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Uncertain Multi-Criteria Optimization Problems II

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

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 42707

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Dr. Dragan Pamucar

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Department of logistics, University of Defence, Belgrade, Pavla Jurišića Šturma 33, 11000 Belgrade, Serbia
Interests: multi-criteria decision making problems; computational intelligence; sustainability neuro-fuzzy systems; fuzzy; rough and intuitionistic fuzzy set theory; neutrosophic theory
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Dr. Darko Božanić

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Military Academy, University of Defence in Belgrade, Pavla Jurišića Šturma 33, Belgrade 11000, Serbia
Interests: multicriteria decision-making problems; neuro-fuzzy systems; fuzzy, rough, and intuitionistic fuzzy set theory; neutrosophic theory
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Special Issue Information

Dear Colleagues,

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relations used when modeling optimization problems. Moreover, the notion of symmetry appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better with respect to one objective may be a compromising one for other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories like probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems are not yet to be explored in-depth and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed on various uncertain frameworks with special emphasis on optimization problems.

This Special Issue on “Uncertain Multi-Criteria Optimization Problems” aims to incorporate recent developments in the area of applied science. Topics include, but are not limited to, the following:

Theoretical foundations of MCDM using uncertainty,
Aggregation operators and application in MCDM
Multi-criteria in production and logistics
Risk analysis/modeling, sensitivity/robustness analysis
Multi-criteria network optimization
Mathematical programming in MCDM under uncertainty
New trends in multi-criteria decision-making

Prof. Dr. Dragan Pamucar
Dr. Darko Bozanic
Guest Editors

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Published Papers (13 papers)

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Research

19 pages, 348 KiB

Open AccessArticle

Harmonic Aggregation Operator with Trapezoidal Picture Fuzzy Numbers and Its Application in a Multiple-Attribute Decision-Making Problem

by Chittaranjan Shit, Ganesh Ghorai, Qin Xin and Muhammad Gulzar

Symmetry 2022, 14(1), 135; https://doi.org/10.3390/sym14010135 - 11 Jan 2022

Cited by 15 | Viewed by 2694

Abstract

Picture fuzzy sets (PFSs) can be used to handle real-life problems with uncertainty and vagueness more effectively than intuitionistic fuzzy sets (IFSs). In the process of information aggregation, many aggregation operators under PFSs are used by different authors in different fields. In this article, a multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information. Three harmonic mean operators are developed namely trapezoidal picture fuzzy weighted harmonic mean (TrPFWHM) operator, trapezoidal picture fuzzy order weighted harmonic mean (TrPFOWHM) operator and trapezoidal picture fuzzy hybrid harmonic mean (TrPFHHM) operator. The related properties about these operators are also studied. At last, an MADM problem is considered to interrelate among these operators. Furthermore, a numerical instance is considered to explain the productivity of the proposed operators. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

35 pages, 1914 KiB

Open AccessArticle

Certain Operations on Picture Fuzzy Graph with Application

by Muhammad Shoaib, Waqas Mahmood, Qin Xin and Fairouz Tchier

Symmetry 2021, 13(12), 2400; https://doi.org/10.3390/sym13122400 - 12 Dec 2021

Cited by 16 | Viewed by 2832

Abstract

Fuzzy graphs (FGs) can play a useful role in natural and human-made structures, including process dynamics in physical, biological, and social systems. Since issues in everyday life are often uncertain due to inconsistent and ambiguous information, it is extremely difficult for an expert to model those difficulties using an FG. Indeterminate and inconsistent information related to real-valued problems can be studied through a picture of the fuzzy graph (PFG), while the FG does not provide mathematically acceptable information. In this regard, we are interested in reducing the limitations of FGs by introducing some new definitions and results for the PFG. This paper aims to describe and explore a few properties of PFGs, including the maximal product (MP), symmetric difference (SD), rejection (RJ), and residue product (RP). Furthermore, we also discuss the degree and total degree of nodes in a PFG. This study also demonstrates the application of a PFG in digital marketing and social networking. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

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23 pages, 961 KiB

Open AccessArticle

by Bartosz Paradowski, Andrii Shekhovtsov, Aleksandra Bączkiewicz, Bartłomiej Kizielewicz and Wojciech Sałabun

Symmetry 2021, 13(10), 1874; https://doi.org/10.3390/sym13101874 - 5 Oct 2021

Cited by 46 | Viewed by 3257

Abstract

Decision support systems (DSS) are currently developing rapidly and are increasingly used in various fields. More often, those systems are inseparable from information-based systems and computer systems. Therefore, from a methodical point of view, the algorithms implemented in the DSS play a critical role. In this aspect, multi-criteria decision support (MCDA) methods are widely used. As research progresses, many MCDA methods and algorithms for the objective identification of the significance of individual criteria of the MCDA models were developed. In this paper, an analysis of available objective methods for criteria weighting is presented. Additionally, the authors presented the implementation of the system that provides easy and accessible weight calculations for any decision matrix with the possibility of comparing results of different weighting methods. The results of weighting methods were compared using carefully selected similarity coefficients to emphasise the correlation of the resulting weights. The performed research shows that every method should provide distinctive weights considering input data, emphasising the importance of choosing the correct method for a given multi-criteria decision support model and DSS. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

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17 pages, 344 KiB

Open AccessArticle

Hesitant Fuzzy Linear Regression Model for Decision Making

by Ayesha Sultan, Wojciech Sałabun, Shahzad Faizi and Muhammad Ismail

Symmetry 2021, 13(10), 1846; https://doi.org/10.3390/sym13101846 - 2 Oct 2021

Cited by 11 | Viewed by 2292

Abstract

An expert may experience difficulties in decision making when evaluating alternatives through a single assessment value in a hesitant environment. A fuzzy linear regression model (FLRM) is used for decision-making purposes, but this model is entirely unreasonable in the presence of hesitant fuzzy information. In order to overcome this issue, in this paper, we define a hesitant fuzzy linear regression model (HFLRM) to account for multicriteria decision-making (MCDM) problems in a hesitant environment. The HFLRM provides an alternative approach to statistical regression for modelling situations where input–output variables are observed as hesitant fuzzy elements (HFEs). The parameters of HFLRM are symmetric triangular fuzzy numbers (STFNs) estimated through solving the linear programming (LP) model. An application example is presented to measure the effectiveness and significance of our proposed methodology by solving a MCDM problem. Moreover, the results obtained employing HFLRM are compared with the MCDM tool called technique for order preference by similarity to ideal solution (TOPSIS). Finally, Spearman’s rank correlation test is used to measure the significance for two sets of ranking. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

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52 pages, 2364 KiB

Open AccessArticle

A Comparative Analysis of Multi-Criteria Decision-Making Methods for Resource Selection in Mobile Crowd Computing

by Pijush Kanti Dutta Pramanik, Sanjib Biswas, Saurabh Pal, Dragan Marinković and Prasenjit Choudhury

Symmetry 2021, 13(9), 1713; https://doi.org/10.3390/sym13091713 - 16 Sep 2021

Cited by 56 | Viewed by 6206

Abstract

In mobile crowd computing (MCC), smart mobile devices (SMDs) are utilized as computing resources. To achieve satisfactory performance and quality of service, selecting the most suitable resources (SMDs) is crucial. The selection is generally made based on the computing capability of an SMD, which is defined by its various fixed and variable resource parameters. As the selection is made on different criteria of varying significance, the resource selection problem can be duly represented as an MCDM problem. However, for the real-time implementation of MCC and considering its dynamicity, the resource selection algorithm should be time-efficient. In this paper, we aim to find out a suitable MCDM method for resource selection in such a dynamic and time-constraint environment. For this, we present a comparative analysis of various MCDM methods under asymmetric conditions with varying selection criteria and alternative sets. Various datasets of different sizes are used for evaluation. We execute each program on a Windows-based laptop and also on an Android-based smartphone to assess average runtimes. Besides time complexity analysis, we perform sensitivity analysis and ranking order comparison to check the correctness, stability, and reliability of the rankings generated by each method. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

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17 pages, 1672 KiB

Open AccessArticle

Wastewater Plant Reliability Prediction Using the Machine Learning Classification Algorithms

by Lazar Z. Velimirović, Radmila Janković, Jelena D. Velimirović and Aleksandar Janjić

Symmetry 2021, 13(8), 1518; https://doi.org/10.3390/sym13081518 - 18 Aug 2021

Cited by 6 | Viewed by 3088

Abstract

One way to optimize wastewater treatment system infrastructure, its operations, monitoring, maintenance and management is through development of smart forecasting, monitoring and failure prediction systems using machine learning modeling. The aim of this paper was to develop a model that was able to predict a water pump failure based on the asymmetrical type of data obtained from sensors such as water levels, capacity, current and flow values. Several machine learning classification algorithms were used for predicting water pump failure. Using the classification algorithms, it was possible to make predictions of future values with a simple input of current values, as well as predicting probabilities of each sample belonging to each class. In order to build a prediction model, an asymmetrical type dataset containing the aforementioned variables was used. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

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21 pages, 320 KiB

Open AccessArticle

A Certain Structure of Bipolar Fuzzy Subrings

by Hanan Alolaiyan, Muhammad Haris Mateen, Dragan Pamucar, Muhammad Khalid Mahmmod and Farrukh Arslan

Symmetry 2021, 13(8), 1397; https://doi.org/10.3390/sym13081397 - 1 Aug 2021

Cited by 7 | Viewed by 2281

Abstract

The role of symmetry in ring theory is universally recognized. The most directly definable universal relation in a symmetric set theory is isomorphism. This article develops a certain structure of bipolar fuzzy subrings, including bipolar fuzzy quotient ring, bipolar fuzzy ring homomorphism, and [...] Read more.

(α, β)

-cut of bipolar fuzzy set and investigate the algebraic attributions of this phenomenon. We also define the support set of bipolar fuzzy set and prove various important properties relating to this concept. Additionally, we define bipolar fuzzy homomorphism by using the notion of natural ring homomorphism. We also establish a bipolar fuzzy homomorphism between bipolar fuzzy subring of the quotient ring and bipolar fuzzy subring of this ring. We constituted a significant relationship between two bipolar fuzzy subrings of quotient rings under a given bipolar fuzzy surjective homomorphism. We present the construction of an induced bipolar fuzzy isomorphism between two related bipolar fuzzy subrings. Moreover, to discuss the symmetry between two bipolar fuzzy subrings, we present three fundamental theorems of bipolar fuzzy isomorphism. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

31 pages, 1034 KiB

Open AccessArticle

Novel Approach for Third-Party Reverse Logistic Provider Selection Process under Linear Diophantine Fuzzy Prioritized Aggregation Operators

by Muhammad Riaz, Hafiz Muhammad Athar Farid, Muhammad Aslam, Dragan Pamucar and Darko Bozanić

Symmetry 2021, 13(7), 1152; https://doi.org/10.3390/sym13071152 - 27 Jun 2021

Cited by 51 | Viewed by 3054

Abstract

Aggregation operators are fundamental concept for information fusion in real-life problems. Many researchers developed aggregation operators for multi-criteria decision-making (MCDM) under uncertainty. Unfortunately, the existing operators can be utilized under strict limitations and constraints. In this manuscript, we focused on new prioritized aggregation operators which remove the strict limitations of the existing operators. The addition of reference parameters associated with membership and non-membership grades in the linear Diophantine Fuzzy sets provide a robust modeling for MCDM problems. The primary objective of this manuscript is to introduce new aggregation operators for modeling uncertainty by using linear Diophantine Fuzzy information. For this objective we develop aggregation operators (AO) namely, "linear Diophantine Fuzzy prioritized weighted average" (LDFPWA) operator and "linear Diophantine Fuzzy prioritized weighted geometric" (LDFPWG) operator. Certain essential properties of new prioritized AOs are also proposed. A secondary objective is to discuss a practical application of third party reverse logistic provider (3PRLP) optimization problem. The efficiency, superiority, and rationality of the proposed approach is analyzed by a numerical example to discuss 3PRLP. The symmetry of optimal decision and ranking of feasible alternatives is followed by a comparative analysis. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

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26 pages, 2872 KiB

Open AccessArticle

Interval Valued T-Spherical Fuzzy Information Aggregation Based on Dombi t-Norm and Dombi t-Conorm for Multi-Attribute Decision Making Problems

by Kifayat Ullah, Harish Garg, Zunaira Gul, Tahir Mahmood, Qaisar Khan and Zeeshan Ali

Symmetry 2021, 13(6), 1053; https://doi.org/10.3390/sym13061053 - 10 Jun 2021

Cited by 40 | Viewed by 3503

Abstract

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. Expressing the information under uncertainty using closed subintervals of [0, 1] is beneficial and effective instead of using crisp numbers from [0, 1]. The goal of this paper is to enhance the notion of Dombi aggregation operators (DAOs) by introducing the DAOs in the interval-valued T-spherical fuzzy (IVTSF) environment where the uncertain and ambiguous information is described with the help of membership grade (MG), abstinence grade (AG), non-membership grade (NMG), and refusal grade (RG) using closed sub-intervals of [0, 1]. One of the key benefits of the proposed work is that in the environment of information loss is reduced to a negligible limit. We proposed concepts of IVTSF Dombi weighted averaging (IVTSFDWA) and IVTSF Dombi weighted geometric (IVTSFDWG) operators. The diversity of the IVTSF DAOs is proved and the influences of the parameters, associated with DAOs, on the ranking results are observed in a MADM problem where it is discussed how a decision can be made when there is asymmetric information about alternatives. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

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18 pages, 321 KiB

Open AccessArticle

Linear Diophantine Fuzzy Relations and Their Algebraic Properties with Decision Making

by Saba Ayub, Muhammad Shabir, Muhammad Riaz, Muhammad Aslam and Ronnason Chinram

Symmetry 2021, 13(6), 945; https://doi.org/10.3390/sym13060945 - 26 May 2021

Cited by 58 | Viewed by 4198

Abstract

Binary relations are most important in various fields of pure and applied sciences. The concept of linear Diophantine fuzzy sets (LDFSs) proposed by Riaz and Hashmi is a novel mathematical approach to model vagueness and uncertainty in decision-making problems. In LDFS theory, the use of reference or control parameters corresponding to membership and non-membership grades makes it most accommodating towards modeling uncertainties in real-life problems. The main purpose of this paper is to establish a robust fusion of binary relations and LDFSs, and to introduce the concept of linear Diophantine fuzzy relation (LDF-relation) by making the use of reference parameters corresponding to the membership and non-membership fuzzy relations. The novel concept of LDF-relation is more flexible to discuss the symmetry between two or more objects that is superior to the prevailing notion of intuitionistic fuzzy relation (IF-relation). Certain basic operations are defined to investigate some significant results which are very useful in solving real-life problems. Based on these operations and their related results, it is analyzed that the collection of all LDF-relations gives rise to some algebraic structures such as semi-group, semi-ring and hemi-ring. Furthermore, the notion of score function of LDF-relations is introduced to analyze the symmetry of the optimal decision and ranking of feasible alternatives. Additionally, a new algorithm for modeling uncertainty in decision-making problems is proposed based on LDFSs and LDF-relations. A practical application of proposed decision-making approach is illustrated by a numerical example. Proposed LDF-relations, their operations, and related results may serve as a foundation for computational intelligence and modeling uncertainties in decision-making problems. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

36 pages, 417 KiB

Open AccessArticle

Interval Valued T-Spherical Fuzzy Soft Average Aggregation Operators and Their Applications in Multiple-Criteria Decision Making

by Tahir Mahmood, Jabbar Ahmmad, Zeeshan Ali, Dragan Pamucar and Dragan Marinkovic

Symmetry 2021, 13(5), 829; https://doi.org/10.3390/sym13050829 - 9 May 2021

Cited by 14 | Viewed by 2205

Abstract

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. Multiple-criteria decision making (MCDM) is a very effective and well-known tool to investigate fuzzy information more effectively. However, the selection of houses cannot be done by utilizing symmetry information, because enterprises do not have complete information, so asymmetric information should be used when selecting enterprises. In this paper, the notion of soft set

(S_{f t} S)

and interval-valued T-spherical fuzzy set (IVT-SFS) are combined to produce a new and more effective notion called interval-valued T-spherical fuzzy soft set

(I V T - S F S_{f t} S)

. It is a more general concept and provides more space and options to decision makers (DMs) for making their decision in the field of fuzzy set theory. Moreover, some average aggregation operators like interval-valued T-spherical fuzzy soft weighted average

(I V T - S F S_{f t} W A)

operator, interval-valued T-spherical fuzzy soft ordered weighted average

(I V T - S F S_{f t} O W A)

operator, and interval-valued T-spherical fuzzy soft hybrid average

(I V T - S F S_{f t} H A)

operators are explored. Furthermore, the properties of these operators are discussed in detail. An algorithm is developed and an application example is proposed to show the validity of the present work. This manuscript shows how to make a decision when there is asymmetric information about an enterprise. Further, in comparative analysis, the established work is compared with another existing method to show the advantages of the present work. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

20 pages, 627 KiB

Open AccessArticle

Application of Interval Fuzzy Logic in Selecting a Sustainable Supplier on the Example of Agricultural Production

by Adis Puška, Miroslav Nedeljković, Sarfaraz Hashemkhani Zolfani and Dragan Pamučar

Symmetry 2021, 13(5), 774; https://doi.org/10.3390/sym13050774 - 29 Apr 2021

Cited by 35 | Viewed by 2892

Abstract

The selection of sustainable suppliers (SSS) is the first step in applying a sustainable supply chain and sustainable production. Therefore, it is necessary to select the supplier that best meets the set sustainability criteria. However, the selection of suppliers cannot be done by applying symmetric information, because the company does not have complete information, so asymmetric information should be used when selecting suppliers. Since the SSS applies three main sustainability criteria, environmental, social, and economic criteria, this decision-making problem is solved by applying multi-criteria decision-making (MCDM). In order to solve the SSS for the needs of agricultural production, interval fuzzy logic was applied in this research, and six suppliers with whom agricultural pharmacies in Semberija work were taken into consideration. The application of interval fuzzy logic was performed using the methods PIPRECIA (Pivot pairwise relative criteria importance assessment) and MABAC (Multi-Attributive Border Approximation Area Comparison). Using the PIPRECIA method, the weights of criteria and sub-criteria were determined. Results of this method showed that the most significant are economic criteria, followed by the social criteria. The ecological criteria are the least important. The supplier ranking was performed using the MABAC method. The results showed that supplier A4 best meets the sustainability criteria, while supplier A6 is the worst. These results were confirmed using other MCDM methods, followed by the sensitivity analysis. According to the attained results, agricultural producers from Semberija should buy the most products from suppliers A4, in order to better apply sustainability in production. This paper showed how to decision make when there is asymmetric information about suppliers. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

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31 pages, 871 KiB

Open AccessArticle

M-Parameterized N-Soft Topology-Based TOPSIS Approach for Multi-Attribute Decision Making

by Muhammad Riaz, Ayesha Razzaq, Muhammad Aslam and Dragan Pamucar

Symmetry 2021, 13(5), 748; https://doi.org/10.3390/sym13050748 - 25 Apr 2021

Cited by 9 | Viewed by 2453

Abstract

In this article, we presented the notion of M-parameterized N-soft set (MPNSS) to assign independent non-binary evaluations to both attributes and alternatives. The MPNSS is useful for making explicit the imprecise data which appears in ranking, rating, and grading positions. The proposed model is superior to existing concepts of soft set (SS), fuzzy soft sets (FSS), and N-soft sets (NSS). The concept of M-parameterized N-soft topology (MPNS topology) is defined on MPNSS by using extended union and restricted intersection of MPNS-power whole subsets. For these objectives, we define basic operations on MPNSSs and discuss various properties of MPNS topology. Additionally, some methods for multi-attribute decision making (MADM) techniques based on MPNSSs and MPNS topology are provided. Furthermore, the TOPSIS (technique for order preference by similarity to an ideal solution) approach under MPNSSs and MPNS topology is established. The symmetry of the optimal decision is illustrated by interesting applications of proposed models and new MADM techniques are demonstrated by certain numerical illustrations and well justified by comparison analysis with some existing techniques. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems II)

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