of the proposed approaches by using various cases. Full article
(This article belongs to the Special Issue Various Generalizations of Fuzzy Sets and Their Applications in Engineering and Management)
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11 pages, 572 KiB  
Article
Fuzzy Testing Method of Process Incapability Index
by Kuen-Suan Chen, Tsun-Hung Huang, Jin-Shyong Lin, Wen-Yang Kao and Wei Lo
Mathematics 2024, 12(5), 623; https://doi.org/10.3390/math12050623 - 20 Feb 2024
Viewed by 686
Abstract
The process capability index is a tool for quality measurement and analysis widely used in the industry. It is also a good tool for the sales department to communicate with customers. Although the value of the process capability index can be affected by [...] Read more.
The process capability index is a tool for quality measurement and analysis widely used in the industry. It is also a good tool for the sales department to communicate with customers. Although the value of the process capability index can be affected by the accuracy and precision of the process, the index itself cannot be differentiated. Therefore, the process incapability index is directly divided into two items, accuracy and precision, based on the expected value of the Taguchi process loss function. In fact, accuracy and precision are two important reference items for improving the manufacturing process. Thus, the process incapability index is good for evaluating process quality. The process incapability index contains two unknown parameters, so it needs to be estimated with sample data. Since point estimates are subject to misjudgment incurred by the inaccuracy of sampling, and since modern businesses are in the era of rapid response, the size of sampling usually tends to be small. A number of studies have suggested that a fuzzy testing method built on the confidence interval be adopted at this time because it integrates experts and the experience accumulated in the past. In addition to a decrease in the possibility of misjudgment resulting from sampling error, this method can improve the test accuracy. Therefore, based on the confidence interval of the process incapability index, we proposed the fuzzy testing method to assess whether the process capability can attain a necessary level of quality. If the quality level fails to meet the requirement, then an improvement must be made. If the quality level exceeds the requirement, then it is equivalent to excess quality, and a resource transfer must be considered to reduce costs. Full article
(This article belongs to the Special Issue Various Generalizations of Fuzzy Sets and Their Applications in Engineering and Management)
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