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Axioms
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The Application of Fuzzy Decision-Making Theory and Method
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The Application of Fuzzy Decision-Making Theory and Method

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Logic".

Deadline for manuscript submissions: closed (20 June 2024) | Viewed by 13210

Special Issue Editors

Prof. Jun Ye

E-Mail Website
Guest Editor
School of Civil and Environmental Engineering, Ningbo University, Ningbo 315211, China
Interests: soft computing; fuzzy decision theory and method; robot intelligent control; pattern recognition and fault diagnosis; neutrosophic theory; rock mechanics; engineering modeling; optimization design
Special Issues, Collections and Topics in MDPI journals
Dr. Yanhui Guo

E-Mail Website
Guest Editor
Department of Data Analytics, University of Illinois Springfield, Springfield, IL 62703, USA
Interests: image processing; medical image processing; pattern recognition; computer vision; data science
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Shuping Wan

E-Mail Website
Guest Editor
School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China
Interests: decision making; fuzzy theory and applications; soft computing; decision making theory and method; game theory and information fusion

Special Issue Information

Dear Colleagues,

Since imprecision, incompleteness, and uncertainty are rife in real-life problems, the fuzzy theory proposed by Zadeh has been widely applied in various fields. Thus, the actual decision problem becomes more and more complex in current decision-making environments. Therefore, it is difficult for classical fuzzy theory to deal with complicated decision-making problems in imprecise, incomplete, inconsistent, and indeterminate environments. In these cases, classical fuzzy theory has been extended to hesitant fuzzy theory, fuzzy multivalued theory, fuzzy cubic theory, intuitionistic fuzzy theory, neutrosophic theory, and so on. Many advanced fuzzy theories are gaining significant attention in fuzzy decision-making areas, and more and more researchers have developed various fuzzy decision-making theories, methods, and applications. Especially in recent years, various advanced fuzzy theories and decision-making methods have led to new developments and achievements in various fuzzy decision-making theories, methods, and applications in the science and engineering fields.

The focus of this Special Issue is on advanced fuzzy theories and methods to solve various fuzzy decision-making problems and applications. All articles submitted to this Special Issue may also focus on various advanced fuzzy decision theories and methods, and applications in the science and engineering fields. We invite researchers to contribute original research articles and review articles, which will motivate continuous research on various fuzzy decision-making theories and methods and applications to solve different decision-making problems in imprecise, incomplete, and uncertain environments.

Prof. Jun Ye
Dr. Yanhui Guo
Prof. Dr. Shuping Wan
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. Axioms is an international peer-reviewed open access monthly 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 2400 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 decision-making theory, method, and application
  • fuzzy credibility number decision-making theory, method, and applicatio
  • fuzzy multivalued decision-making theory, method, and application
  • fuzzy cubic decision-making theory, method, and application
  • cubic fuzzy multivalued decision-making theory, method, and application
  • hesitant fuzzy decision-making theory, method, and application
  • intuitionistic fuzzy decision-making theory, method, and application
  • intuitionistic fuzzy/orthopair Z-number decision-making theory, method, and application
  • intuitionistic fuzzy credibility number decision-making theory, method, and application
  • neutrosophic decision-making theory, method, and application
  • neutrosophic Z-number decision-making theory, method, and application
  • neutrosophic multivalued decision-making theory, method, and application

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Published Papers (8 papers)

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Research

9 pages, 932 KiB  
Article
Neutrosophic Analysis of Experimental Data Using Neutrosophic Graeco-Latin Square Design
by Pranesh Kumar, Mahdieh Moazzamigodarzi and Mohamadtaghi Rahimi
Axioms 2024, 13(8), 559; https://doi.org/10.3390/axioms13080559 - 16 Aug 2024
Viewed by 661
Abstract
Experimental designs are commonly used to produce valid, defensible, and supportable conclusions. Among commonly used block designs, the class of Latin square designs is used to study factors or treatment levels expressed as Latin letters and applying two blocking factors in rows and [...] Read more.
Experimental designs are commonly used to produce valid, defensible, and supportable conclusions. Among commonly used block designs, the class of Latin square designs is used to study factors or treatment levels expressed as Latin letters and applying two blocking factors in rows and columns to simultaneously control two sources of nuisance variability. Another block design in which the error can be controlled by blocking three nuisance factors is obtained by simply using two superimposed Latin square designs, with one using the Latin letters and the other using the Greek letters. Such a design is termed as a Graeco-Latin square (GLS) design. While observing or measuring data in field or lab experiments, it is often noted to have vague, incomplete, and imprecise data for whatsoever reasons. In this regard, researchers have proposed various emerging approaches, which are based on fuzzy, intuitionistic fuzzy, and neutrosophic logic, and provide deeper understanding, analysis, and interpretations of the data. In this paper, we provide a brief review of the history of GLS designs and propose a neutrosophic Graeco-Latin square design, its model, and the analysis. To illustrate this, we have considered an experimental study which analyzes the effects of different formulations of a rocket propellant, which are used in aircrew escape systems, on the observed burning rate. Full article
(This article belongs to the Special Issue The Application of Fuzzy Decision-Making Theory and Method)
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25 pages, 3202 KiB  
Article
Fuzzy Algorithm Applied to Factors Influencing Competitiveness: A Case Study of Brazil and Peru through Affinities Theory
by Luciano Barcellos-Paula, Aline Castro-Rezende and Daniela Fantoni Alvares
Axioms 2023, 12(11), 1038; https://doi.org/10.3390/axioms12111038 - 8 Nov 2023
Cited by 1 | Viewed by 1950
Abstract
Innovation plays a crucial role in the economy of nations worldwide. In Latin America, countries foster competitiveness through public and private incentives to support innovation. Moreover, entrepreneurship incentives seek to improve countries’ performance, although factors such as low business growth rates and informality [...] Read more.
Innovation plays a crucial role in the economy of nations worldwide. In Latin America, countries foster competitiveness through public and private incentives to support innovation. Moreover, entrepreneurship incentives seek to improve countries’ performance, although factors such as low business growth rates and informality can compromise it. Despite the efforts, there are several difficulties in achieving competitiveness, and few studies in developing countries. Therefore, the article explores the relationship between the factors that influence competitiveness, especially the role of innovation and entrepreneurship in Brazil and Peru. The research uses quantitative-qualitative methodology through modeling and simulation and a case study. The authors use the Affinities Theory to verify the relationship between the indicators that make up the competitiveness landscape and its most significant and attractive factors, adapting the methodology established by the International Institute for Management Development (IMD) World Competitiveness ranking. As a result, this algorithm allows us to know the relationships between five factors of economic attractiveness and four competitiveness indicators. As its main contributions, the study advances the frontier of knowledge about innovation and entrepreneurship, as few studies explore competitiveness in developing countries. Also, it offers a detailed explanation of the application of this algorithm, allowing researchers to reproduce this methodology in other scenarios. Practically, it might support policymakers in formulating development strategies and stimuli for business competitiveness. In addition, academic and business leaders can strengthen university-business collaboration with applied research in innovation and entrepreneurship. One limitation would be the number of countries participating in the research. The authors suggest future lines of research. Full article
(This article belongs to the Special Issue The Application of Fuzzy Decision-Making Theory and Method)
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27 pages, 888 KiB  
Article
Probabilistic Interval-Valued Fermatean Hesitant Fuzzy Set and Its Application to Multi-Attribute Decision Making
by Chuanyang Ruan and Xiangjing Chen
Axioms 2023, 12(10), 979; https://doi.org/10.3390/axioms12100979 - 17 Oct 2023
Cited by 4 | Viewed by 1516
Abstract
It is difficult to describe the hesitation and uncertainty of experts by single-valued information, and the differences in the importance of attributes are often ignored during the decision-making process. This paper introduces the probability and interval values into Fermatean hesitant fuzzy set (FHFS) [...] Read more.
It is difficult to describe the hesitation and uncertainty of experts by single-valued information, and the differences in the importance of attributes are often ignored during the decision-making process. This paper introduces the probability and interval values into Fermatean hesitant fuzzy set (FHFS) and creatively proposes the probabilistic interval-valued Fermatean hesitant fuzzy set (PIVFHFS) to deal with information loss. This new fuzzy set allows decision makers to use interval-valued information with probability to express their quantitative evaluation, which broadens the range of information expression, effectively reflects the important degree of different membership degrees, and can describe uncertain information more completely and accurately. Under the probabilistic interval-valued Fermatean hesitant fuzzy environment, several new aggregation operators based on Hamacher operation are proposed, including the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher weighted averaging (PIVFHFHWA) operator and geometric (PIVFHFHWG) operator, and their basic properties and particular forms are studied. Then, considering the general correlation between different attributes, this paper defines the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher Choquet integral averaging (PIVFHFHCIA) operator and geometric (PIVFHFHCIG) operator and discusses related properties. Finally, a multi-attribute decision-making (MADM) method is presented and applied to the decision-making problem of reducing carbon emissions of manufacturers in the supply chain. The stability and feasibility of this method are demonstrated by sensitivity analysis and comparative analysis. The proposed new operators can not only consider the correlation between various factors but also express the preference information of decision makers more effectively by using probability, thus avoiding information loss in decision-making progress to some extent. Full article
(This article belongs to the Special Issue The Application of Fuzzy Decision-Making Theory and Method)
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25 pages, 6422 KiB  
Article
Evaluation of Key Factors for Promoting Green Construction Practices Based on a Hybrid Decision-Making Framework: A Case Study on the Renovation of Old Residential Communities in China
by Guoshuai Sun, Mingzhu Li, Jiuying Dong, Shuping Wan and Jiao Feng
Axioms 2023, 12(10), 971; https://doi.org/10.3390/axioms12100971 - 16 Oct 2023
Cited by 1 | Viewed by 1496
Abstract
The multi-criteria group decision-making approach, rooted in fuzzy mathematics theory, is employed to address the globally significant issue of green construction in this paper. The construction industry is one of the most prominent contributors to carbon emissions, which is evident throughout the entire [...] Read more.
The multi-criteria group decision-making approach, rooted in fuzzy mathematics theory, is employed to address the globally significant issue of green construction in this paper. The construction industry is one of the most prominent contributors to carbon emissions, which is evident throughout the entire supply chain. Meanwhile, the renovation of old residential communities is a large-scale urban construction project in China. In striving to advance the sustainable development of the construction industry and meet decarbonization goals, the attention has shifted towards green construction in the renovation of old residential communities. However, substantial gaps persist in both technical innovation and practical application of green construction. This study aims to identify the factors that influence the popularization and implementation of green construction practices in the renovation of old residential communities. To achieve this, a comprehensive decision-making approach is sought, and these factors are thoroughly investigated. In this paper, we propose a hybrid decision-making framework that incorporates grounded theory, the fuzzy decision-making and trial evaluation laboratory (DEMATEL) method, and the analytic network process (ANP) method. Leveraging triangular fuzzy numbers and other fuzzy mathematical theories, this approach is designed to assess the factors that influence the popularization and implementation of green construction practices, uncovering their interrelationships and mechanisms. The results indicate the comprehensive nature of advancing green construction practices, encompassing the entire supply chain involved in the renovation of old residential communities. Among these factors, social participation and market environment emerge as the most influential. Building upon these conclusions, this paper offers specific recommendations. Ultimately, this study equips the construction industry with both a theoretical foundation and a methodological framework to popularize and implement green construction practices effectively. Full article
(This article belongs to the Special Issue The Application of Fuzzy Decision-Making Theory and Method)
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20 pages, 722 KiB  
Article
Leadership Competencies in the Financial Industry during Digital Transformation: An Evaluation Framework Using the Z-DEMATEL Technique
by Min-Hsu Wang, Chien-Cheng Chen, Kai-Ying Chen and Huai-Wei Lo
Axioms 2023, 12(9), 855; https://doi.org/10.3390/axioms12090855 - 3 Sep 2023
Cited by 6 | Viewed by 2271
Abstract
In today’s digital age, the financial industry, a cornerstone of the global economy, is undergoing monumental shifts. While business performance hinges on proficient leadership, the seismic wave of digital transformation poses new challenges and magnifies the need for specific leadership competencies. The urgency [...] Read more.
In today’s digital age, the financial industry, a cornerstone of the global economy, is undergoing monumental shifts. While business performance hinges on proficient leadership, the seismic wave of digital transformation poses new challenges and magnifies the need for specific leadership competencies. The urgency is clear: adapt or become obsolete. However, there is a lack of clarity regarding which competencies are essential during such transformations. To address this gap, the purpose of this study is to identify the leadership competencies that leaders in the financial industry should possess during the digital transformation process and to determine the influential relationships among these competencies and which ones are highly influential. This paper extensively investigates the criteria for evaluating leadership competencies and integrates expert judgments to construct an evaluation framework for leadership competencies during digital transformation. The Z-based decision-making trial and evaluation laboratory (Z-DEMATEL) technique was applied to identify the influential relationships among the criteria and generate influence weights for each criterion. In addition, based on the results of Z-DEMATEL, an Influence Classification Map (ICM) was plotted that categorized the criteria into four groups: core, driving, independent, and impact. Management implications and improvement suggestions are provided accordingly. Z-DEMATEL enhances the general form of fuzzy DEMATEL. By integrating the Z-fuzzy theory, Z-DEMATEL not only accounts for the uncertainty of the evaluation environment but also measures the confidence level of experts. Taking Taiwan’s financial industry as a case study, this study revealed that “vision and imagination,” “critical analysis,” and “strategic perspective” were the top three criteria with higher weights, while “critical analysis” and “interpersonal sensitivity” were the core criteria. Business managers can use the results to design leadership training programs that meet the requirements of digital transformation and ultimately improve the performance of organizations during the transformation. Moreover, the concepts and methods presented in this study can be applied to other industries that are embarking on their digital transformation journeys. Full article
(This article belongs to the Special Issue The Application of Fuzzy Decision-Making Theory and Method)
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10 pages, 263 KiB  
Article
MAGDM Model Using an Intuitionistic Fuzzy Matrix Energy Method and Its Application in the Selection Issue of Hospital Locations
by Weiming Li and Jun Ye
Axioms 2023, 12(8), 766; https://doi.org/10.3390/axioms12080766 - 5 Aug 2023
Cited by 4 | Viewed by 1088
Abstract
Matrix energy is a valid mathematical tool for representing collective information. However, it is not used in the existing literature for fuzzy sets, intuitionistic fuzzy sets, and multi-attribute group decision making (MAGDM) problems, which highlights research gaps. Motivated by both matrix energy and [...] Read more.
Matrix energy is a valid mathematical tool for representing collective information. However, it is not used in the existing literature for fuzzy sets, intuitionistic fuzzy sets, and multi-attribute group decision making (MAGDM) problems, which highlights research gaps. Motivated by both matrix energy and the research gaps, this study aims to extend matrix energy to the energy of an intuitionistic fuzzy matrix (IFM) and to utilize the IFM energy method in the MAGDM problem, which fully contains all the IFM information on attribute weights, decision maker weights, and attribute values. To achieve these objectives, this paper first proposes IFM energy in terms of the true matrix energy and false matrix energy; then, it develops a MAGDM model using the IFM energy method and the score and accuracy equations of IFM energy. Then, the developed MAGDM model is applied to the selection problem of hospital locations in Shaoxing City, China to demonstrate the practicality and validity of the developed model. Compared with existing intuitionistic fuzzy MAGDM methods, the developed MAGDM model using the IFM energy method reveals its superiority and novelty in complete IFM information expressions and the MAGDM method because the existing MAGDM methods containing intuitionistic fuzzy set information have difficulty tackling MAGDM problems containing all the IFM information on attribute weights, decision maker weights, and attribute values. Full article
(This article belongs to the Special Issue The Application of Fuzzy Decision-Making Theory and Method)
12 pages, 10450 KiB  
Article
An Interval Type-3 Fuzzy–Fractal Approach for Plant Monitoring
by Patricia Melin and Oscar Castillo
Axioms 2023, 12(8), 741; https://doi.org/10.3390/axioms12080741 - 28 Jul 2023
Cited by 9 | Viewed by 1421
Abstract
In this article, a plant monitoring approach based on a hybrid mixture of type-3 fuzzy logic (T3FL) and the fractal dimension (FD) is presented. The main reason for combining type-3 and the fractal dimension is to take advantage of both their capabilities in [...] Read more.
In this article, a plant monitoring approach based on a hybrid mixture of type-3 fuzzy logic (T3FL) and the fractal dimension (FD) is presented. The main reason for combining type-3 and the fractal dimension is to take advantage of both their capabilities in solving the problem of monitoring a plant. Basically, T3FL helps in handling the uncertainty in monitoring the variables of a nonlinear system, while the FD helps to capture the signal complexity by finding key or hidden patterns in the data. The FD is utilized to estimate data complexity of the process variables being monitored. We utilize the box counting algorithm to approximate the values of the FD. A set of T3FL rules is utilized to model monitoring knowledge. The proposed approach was tested with a plant studied in previous works, which was solved with type-1 and type-2 fuzzy logic, and now type-3 is able to surpass the performance of previous approaches for this problem. The main contribution is the T3FL and FD hybrid proposal for plant monitoring, which has not been presented before in the literature. Simulation results illustrate the potential advantage of utilizing the T3FL and FD combination in this area. Full article
(This article belongs to the Special Issue The Application of Fuzzy Decision-Making Theory and Method)
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15 pages, 426 KiB  
Article
Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets
by Wenjuan Ren, Zhanpeng Yang and Xipeng Li
Axioms 2023, 12(4), 376; https://doi.org/10.3390/axioms12040376 - 14 Apr 2023
Cited by 2 | Viewed by 1309
Abstract
The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric [...] Read more.
The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromov–Hausdorff metric to measure the distance between any two MIMs. We then constructed a kind of metric information matrix distance knowledge measure for IFS. The proposed distance measures have the ability to measure the distance between two incomplete intuitionistic fuzzy sets. In order to reduce the information confusion caused by the disorder of MIM, we defined a homogenous metric information matrix distance by rearranging MIM. Some theorems are given to show the properties of the constructed distance measures. At the end of the paper, some numerical experiments are given to show that the proposed distances can recognize different patterns represented by IFS. Full article
(This article belongs to the Special Issue The Application of Fuzzy Decision-Making Theory and Method)
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