Multi-Criteria Decision Aid Methods in Fuzzy Decision Problems – Part III

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (30 September 2022) | Viewed by 22968

Special Issue Editors

Faculty of Economics, Finance and Management, University of Szczecin, Cukrowa 8, 71-004 Szczecin, Poland
Interests: multi-criteria decision analysis/making; MCDA methods; sustainable management; sustainability assessment; fuzzy sets
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Special Issue Information

Dear Colleagues, 

After the success of two parts of the Special Issue entitled “Multi-Criteria Decision Aid Methods in Fuzzy Decision Problems” (https://www.mdpi.com/journal/symmetry/special_issues/Multi_Criteria_Decision_fuzzy_decision, https://www.mdpi.com/journal/symmetry/special_issues/Multi-Criteria_fuzzy_decision_II), we are glad to announce the Special Issue “Multi-Criteria Decision Aid Methods in Fuzzy Decision Problems—Part III”.

In both previous editions of the Special Issue in 2018–2019 and 2019–2021, we cooperated with excellent scholars/scientific groups and published important high-level articles (almost 70 in total) which have seen frequent citation, according to the data from the Web of Science (currently over 460 citations in total) and Scopus (currently over 510 citations in total).

Our goal is to increase knowledge and develop the decision sciences in the field of uncertain and imprecise information. The research can make a great contribution to management, sustainability, energy, marketing, e-commerce, etc. Thus, we will continue the Special Issue in this third part of “Multi-Criteria Decision Aid Methods in Fuzzy Decision Problems”. 

The notion of symmetry is of particular importance in Multi-Criteria Decision Aid (MCDA). Symmetry, asymmetry, and antisymmetry are basic characteristics of binary relations used when modelling the decision-maker’s preferences. Moreover, the notion of symmetry has appeared in many articles about the fuzzy set theory which is employed in MCDA methods.

Fuzzy set theory makes it possible to capture uncertainty, imprecision, inaccurate definition of a decision problem, and, as a consequence, fuzzing the problem. Fuzzing may include input data representing alternatives, weights of criteria, or the decision-maker’s preferences. The first type of fuzzing takes place when the decision-maker is not able to precisely evaluate the weights of criteria or the consequences of individual alternatives. The fuzzy MCDA methods deal with this kind of fuzzing. Next, the fuzzing of the decision-maker’s preferences takes place when they cannot determine to what degree (if at all) one alternative is better than another with regard to a defined criterion. The decision-maker’s fuzzy preferences are used in some outranking MCDA methods. Furthermore, the fuzzy outranking methods deal with both types of fuzzing. 

This Special Issue invites contributions dealing with:

  • The preparation and development of MCDA methods capable of capturing the fuzziness (uncertainty, imprecision, and inaccurate definition) of the decision problem;
  • The application of MCDA methods in fuzzy decision problems in the area of management, logistics, sustainability, marketing, finance, electronic markets, social media, and others.

Survey and theoretical articles, as well as application papers, are welcome. 

Dr. Paweł Ziemba
Prof. Dr. Samarjit Kar
Guest Editors

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Keywords

  • fuzzy (uncertain, imprecise, ill-determined) decision problems
  • multi-criteria decision aid/analysis/making
  • applications of fuzzy MCDA/MCDM methods
  • applications of outranking MCDA/MCDM methods
  • fuzzy MCDA/MCDM methods
  • fuzzy AHP/ANP
  • fuzzy TOPSIS
  • fuzzy DEMATEL
  • outranking MCDA/MCDM methods
  • (fuzzy) PROMETHEE
  • (fuzzy) ELECTRE

Published Papers (10 papers)

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Research

22 pages, 378 KiB  
Article
Distances and Similarity Measures of Q-Rung Orthopair Fuzzy Sets Based on the Hausdorff Metric with the Construction of Orthopair Fuzzy TODIM
by Zahid Hussain, Sahar Abbas and Miin-Shen Yang
Symmetry 2022, 14(11), 2467; https://doi.org/10.3390/sym14112467 - 21 Nov 2022
Cited by 5 | Viewed by 1659
Abstract
In recent years, q-rung orthopair fuzzy sets (q-ROFSs), a novel and rigorous generalization of the fuzzy set (FS) coined by Yager in 2017, have been used to manage inexplicit and indefinite information in daily life with a high precision and greater accuracy than [...] Read more.
In recent years, q-rung orthopair fuzzy sets (q-ROFSs), a novel and rigorous generalization of the fuzzy set (FS) coined by Yager in 2017, have been used to manage inexplicit and indefinite information in daily life with a high precision and greater accuracy than intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). The characterization of a measure of similarity between q-ROFSs is important, as they have applications in different areas, including pattern recognition, clustering, image segmentation and decision making. Therefore, this article is dedicated to the construction of a measure of similarity between q-ROFSs based on the Hausdorff metric. This is a very useful tool for establishing the similarity between two objects. Furthermore, some axiomatic definitions of the distances and similarity measures of q-ROFSs are also presented. In this article, we first present a novel method to calculate the distance between q-ROFSs based on the Hausdorff metric. We then utilize our proposed distance measure to construct the degree of similarity between q-ROFSs. We provide some properties for the proposed similarity measures. We offer several numerical examples related to pattern recognition and characterization linguistic variables to demonstrate the usefulness of the proposed similarity measures. We construct an algorithm for orthopair fuzzy TODIM (interactive and multi-criteria decision making, in Portuguese) based on our proposed methods. Finally, we use the constructed orthopair fuzzy TODIM method to address problems related to daily life settings involving multi-criteria decision making (MCDM). The numerical results show that the proposed similarity measures are suitable, applicable and well-suited to the contexts of pattern recognition, queries with fuzzy linguistic variables and MCDM. Full article
27 pages, 1659 KiB  
Article
A Behavior-Simulated Spherical Fuzzy Extension of the Integrated Multi-Criteria Decision-Making Approach
by Minh-Tai Le and Nhat-Luong Nhieu
Symmetry 2022, 14(6), 1136; https://doi.org/10.3390/sym14061136 - 31 May 2022
Cited by 9 | Viewed by 1780
Abstract
Since its inception in 1965, fuzzy sets have been developed for many years and are widely used in multi-criteria decision making (MCDM) problems. Recently, spherical fuzzy sets (SFS), one of the most recent fuzzy sets, have been applied to extend and reinforce MCDM [...] Read more.
Since its inception in 1965, fuzzy sets have been developed for many years and are widely used in multi-criteria decision making (MCDM) problems. Recently, spherical fuzzy sets (SFS), one of the most recent fuzzy sets, have been applied to extend and reinforce MCDM methods. To contribute to this development, the aim of this study is to propose a novel SFS extension of the integrated MCDM method that takes into account the psychological behavior of decision makers. In the proposed approach, the evaluation criteria are first weighted by the spherical fuzzy Decision-Making Trial and Evaluation Laboratory (SF DEMATEL) method based on symmetrical linguistic comparison matrices. Another notable advantage of this process is determining the interrelationship between the evaluation criteria. In the next stage, the spherical fuzzy Interactive Multi-Criteria Decision-Making method in the Monte Carlo simulation environment (SF TODIM’MC) was applied to evaluate the alternatives. This method allows the process of evaluating alternatives to be performed continuously with different psychological behavioral parameters, which are considered as asymmetric information. As a result, the influence of the decision maker’s psychological behavior on the evaluation results is analyzed comprehensively. The robustness of the proposed approaches is verified through their application to prioritizing post-COVID-19 operational strategies in the Vietnam logistics sector. Numerical results have provided a cause-and-effect relationship between the negative effects of the pandemic and their weights. Furthermore, the results of prioritizing the operational strategies in the simulated environment provide rankings corresponding to different levels of risk aversion. Based on the results, the proposed spherical fuzzy approach is promising for expert-based decision-making problems under psycho-behavioral influence. Full article
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16 pages, 1514 KiB  
Article
Uncertainty of Preferences in the Assessment of Supply Chain Management Systems Using the PROMETHEE Method
by Paweł Ziemba and Izabela Gago
Symmetry 2022, 14(5), 1043; https://doi.org/10.3390/sym14051043 - 19 May 2022
Cited by 8 | Viewed by 1695
Abstract
The use of Supply Chain Management (SCM) systems allows for the improvement of an organization’s operations. Companies use many Enterprise Resource Planning (ERP) systems that also include SCM functionalities. As a result, the selection of the right system to be used in the [...] Read more.
The use of Supply Chain Management (SCM) systems allows for the improvement of an organization’s operations. Companies use many Enterprise Resource Planning (ERP) systems that also include SCM functionalities. As a result, the selection of the right system to be used in the enterprise is a complex problem. The use of multi-criteria decision aid (MCDA) methods provides the possibility of system ordering in a ranking, based on an asymmetric preference relation, symmetric indifference and incomparability relations. The aim of the article is to evaluate ERP systems in terms of their support for SCM. The scientific contribution of the article is the study of the impact of various degrees of uncertainty of the decision-maker’s preferences on the evaluation results and the analysis of the impact of various approaches to the preferences of alternatives on the final ranking. An approach based on MCDA Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) was used for the study. The decision model uses 12 criteria, three different preference functions and two variants of the PROMETHEE method (I and II). In this way, a total of six rankings were built, and each of them includes seven systems, supporting the management of the supply chain. As a result of the study, it was found that the highest functionality in logistics is characterized by the Oracle E-Business Suite system, which is more functional than SAP ERP and JD Edwards EnterpriseOne. The remaining analysed systems offer much less functionality. The applied approach, which was possible with the use of various preference functions, allowed three different levels of uncertainty in the preferences of decision-makers to be taken into account in the study. Moreover, the application of two different variants of the PROMETHEE method made it possible for the obtained solution to take into account the uncertainty of positions taken by individual ERP systems in the final rankings. Full article
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28 pages, 5091 KiB  
Article
On Multi-Objective Minimum Spanning Tree Problem under Uncertain Paradigm
by Saibal Majumder, Partha Sarathi Barma, Arindam Biswas, Pradip Banerjee, Bijoy Kumar Mandal, Samarjit Kar and Paweł Ziemba
Symmetry 2022, 14(1), 106; https://doi.org/10.3390/sym14010106 - 8 Jan 2022
Cited by 12 | Viewed by 2165
Abstract
Minimum spanning tree problem (MSTP) has allured many researchers and practitioners due to its varied range of applications in real world scenarios. Modelling these applications involves the incorporation of indeterminate phenomena based on their subjective estimations. Such phenomena can be represented rationally using [...] Read more.
Minimum spanning tree problem (MSTP) has allured many researchers and practitioners due to its varied range of applications in real world scenarios. Modelling these applications involves the incorporation of indeterminate phenomena based on their subjective estimations. Such phenomena can be represented rationally using uncertainty theory. Being a more realistic variant of MSTP, in this article, based on the principles of the uncertainty theory, we have studied a multi-objective minimum spanning tree problem (MMSTP) with indeterminate problem parameters. Subsequently, two uncertain programming models of the proposed uncertain multi-objective minimum spanning tree problem (UMMSTP) are developed and their corresponding crisp equivalence models are investigated, and eventually solved using a classical multi-objective solution technique, the epsilon-constraint method. Additionally, two multi-objective evolutionary algorithms (MOEAs), non-dominated sorting genetic algorithm II (NSGAII) and duplicate elimination non-dominated sorting evolutionary algorithm (DENSEA) are also employed as solution methodologies. With the help of the proposed UMMSTP models, the practical problem of optimizing the distribution of petroleum products was solved, consisting in the search for symmetry (balance) between the transportation cost and the transportation time. Thereafter, the performance of the MOEAs is analyzed on five randomly developed instances of the proposed problem. Full article
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36 pages, 2195 KiB  
Article
A New Integrated FUCOM–CODAS Framework with Fermatean Fuzzy Information for Multi-Criteria Group Decision-Making
by Sanjib Biswas, Dragan Pamucar, Samarjit Kar and Shib Sankar Sana
Symmetry 2021, 13(12), 2430; https://doi.org/10.3390/sym13122430 - 15 Dec 2021
Cited by 33 | Viewed by 4024
Abstract
Smartphones have become an inevitable part of every facet of modern society. The selection of a particular smartphone brand from multiple options that are available is a complex and dynamic decision-making problem, involving multiple conflicting criteria that are associated with imprecise asymmetric information [...] Read more.
Smartphones have become an inevitable part of every facet of modern society. The selection of a particular smartphone brand from multiple options that are available is a complex and dynamic decision-making problem, involving multiple conflicting criteria that are associated with imprecise asymmetric information imposed by the uncertainty of the consumers. In this paper, we propose a novel hybrid full consistency method (FUCOM) and a combinative distance based assessment (CODAS) based on the multi-criteria group decision-making (MAGDM) framework in the Fermatean fuzzy (FF) domain for smartphone brand selection. We derive the criteria using the UTAUT2 (unified theory of acceptance and ese of technology) model. A group of 15 decision makers (DMs) participated in our study. We compare 14 leading smartphone brands in India and find that the brands having superior features of a good quality and selling a brand image at a affordable price outperform other smartphones. To check the validity of our framework, we compare the results using extant multi-criteria decision-making (MCDM) models. We observe our model provides a consistent solution. Furthermore, we carry out a sensitivity analysis for ascertaining the robustness and stability of the results generated by our model. The results of the sensitivity analysis show that our proposed framework delivers a stable and robust solution. Full article
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20 pages, 1389 KiB  
Article
A Proposed Framework for Developing FMEA Method Using Pythagorean Fuzzy CODAS
by Sara Almeraz-Durán, Luis Asunción Pérez-Domínguez, David Luviano-Cruz, Jesús Israel Hernández Hernández, Roberto Romero López and Delia J. Valle-Rosales
Symmetry 2021, 13(12), 2236; https://doi.org/10.3390/sym13122236 - 23 Nov 2021
Cited by 8 | Viewed by 1700
Abstract
The purpose of this research article is to develop a hybridization between the Failure Mode and Effect Analysis (FMEA) method and the Combinative Distance-Based Assessment (CODAS) method under Pythagorean Fuzzy environment. The traditional FMEA procedure is based on the multiplication between the parameters [...] Read more.
The purpose of this research article is to develop a hybridization between the Failure Mode and Effect Analysis (FMEA) method and the Combinative Distance-Based Assessment (CODAS) method under Pythagorean Fuzzy environment. The traditional FMEA procedure is based on the multiplication between the parameters of severity, occurrence, and detectability where everyone has equal relative importance; therefore, different combinations of these parameters can generate the same result creating uncertainty in the analysis. In this mode, the hybridization proposed in this research deal with relative importance of each parameter; in the fact to have a more suitable combination which consider the level of knowledge of the experts in the assessment. Finally, a numerical case was carried out concerning the public transportation service to validate our proposal; the results show that 31 failure modes and potential risks can be evaluated using user perceptions, a dominant with high level of knowledge about the public transportation service and an apprentice or common user, as team of experts and exploiting the subjectivity of the information in a mathematical model. Also, we compare the results with a variation of the proposed model with the multi-criteria method multi-objective optimization method by relationship analysis (MOORA); it was observed that the convergence of the failure modes depends on the nature of the mathematical model even under the same conditions at the start. Full article
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21 pages, 389 KiB  
Article
Rough q-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making
by Muhammad Asim Bilal, Muhammad Shabir and Ahmad N. Al-Kenani
Symmetry 2021, 13(11), 2010; https://doi.org/10.3390/sym13112010 - 23 Oct 2021
Cited by 5 | Viewed by 1987
Abstract
Yager recently introduced the q-rung orthopair fuzzy set to accommodate uncertainty in decision-making problems. A binary relation over dual universes has a vital role in mathematics and information sciences. During this work, we defined upper approximations and lower approximations of q-rung [...] Read more.
Yager recently introduced the q-rung orthopair fuzzy set to accommodate uncertainty in decision-making problems. A binary relation over dual universes has a vital role in mathematics and information sciences. During this work, we defined upper approximations and lower approximations of q-rung orthopair fuzzy sets using crisp binary relations with regard to the aftersets and foresets. We used an accuracy measure of a q-rung orthopair fuzzy set to search out the accuracy of a q-rung orthopair fuzzy set, and we defined two types of q-rung orthopair fuzzy topologies induced by reflexive relations. The novel concept of a rough q-rung orthopair fuzzy set over dual universes is more flexible when debating the symmetry between two or more objects that are better than the prevailing notion of a rough Pythagorean fuzzy set, as well as rough intuitionistic fuzzy sets. Furthermore, using the score function of q-rung orthopair fuzzy sets, a practical approach was introduced to research the symmetry of the optimal decision and, therefore, the ranking of feasible alternatives. Multiple criteria decision making (MCDM) methods for q-rung orthopair fuzzy sets cannot solve problems when an individual is faced with the symmetry of a two-sided matching MCDM problem. This new approach solves the matter more accurately. The devised approach is new within the literature. In this method, the main focus is on ranking and selecting the alternative from a collection of feasible alternatives, reckoning for the symmetry of the two-sided matching of alternatives, and providing a solution based on the ranking of alternatives for an issue containing conflicting criteria, to assist the decision-maker in a final decision. Full article
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27 pages, 411 KiB  
Article
Overlap Functions Based (Multi-Granulation) Fuzzy Rough Sets and Their Applications in MCDM
by Xiaofeng Wen and Xiaohong Zhang
Symmetry 2021, 13(10), 1779; https://doi.org/10.3390/sym13101779 - 24 Sep 2021
Cited by 9 | Viewed by 1513
Abstract
Through a combination of overlap functions (which have symmetry and continuity) and a fuzzy β-covering fuzzy rough set (FCFRS), a new class of FCFRS models is established, and the basic properties of the new fuzzy β-neighborhood lower and upper approximate operators [...] Read more.
Through a combination of overlap functions (which have symmetry and continuity) and a fuzzy β-covering fuzzy rough set (FCFRS), a new class of FCFRS models is established, and the basic properties of the new fuzzy β-neighborhood lower and upper approximate operators are analyzed and studied. Then the model is extended to the case of multi-granulation, and the properties of a multi-granulation optimistic fuzzy rough set are mainly investigated. By theoretical analysis for the fuzzy covering (multi-granulation) fuzzy rough sets, the solutions to problems in multi-criteria decision-making (MCDM) and multi-criteria group decision-making (MCGDM) problem methods are built, respectively. To fully illustrate these methodologies, effective examples are developed. By comparing the method proposed in this paper with the existing methods, we find that the method proposed is more suitable for solving decision making problems than the traditional methods, while the results obtained are more helpful to decision makers. Full article
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18 pages, 311 KiB  
Article
On Fundamental Theorems of Fuzzy Isomorphism of Fuzzy Subrings over a Certain Algebraic Product
by Alaa Altassan, Muhammad Haris Mateen and Dragan Pamucar
Symmetry 2021, 13(6), 998; https://doi.org/10.3390/sym13060998 - 3 Jun 2021
Cited by 7 | Viewed by 2480
Abstract
In this study, we define the concept of an ω-fuzzy set ω-fuzzy subring and show that the intersection of two ω-fuzzy subrings is also an ω-fuzzy subring of a given ring. Moreover, we give the notion of an ω [...] Read more.
In this study, we define the concept of an ω-fuzzy set ω-fuzzy subring and show that the intersection of two ω-fuzzy subrings is also an ω-fuzzy subring of a given ring. Moreover, we give the notion of an ω-fuzzy ideal and investigate different fundamental results of this phenomenon. We extend this ideology to propose the notion of an ω-fuzzy coset and develop a quotient ring with respect to this particular fuzzy ideal analog into a classical quotient ring. Additionally, we found an ω-fuzzy quotient subring. We also define the idea of a support set of an ω-fuzzy set and prove various important characteristics of this phenomenon. Further, we describe ω-fuzzy homomorphism and ω-fuzzy isomorphism. We establish an ω-fuzzy homomorphism between an ω-fuzzy subring of the quotient ring and an ω-fuzzy subring of this ring. We constitute a significant relationship between two ω-fuzzy subrings of quotient rings under the given ω-fuzzy surjective homomorphism and prove some more fundamental theorems of ω-fuzzy homomorphism for these specific fuzzy subrings. Finally, we present three fundamental theorems of ω-fuzzy isomorphism. Full article
22 pages, 4775 KiB  
Article
Comparative Analysis of Hybrid Fuzzy MCGDM Methodologies for Optimal Robot Selection Process
by Tabasam Rashid, Asif Ali, Juan L. G. Guirao and Adrián Valverde
Symmetry 2021, 13(5), 839; https://doi.org/10.3390/sym13050839 - 10 May 2021
Cited by 11 | Viewed by 2401
Abstract
The generalized interval-valued trapezoidal fuzzy best-worst method (GITrF-BWM) provides more reliable and more consistent criteria weights for multiple criteria group decision making (MCGDM) problems. In this study, GITrF-BWM is integrated with the extended TOPSIS (technique for order preference by similarity to the ideal [...] Read more.
The generalized interval-valued trapezoidal fuzzy best-worst method (GITrF-BWM) provides more reliable and more consistent criteria weights for multiple criteria group decision making (MCGDM) problems. In this study, GITrF-BWM is integrated with the extended TOPSIS (technique for order preference by similarity to the ideal solution) and extended VIKOR (visekriterijumska optimizacija i kompromisno resenje) methods for the selection of the optimal industrial robot using fuzzy information. For a criteria-based selection process, assigning weights play a vital role and significantly affect the decision. Assigning weights based on direct opinions of decision makers can be biased, so weight deriving models, such as GITrF-BWM, overcome this discrepancy. In previous studies, generalized interval-valued trapezoidal fuzzy weights were not derived by using any MCGDM method for the robot selection process. For this study, both subjective and objective criteria are considered. The preferences of decision makers are provided with the help of linguistic terms that are then converted into fuzzy information. The stability and reliability of the methods were tested by performing sensitivity analysis, which showed that the ranking results of both the methodologies are not symmetrical, and the integration of GITrF-BWM with the extended TOPSIS method provides stable and reliable results as compared to the integration of GITrF-BWM with the extended VIKOR method. Hence, the proposed methodology provides robust optimal industrial robot selection. Full article
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