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Algorithms for Multi-Criteria Decision-Making under Uncertainty

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A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 13815

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Dr. Željko Stević

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Guest Editor

Department for Transport Engineering, Faculty of Transport and Traffic Engineering, University of East Sarajevo, Vojvode Mišića 52, 74000 Doboj, Bosnia and Herzegovina
Interests: logistics; supply chain management; transport; traffic engineering; multicriteria decision-making problems; rough set theory; sustainability; fuzzy set theory; neutrosophic theory
Special Issues, Collections and Topics in MDPI journals

Dr. Abbas Mardani

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Guest Editor

Faculty of Management, Universiti Teknologi Malaysia (UTM), Johor Bahru, Malaysia
Interests: operation management; sustainable supply chain management; circular economy big data; fuzzy decision making; industry 4.0
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Edmundas Kazimieras Zavadskas

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Guest Editor

Research Institute of Sustainable Construction, Vilnius Gediminas Technical University, LT-10223 Vilnius, Lithuania
Interests: operations research; optimization and decision analysis; multicriteria decision making; multiattribute decision making (MADM); decision support systems; civil engineering; energy; sustainable development; fuzzy sets theory; fuzzy multicriteria decision making; sustainability; management; game theory and economical computing knowledge management
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Decision-making is one of the most important topics in various fields and refers to how to make the right decisions so as to reach a final goal. Therefore, the use of the multi-criteria decision-making (MCDM) method for solving problems in different fields is very popular and helps in making extremely important decisions, especially under uncertainty. MCDM is an effective systematic and quantitative way to deal with problems in the presence of a number of alternatives and several usually conflicting criteria. Decision-making regarding very complex problems, including business-related decisions and real-life decisions, requires an appropriate and reliable decision support system (DSS). Planning and appropriate decision-making requires the use of analytical methods that examine trade-offs, consider multiple scientific, political, economic, ecological and social dimensions, and reduce possible conflicts in an optimizing framework. MCDM approaches are considered the established methods to aid decision-makers in taking suitable decisions, and their applications are growing in popularity in many fields.

The need for the application of uncertainty models has manifested in the fact that many complex engineering systems include conflict factors. Computational methods (e.g., fuzzy set theory, neutrosophic theory, rough set theory, grey theory, Dempster-Shafer evidence theory, etc.) have everyday applications in decision-making about problems in complex engineering systems. In the last few years, applications of uncertainty models have been extended to solve real-world problems and other disciplines.

We hope that this Special Issue will stimulate both theoretical and applied research on the MCDM under uncertainty and related fields. It is certainly impossible in this short editorial to provide a more comprehensive description of all 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 actually important issue of decision-making.

Dr. Željko Stević
Dr. Abbas Mardani
Prof. Dr. Edmundas Kazimieras Zavadskas
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. Symmetry 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

innovative applications of uncertainty models
integration of novel uncertainty models
fuzzy set theory
rough set theory
neutrosophic set theory
grey set theory
mathematical programming in MCDM
new trends in multi-criteria evaluation

Published Papers (10 papers)

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Research

22 pages, 4003 KiB

Open AccessArticle

A Robust-Reliable Decision-Making Methodology Based on a Combination of Stakeholders’ Preferences Simulation and KDD Techniques for Selecting Automotive Platform Benchmark

by Asad Saghari, Ivana Budinská, Masoud Hosseinimehr and Shima Rahmani

Symmetry 2023, 15(3), 750; https://doi.org/10.3390/sym15030750 - 18 Mar 2023

Cited by 3 | Viewed by 1218

Abstract

The automotive family design is known as one of the most complex engineering design problems with multiple groups of stakeholders involved from different domains of interest and contradictory attributes. Taking into account all stakeholders’ preferences, which are generally symmetrical, non-deterministic distributions around a mean value, and determining the right value of attributes for each alternative are two basic challenges for these types of decision-making problems. In this research, the possibility to achieve a robust-reliable decision by focusing on the two aforementioned challenges is explored. In the proposed methodology, a random simulation technique is used to elicit stakeholders’ preferences and determine the relative importance of attributes. The decision space and values of attributes are determined using the Knowledge Discovery in Databases (KDD) technique, and to achieve a robust-reliable decision, statistical and sensitivity analyses are performed. By implementing this methodology, the decision-maker is assured that the preferences of all stakeholders are taken into account and the determined values for attributes are reliable with the least degree of uncertainty. The proposed methodology aims to select benchmark platforms for the development of an automotive family. The decision space includes 546 automobiles in 11 different segments based on 34 platforms. There are 6223 unique possible states of stakeholders’ preferences. As a result, five platforms with the highest degree of desirability and robustness to diversity and uncertainty in the stakeholders’ preferences are selected. The presented methodology can be implemented in complex decision-making problems, including a large and diverse number of stakeholders and multiple attributes. In addition, this methodology is compatible with many Multi-Attribute Decision-Making (MADM) techniques, including SAW, AHP, SWARA, and TOPSIS. Full article

(This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making under Uncertainty)

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26 pages, 343 KiB

Open AccessArticle

A Large Group Emergency Decision Making Method Considering Scenarios and Unknown Attribute Weights

by Pingping Wang and Jiahua Chen

Symmetry 2023, 15(1), 223; https://doi.org/10.3390/sym15010223 - 12 Jan 2023

Cited by 5 | Viewed by 991

Abstract

Once an emergency event (EE) happens, emergency decision-making (EDM) plays a key role in mitigating the loss. EDM is a complex problem. Compared with conventional decision-making problems, more experts participate in decision-making. It usually has the feature of large group emergency decision-making (LGEDM). This paper proposes a large group emergency decision-making method based on Bayesian theory, relative entropy, and Euclidean distance, which is used for large group emergency decision-making with uncertain probabilities of occurrence, unknown attribute weights, and expert weights. In order to improve the accuracy of decision-making, Bayesian method is introduced into the calculation of scenario probability in the process of LGEDM. In the decision-making process, the experts’ risk preference is considered. The experts’ decision preference information is a symmetric and uniformly distributed interval value. The perceived utility values of the experts are obtained by introducing prospect theory. Euclidean distance is used to measure the contributions of experts to aggregation similarity, and different weights are given to experts according to their contributions. A relative entropy model with completely unknown weight information constraints is established to obtain attribute weights, which takes into account the differences of different alternatives under the same attribute and the differences between alternatives and the ideal solution. An example of nuclear power emergency decision-making illustrates the effectiveness of this method. Full article

(This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making under Uncertainty)

19 pages, 326 KiB

Open AccessArticle

A Novel Framework of q-Rung Orthopair Fuzzy Sets in Field

by Kholood Alnefaie, Qin Xin, Ahmad Almutlg, El-Sayed A. Abo-Tabl and M. Haris Mateen

Symmetry 2023, 15(1), 114; https://doi.org/10.3390/sym15010114 - 31 Dec 2022

Cited by 2 | Viewed by 904

Abstract

In this manuscript, we proposed a novel framework of the q-rung orthopair fuzzy subfield (q-ROFSF) and illustrate that every Pythagorean fuzzy subfield is a q-rung orthopair fuzzy subfield of a certain field. We extend this theory and discuss its diverse basic algebraic characteristics in detail. Furthermore, we prove some fundamental results and establish helpful examples related to them. Moreover, we present the homomorphic images and pre-images of the q-rung orthopair fuzzy subfield (q-ROFSF) under field homomorphism. We provide a novel ideology of a non-standard fuzzy subfield in the extension of the q-rung orthopair fuzzy subfield (q-ROFSF). Full article

(This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making under Uncertainty)

27 pages, 1091 KiB

Open AccessArticle

An Innovative Hybrid Multi-Criteria Decision-Making Approach under Picture Fuzzy Information

by Ghous Ali, Muhammad Zain Ul Abidin, Qin Xin and Ferdous M. O. Tawfiq

Symmetry 2022, 14(11), 2434; https://doi.org/10.3390/sym14112434 - 17 Nov 2022

Viewed by 1135

Abstract

These days, multi-criteria decision-making (MCDM) approaches play a vital role in making decisions considering multiple criteria. Among these approaches, the picture fuzzy soft set model is emerging as a powerful mathematical tool for handling various kinds of uncertainties in complex real-life MCDM situations because it is a combination of two efficient mathematical tools, namely, picture fuzzy sets and soft sets. However, the picture fuzzy soft set model is deficient; that is, it fails to tackle information symmetrically in a bipolar soft environment. To overcome this difficulty, in this paper, a model named picture fuzzy bipolar soft sets (P

_{R}

FBSSs, for short) is proposed, which is a natural hybridization of two models, namely, picture fuzzy sets and bipolar soft sets. An example discussing the selection of students for a scholarship is added to illustrate the initiated model. Some novel properties of P

_{R}

FBSSs such as sub-set, super-set, equality, complement, relative null and absolute P

_{R}

FBSSs, extended intersection and union, and restricted intersection and union are investigated. Moreover, two fundamental operations of P

_{R}

FBSSs, namely, the AND and OR operations, are studied. Thereafter, some new results (De Morgan’s law, commutativity, associativity, and distributivity) related to these proposed notions are investigated and explained through corresponding numerical examples. An algorithm is developed to deal with uncertain information in the P

_{R}

FBSS environment. To show the efficacy and applicability of the initiated technique, a descriptive numerical example regarding the selection of the best graphic designer is explored under P

_{R}

FBSSs. In the end, concerning both qualitative and quantitative perspectives, a detailed comparative analysis of the initiated model with certain existing models is provided. Full article

(This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making under Uncertainty)

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30 pages, 1143 KiB

Open AccessArticle

Ranking of Downstream Fish Passage Designs for a Hydroelectric Project under Spherical Fuzzy Bipolar Soft Framework

by Ghous Ali, Muhammad Zain Ul Abidin, Qin Xin and Ferdous M. O. Tawfiq

Symmetry 2022, 14(10), 2141; https://doi.org/10.3390/sym14102141 - 13 Oct 2022

Cited by 3 | Viewed by 1170

Abstract

Nowadays, several real-world decision-making problems concerning falling economies, power crises, depleting resources, etc., require efficient decision-making. To solve such problems, researchers proposed several hybrid models by combining the spherical fuzzy sets with other theories, such as spherical fuzzy soft sets, which is an efficient tool to deal with the uncertainties concerning positive, neutral, and negative memberships in the soft environment. However, all the existing hybridizations of spherical fuzzy sets fail to deal with information symmetrically in a bipolar soft environment. Accordingly, this paper presents a novel hybrid model called spherical fuzzy bipolar soft sets (SFBSSs) by fusing spherical fuzzy sets and bipolar soft sets, considering the opposite sets of parameters in symmetry. An example considering the selection of a chief management officer (CMO) for a multi-national company illustrates the proposed model in detail. In addition, some symmetric properties and algebraic operations of the initiated model, including subset, complement, relative null SFBSSs, relative absolute SFBSSs, extended union, extended intersection, restricted union, restricted intersection, AND, and OR operations, are discussed and illustrated via numerical examples. Further, some fundamental results, namely, commutativity, associativity, distribution, and De Morgan’s laws are presented for SFBSSs. Moreover, by considering the massive impact of hydropower in combating the energy crisis and possible dangers to fish migration, a multi-attribute decision-making problem concerning the ranking of downstream fish passage designs for a hydroelectric project is modeled and solved under the developed algorithm based on SFBSSs. Finally, a comparative analysis discusses the supremacy of the initiated model over its building blocks. Full article

(This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making under Uncertainty)

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34 pages, 4857 KiB

Open AccessArticle

A New Aggregated Multi-Criteria Approach for Evaluation of the Autonomous Metro Systems’ Performance in the European Countries

by Svetla Stoilova

Symmetry 2022, 14(10), 2025; https://doi.org/10.3390/sym14102025 - 27 Sep 2022

Cited by 1 | Viewed by 1451

Abstract

The present study aims to create groups of symmetrical autonomous metro lines that are united by common features. An integrated six-step methodology which proposes a new aggregated approach for multi-criteria evaluation of fully autonomous metro systems was proposed. The first step determines the criteria to assess the autonomous metro system. Eight criteria connected to the safety, infrastructural and technological development of the autonomous metro system were chosen. In the second step, 20 fully autonomous metro systems in European countries were selected as alternatives. The determination of the criteria weights was performed in the third step based on objective, subjective and combined approaches. For this purpose, the Shannon Entropy method and BWM (Best Worst method) were applied. The fourth step presents the ranking of the autonomous metro system by using multi-criteria methods. Three approaches were studied: distance-based, utility-based and outranking approaches. The distance-based approach includes the TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) and EDAS (Evaluation Based on Distance from Average Solution) methods; the utility-based approach includes MOORA (Multi-Objective Optimization on the Basis of Ratio Analysis) and COPRAS (COmplex PRoportional Assessment) methods; the outranking approach includes the PROMETHEE (Preference Ranking Organization METHod for Enrichment of Evaluations) method. The final ranking based on the new aggregative approach was carried out in the fifth step. Thus, Laplace’s criterion was applied to the final ranking. The Hurwitz’s criterion was used to verify the results. In the sixth step, the verification of the results was performed by applying cluster analysis. In was found that Line 1 in Paris is the best. Line 14 in Paris and Line D in Lyon were ranking in the second and third position, respectively. The autonomous metro in Brescia, Line C in Rome, and Line M2 in Lausanne were placed at the end of the ranking. Finally, four clearly formed groups of autonomous metro were proposed. The novelty of this study and its main advantage entails the elaboration of a new aggregated approach of multi-criteria methods, evaluation of the autonomous metro systems’ performance and determination for the groups of symmetrical autonomous lines in European countries. Full article

(This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making under Uncertainty)

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14 pages, 279 KiB

Open AccessArticle

Some Characterizations of Certain Complex Fuzzy Subgroups

by Abeer Ali Alharbi and Dilshad Alghazzawi

Symmetry 2022, 14(9), 1812; https://doi.org/10.3390/sym14091812 - 01 Sep 2022

Cited by 2 | Viewed by 1032

Abstract

The complex fuzzy environment is an innovative tool to handle ambiguous situations in different mathematical problems. In this article, we commence the abstraction of

(ρ, η)

-complex fuzzy sets,

(ρ, η)

-complex fuzzy subgroupoid, [...] Read more.

The complex fuzzy environment is an innovative tool to handle ambiguous situations in different mathematical problems. In this article, we commence the abstraction of

(ρ, η)

-complex fuzzy sets,

(ρ, η)

-complex fuzzy subgroupoid,

(ρ, η)

-complex fuzzy subgroups and describe important examples of the symmetric group under

(ρ, η)

-complex fuzzy sets. Additionally, we discuss the conjugacy class of the group with respect to

(ρ, η)

-complex fuzzy normal subgroups. We define

(ρ, η)

-complex fuzzy cosets and elaborate upon the certain operation of this analog to group theoretic operation. We prove that factors regarding the

(ρ, η)

-complex fuzzy normal subgroup form a group and establish an ordinary homomorphism. Moreover, we create the

(ρ, η)

-complex fuzzy subgroup of the factor group. Full article

(This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making under Uncertainty)

16 pages, 324 KiB

Open AccessArticle

Revisiting Additive Consistency of Hesitant Fuzzy Linguistic Preference Relations

by Huimin Zhang and Yiyi Dai

Symmetry 2022, 14(8), 1601; https://doi.org/10.3390/sym14081601 - 04 Aug 2022

Cited by 2 | Viewed by 963

Abstract

Consistency has always been a hot topic in the study of decision-making based on preference relations. This paper focuses on the consistency of hesitant fuzzy linguistic preference relations (HFLPRs). Firstly, a new definition of the additive consistency of HFLPRs is given. Secondly, to examine whether an HFLPR is additively consistent, two equivalent programming models are constructed. Thirdly, for inconsistent HFLPRs, the corresponding consistency improvement model is further proposed, where only upper triangular elements in the HFLPRs are considered in view of the symmetry of HFLPRs. Using the consistency improvement model, an inconsistent HFLPR can be adjusted to the consistent one, which retains the original information as much as possible. Fourthly, a hesitant fuzzy linguistic weight vector is introduced and a programming model is constructed to derive the weight vector. Finally, the feasibility and effectiveness of the proposed method are illustrated by numerical examples and comparative analysis. This result demonstrates that the consistency model proposed considers each element of HFLPRs such that the consistent HFLPRs derived fully retain the original information. Moreover, only some preference values in the HFLPR are adjusted, and no preference value is out of range of the predefined HFLTSs. Full article

(This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making under Uncertainty)

24 pages, 542 KiB

Open AccessArticle

Topological Structure of Single-Valued Neutrosophic Hesitant Fuzzy Sets and Data Analysis for Uncertain Supply Chains

by Muhammad Riaz, Yahya Almalki, Sania Batool and Shaista Tanveer

Symmetry 2022, 14(7), 1382; https://doi.org/10.3390/sym14071382 - 05 Jul 2022

Cited by 8 | Viewed by 1340

Abstract

From production to retail, the food supply chain (FSC) encompasses all stages of food production. Food is now transmitted across continents over long ranges. People depend on supply chains for basic necessities such as food, water, drinks, etc. Any disruption in these shipment pipelines poses a serious threat to human life. Supplier selection (SS) has been identified as a crucial component of FSC, which has been contemplated as a multi-criteria decision-making (MCDM) problem in many studies. The failure of some specific MCDM problems is due to failure in contemplating the relationships between alternatives under uncertain circumstances. To address such challenges, we present a contemporary method for designating green suppliers based on single-valued neutrosophic hesitant fuzzy (SVNHF) information, in which the input assessment is taken into account using single-valued neutrosophic hesitant fuzzy numbers (SVNHFNs). The foremost purpose of this analysis is to construct a topological structure on single-valued neutrosophic hesitant fuzzy sets (SVNHFSs) as well as to validate several key properties with examples. We discuss certain properties of SVNHF topology such as the SVNHF closure, SVNHF interior, SVNHF exterior, and SVNHF frontier. We also examine the conceptualization of the SVNHF dense set and SVNHF base in SVNHF topology using comprehensive examples. Eventually, to demonstrate and validate the superiority and inferiority ranking (SIR) method and choice value (CV) method in terms of their rationality and scientific basis, a real-world example of supplier selection in a food supply chain is provided. A comparative analysis is also performed to discuss the symmetry, validity and advantage of the proposed techniques. Full article

(This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making under Uncertainty)

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22 pages, 1387 KiB

Open AccessArticle

Multicriteria Optimization of Logistics Processes Using a Grey FUCOM-SWOT Model

by Vladimir Popović, Dragan Pamučar, Željko Stević, Vesko Lukovac and Srđan Jovković

Symmetry 2022, 14(4), 794; https://doi.org/10.3390/sym14040794 - 11 Apr 2022

Cited by 9 | Viewed by 1990

Abstract

Optimization of logistics processes and activities in the function of supply-chain sustainability is a great challenge for logistics companies. It is necessary to rationalize processes in accordance with the strict requirements of the market, while respecting aspects of sustainability, which is not an easy task. Multicriteria decision making can be a tool that contributes to the optimization of logistics processes in terms of making the right decisions and evaluating different strategies in different logistics subsystems. In this paper, we considered the warehousing system as one of the most important logistics subsystems in a company. Conditions and the possibility of implementing barcode technology in order to optimize warehousing processes were evaluated. We formed a strengths, weaknesses, opportunities, and threats (SWOT) matrix consisting of a total of 27 elements. In order to determine the weights of all factors at the first level of decision making and its indicators at the second level of the decision making hierarchy, an original model was developed. This model involved the creation of a novel grey full-consistency method (FUCOM-G) and integration with a SWOT analysis. Since it was a matter of group decision making, we developed a novel grey Hamy aggregator that, by adequately treating uncertainties and ambiguities, contributed to making more precise decisions. The original grey FUCOM-SWOT model based on the grey Hamy aggregator represents a contribution to the entire field of decision making and optimization of logistics processes. Based on the applied model, the obtained results showed that Weaknesses, as part of the SWOT matrix, are currently the most dominant indicators, and that the implementation of barcode technology in a warehousing system is justified. Full article

(This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making under Uncertainty)

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