Advances in Fuzzy Preference Relations and Decision-Making Methods with Applications

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

Deadline for manuscript submissions: 29 July 2024 | Viewed by 8715

Special Issue Editors


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Guest Editor
School of Automation, Nanjing University of Science and Technology, Nanjing, China
Interests: fuzzy decision making; decision support system; knowledge engineering; information system; railway engineering

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Guest Editor
Faculty of Transport and Traffic Engineering, University of Belgrade, Belgrade, Serbia
Interests: operations research; decision support systems; transportation engineering; multi-criteria decision-making; waste management
Special Issues, Collections and Topics in MDPI journals
School of Cyber Science and Engineering, Nanjing University of Science and Technology, Nanjing, China
Interests: platform economy; pricing strategy; e-commerce; multi-criteria decision-making; recommendation system

Special Issue Information

Dear Colleagues,

Preference relations are matrix structures constructed by a two-by-two comparison of alternatives, where each element represents the degree of preference of one alternative over another. Considering the advantage of fuzzy set theory in expressing the uncertainty of preference information, preference relations are extended into fuzzy environments. Fuzzy preference relations (FPR), interval-valued fuzzy preference relations (IVFPR), intuitionistic fuzzy preference relations (IFPR), Pythagorean fuzzy preference relations (PFPR), q-rung orthopair fuzzy preference relations (q-ROFPR), hesitant fuzzy preference relations (HFPR) and hesitant fuzzy linguistic preference relations (HFLPR) have emerged in recent years. Compared with the traditional preference relation, the FPR and its extensions express and provide feedback on the expert's preference in a more reasonable way. In some decision-making processes, due to subjective factors such as knowledge structure and the judgement level of experts, experts often provide some fuzzy membership values and their extensions when constructing judgement matrices. The FPR and its extensions provide more reasonable feedback on the decision maker's cognitive outcome, describing the uncertainty of the decision maker's preference. The core of the decision-making problem in preference-based relationship environments includes to the ways in which we can define the consistency of preference relationships and how to obtain the weight vector of preference relations.

We hope that this Special Issue will stimulate both theoretical and applied research on fuzzy reference relations and decision-making methods. It is certainly impossible in this short editorial to provide a more comprehensive description of all the potential articles in this Special Issue. However, we sincerely hope that our effort in compiling these articles will enrich our readers and inspire researchers with regard to the seemingly common but indeed important issue of fuzzy preference relations and decision-making methods.

Dr. Zhenyu Zhang
Dr. Vladimir Simic
Dr. Jing Li
Guest Editors

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Keywords

  • fuzzy set theory
  • fuzzy preference relation
  • group decision making
  • decision support system
  • multi-criteria decision making
  • consistency

Published Papers (10 papers)

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Research

20 pages, 622 KiB  
Article
Multiplicative Consistent q-Rung Orthopair Fuzzy Preference Relations with Application to Critical Factor Analysis in Crowdsourcing Task Recommendation
by Xicheng Yin and Zhenyu Zhang
Axioms 2023, 12(12), 1122; https://doi.org/10.3390/axioms12121122 - 14 Dec 2023
Viewed by 835
Abstract
This paper presents a group decision-making (GDM) method based on q-rung orthopair fuzzy preference relations (q-ROFPRs). Firstly, the multiplicative consistent q-ROFPRs (MCq-ROFPRs) and the normalized q-rung orthopair fuzzy priority weight vectors (q-ROFPWVs) are introduced. Then, to obtain q-ROFPWVs, a goal programming model under [...] Read more.
This paper presents a group decision-making (GDM) method based on q-rung orthopair fuzzy preference relations (q-ROFPRs). Firstly, the multiplicative consistent q-ROFPRs (MCq-ROFPRs) and the normalized q-rung orthopair fuzzy priority weight vectors (q-ROFPWVs) are introduced. Then, to obtain q-ROFPWVs, a goal programming model under q-ROFPRs is established to minimize their deviation from the MCq-ROFPRs and minimize the weight uncertainty. Further, a group goal programming model of ideal MCq-ROFPRs is constructed to obtain the expert weights using the compatibility measure between the ideal MCq-ROFPRs and the individual q-ROFPRs. Finally, a GDM method with unknown expert weights is solved by combining the group goal programming model and the simple q-rung orthopair fuzzy weighted geometric (Sq-ROFWG) operator. The effectiveness and practicality of the proposed GDM method are verified by solving the crucial factors in crowdsourcing task recommendation. The results show that the developed GDM method effectively considers the important measures of experts and identifies the crucial factors that are more reliable than two other methods. Full article
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20 pages, 383 KiB  
Article
Decomposition of Fuzzy Relations: An Application to the Definition, Construction and Analysis of Fuzzy Preferences
by María Jesús Campión, Esteban Induráin and Armajac Raventós-Pujol
Axioms 2023, 12(12), 1077; https://doi.org/10.3390/axioms12121077 - 24 Nov 2023
Viewed by 858
Abstract
In this article, we go deeper into the study of some types of decompositions defined by triangular norms and conorms. We work in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions. This allows us to achieve [...] Read more.
In this article, we go deeper into the study of some types of decompositions defined by triangular norms and conorms. We work in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions. This allows us to achieve characterizations of existence and uniqueness for such decompositions. We provide rules to obtain them under some specific conditions. We conclude by applying the results achieved to the study of fuzzy preferences. Full article
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17 pages, 706 KiB  
Article
A New Framework for Sustainable Supplier Selection Based on a Plant Growth Simulation Algorithm
by Jing Li and Weizhong Wang
Axioms 2023, 12(11), 1017; https://doi.org/10.3390/axioms12111017 - 28 Oct 2023
Viewed by 777
Abstract
With the intensification of global competition and the increasing awareness of reducing energy consumption, sustainable supplier selection is crucial for establishing a solid cooperative relationship in sustainable supply chain management. This paper proposes a new framework that considers both the effective expression of [...] Read more.
With the intensification of global competition and the increasing awareness of reducing energy consumption, sustainable supplier selection is crucial for establishing a solid cooperative relationship in sustainable supply chain management. This paper proposes a new framework that considers both the effective expression of uncertain information and the objective weights of decision makers to select sustainable suppliers. We first apply an interval-valued intuitionistic fuzzy set to express the information of decision makers. Moreover, this paper applies a plant growth simulation algorithm to aggregate decision makers’ information. Next, we adopt the similarity measure method to derive the target weight of each decision maker. Then, we apply the score function to rank the candidate sustainable suppliers. Finally, two practical cases are presented to verify the effectiveness of the proposed framework. The outcomes and comparative discussion show that the developed framework is efficient for sustainable supplier selection. Therefore, the proposed framework can be used to establish a solid cooperative relationship in the process of sustainable supply chain management. Full article
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16 pages, 1628 KiB  
Article
Optimizing Material Selection with Fermatean Fuzzy Hybrid Aggregation Operators
by Vladimir Simic, Waseem Ahmad, Srishti Dikshit, Bandar Bin-Mohsin, Mohd Sadim and Mohd Anjum
Axioms 2023, 12(10), 984; https://doi.org/10.3390/axioms12100984 - 18 Oct 2023
Viewed by 1007
Abstract
In the pursuance of engineering excellence and sustainable practices, the optimization of material selection processes plays a crucial role. Using Fermatean fuzzy aggregation Operators (AOs), this study introduces an innovative method for improving material selection procedures. Combining the advantages of Fermatean fuzzy set [...] Read more.
In the pursuance of engineering excellence and sustainable practices, the optimization of material selection processes plays a crucial role. Using Fermatean fuzzy aggregation Operators (AOs), this study introduces an innovative method for improving material selection procedures. Combining the advantages of Fermatean fuzzy set (FrFS) and AOs, the proposed method enables a comprehensive evaluation of materials based on multiple criteria. The authors propose two operators: the “Fermatean fuzzy hybrid weighted arithmetic geometric aggregation (FrFHWAGA) operator” and the “Fermatean fuzzy hybrid ordered weighted arithmetic geometric aggregation (FrFHOWAGA) operator”. This method facilitates informed decision making in a number of industries by taking into account factors such as cost, durability, environmental impact, and availability. This research enables engineers, designers, and decision makers to optimize material selection, resulting in more efficient, cost-effective, and sustainable solutions across multiple domains. Full article
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23 pages, 1500 KiB  
Article
Elevating Decision Management in Sustainable Energy Planning through Spherical Fuzzy Aggregation Operators
by Sana Shahab, Mohd Anjum, Rukhsana Kausar and Yang Yu
Axioms 2023, 12(10), 908; https://doi.org/10.3390/axioms12100908 - 24 Sep 2023
Cited by 2 | Viewed by 869
Abstract
This article introduces a novel paradigm for enhancing the administration of decisions regarding sustainable energy planning. This is achieved by deploying novel spherical fuzzy aggregation operators that have been meticulously tailored to address the inherent complexities of uncertainty and imprecision prevalent in energy [...] Read more.
This article introduces a novel paradigm for enhancing the administration of decisions regarding sustainable energy planning. This is achieved by deploying novel spherical fuzzy aggregation operators that have been meticulously tailored to address the inherent complexities of uncertainty and imprecision prevalent in energy planning datasets. These operators vastly increase the precision and efficacy of decision-making processes, thereby transforming the entire sustainable energy landscape. This study focuses predominantly on the complex domain of multi-attribute decision-making (MADM), in which the interplay of parameters is characterized by a discernible hierarchy of importance. This method generates aggregation operators based on the assignment of non-negative real values to clearly defined priority echelons, a framework known as priority degrees. This effort results in the development of two notable prioritized operators: the “spherical fuzzy prioritized averaging operator with priority degrees” and the “spherical fuzzy prioritized geometric operator with priority degrees”. The efficacy of these conceptual frameworks is vividly demonstrated through the application of extensive case studies, in which observable results clearly demonstrate their superiority over conventional methodologies. The empirical findings unequivocally demonstrate the superiority of the proposed operators, resonating with substantial performance and efficiency improvements. This study not only adds a seminal dimension to the field of sustainable energy management but also reveals a revolutionary application of spherical fuzzy aggregation operators at the forefront of effective decision-making paradigms. The seamless fusion of theoretical innovation and practical utility outlines a path forward, with transformative prospects and far-reaching implications for the sustainable energy landscape. Full article
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16 pages, 5988 KiB  
Article
A Novel Approach for Individual Design Perception Based on Fuzzy Inference System Training with YUKI Algorithm
by Brahim Benaissa, Masakazu Kobayashi, Keita Kinoshita and Hiroshi Takenouchi
Axioms 2023, 12(10), 904; https://doi.org/10.3390/axioms12100904 - 22 Sep 2023
Viewed by 688
Abstract
This paper presents a novel approach for individual design perception modeling using the YUKI algorithm-trained Fuzzy Inference System. The study focuses on understanding how individuals perceive design based on personality traits, particularly openness to experience, using the YUKI algorithm and Fuzzy C-means clustering [...] Read more.
This paper presents a novel approach for individual design perception modeling using the YUKI algorithm-trained Fuzzy Inference System. The study focuses on understanding how individuals perceive design based on personality traits, particularly openness to experience, using the YUKI algorithm and Fuzzy C-means clustering algorithm. The approach generates several Sugeno-type Fuzzy Inference System models to predict design perception, to minimize the Root Mean Squared Error between the model prediction and the actual design perception of participants. The results demonstrate that the suggested method offers more accurate predictions compared to the traditional Fuzzy C-means Fuzzy Inference System and Deep Artificial Neural Networks, and the Root Mean Square deviation for individual design perceptions falls within a satisfactory range of 0.84 to 1.32. The YUKI algorithm-trained Fuzzy Inference System proves effective in clustering individuals based on their level of openness, providing insights into how personality traits influence design perception. Full article
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21 pages, 319 KiB  
Article
Applications of Fuzzy Differential Subordination for a New Subclass of Analytic Functions
by Shahid Khan, Jong-Suk Ro, Fairouz Tchier and Nazar Khan
Axioms 2023, 12(8), 745; https://doi.org/10.3390/axioms12080745 - 28 Jul 2023
Cited by 2 | Viewed by 577
Abstract
This work is concerned with the branch of complex analysis known as geometric function theory, which has been modified for use in the study of fuzzy sets. We develop a novel operator Lα,λm:AnAn [...] Read more.
This work is concerned with the branch of complex analysis known as geometric function theory, which has been modified for use in the study of fuzzy sets. We develop a novel operator Lα,λm:AnAn in the open unit disc Δ using the Noor integral operator and the generalized Sălăgean differential operator. First, we develop fuzzy differential subordination for the operator Lα,λm and then, taking into account this operator, we define a particular fuzzy class of analytic functions in the open unit disc Δ, represented by Rϝλ(m,α,δ). Using the idea of fuzzy differential subordination, several new results are discovered that are relevant to this class. The fundamental theorems and corollaries are presented, and then examples are provided to illustrate their practical use. Full article
21 pages, 349 KiB  
Article
New Applications of Fuzzy Set Concept in the Geometric Theory of Analytic Functions
by Alina Alb Lupaş
Axioms 2023, 12(5), 494; https://doi.org/10.3390/axioms12050494 - 19 May 2023
Viewed by 727
Abstract
Zadeh’s fuzzy set theory offers a logical, adaptable solution to the challenge of defining, assessing and contrasting various sustainability scenarios. The results presented in this paper use the fuzzy set concept embedded into the theories of differential subordination and superordination established and developed [...] Read more.
Zadeh’s fuzzy set theory offers a logical, adaptable solution to the challenge of defining, assessing and contrasting various sustainability scenarios. The results presented in this paper use the fuzzy set concept embedded into the theories of differential subordination and superordination established and developed in geometric function theory. As an extension of the classical concept of differential subordination, fuzzy differential subordination was first introduced in geometric function theory in 2011. In order to generalize the idea of fuzzy differential superordination, the dual notion of fuzzy differential superordination was developed later, in 2017. The two dual concepts are applied in this article making use of the previously introduced operator defined as the convolution product of the generalized Sălgean operator and the Ruscheweyh derivative. Using this operator, a new subclass of functions, normalized analytic in U, is defined and investigated. It is proved that this class is convex, and new fuzzy differential subordinations are established by applying known lemmas and using the functions from the new class and the aforementioned operator. When possible, the fuzzy best dominants are also indicated for the fuzzy differential subordinations. Furthermore, dual results involving the theory of fuzzy differential superordinations and the convolution operator are established for which the best subordinants are also given. Certain corollaries obtained by using particular convex functions as fuzzy best dominants or fuzzy best subordinants in the proved theorems and the numerous examples constructed both for the fuzzy differential subordinations and for the fuzzy differential superordinations prove the applicability of the new theoretical results presented in this study. Full article
20 pages, 361 KiB  
Article
Fuzzy Differential Inequalities for Convolution Product of Ruscheweyh Derivative and Multiplier Transformation
by Alina Alb Lupaş
Axioms 2023, 12(5), 470; https://doi.org/10.3390/axioms12050470 - 13 May 2023
Viewed by 579
Abstract
In this paper, the author combines the geometric theory of analytic function regarding differential superordination and subordination with fuzzy theory for the convolution product of Ruscheweyh derivative and multiplier transformation. Interesting fuzzy inequalities are obtained by the author. Full article
14 pages, 293 KiB  
Article
A New Approach to Involution in Fuzzy C-Algebra via Functional Inequality and Python Implementation
by Ehsan Movahednia and Manuel De la Sen
Axioms 2023, 12(5), 435; https://doi.org/10.3390/axioms12050435 - 27 Apr 2023
Viewed by 727
Abstract
This article explores the stability of involution in fuzzy C-algebras through the use of a functional inequality. We present an approach to obtaining an approximate involution in fuzzy C-algebras by utilizing a fixed-point method. Moreover, for greater clarity, we [...] Read more.
This article explores the stability of involution in fuzzy C-algebras through the use of a functional inequality. We present an approach to obtaining an approximate involution in fuzzy C-algebras by utilizing a fixed-point method. Moreover, for greater clarity, we implemented Python code for the main theorem. Full article
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