Multi-criteria Group Decision-making Problems Research Articles

An optimal Best-Worst prioritization method under a 2-tuple linguistic environment in decision making

Multi-criteria group decision making (MCGDM) deals with decision makers who evaluate alternatives over several criteria. MCGDM problems evolve in tandem with the progress of our society. Such progress has given rise to the large-scale group decision making (LS-GDM) problems in which hundreds of decision makers may participate in the decision process and new challenges to face such as groups’ formation and polarization opinions. Most real world MCGDM problems present changing contexts with uncertainty that cannot be modeled by numerical values. Under these circumstances, the use of linguistic variables and computing with words (CW) processes have provided successfully results. Concretely, the 2-tuple linguistic computational model stands out because its precise linguistic computations and high interpretability. On the other hand, pairwise comparison is a widely used elicitation technique in MCGDM, but a large number of comparisons might lead inconsistent decision makers’ preferences. The Best-Worst method (BWM) reduces the number of pairwise comparisons and the inconsistency in decision makers’ opinions. Several BWM approaches have been proposed to manage linguistic information but none of them take advantage of the 2-tuple linguistic computational process based on the CW approach, which would allow to obtain precise and understandable results. This paper aims to present an extended 2-tuple BWM to reduce the number of pairwise comparisons in MCGDM problems and model the uncertainty associated with them to accomplish accuracy computations and obtaining interpretable results. Moreover, we apply our proposal to LS-GDM scenarios in which polarization opinions and sub-groups identification, ignored from any of BWM proposals, are considered. Finally, the new model is applied to several illustrative MCGDM problems.

A decision support system for detecting and handling biased decision-makers in multi criteria group decision-making problems

Detecting and handling biased decision-makers in the group decision-making process is overlooked in the literature. This paper aims to develop an anti-biased statistical approach, including extreme, moderate, and soft versions, as a decision support system for group decision-making (GDM) to detect and handle the bias. The extreme version starts with eliminating the biased decision-makers (DMs). For this purpose, the DMs with a lower Biasedness Index value than a predefined threshold are removed from the process. Next, it continues with a procedure to mitigate the effect of partially biased DMs by assigning different weights to DMs with respect to their biasedness level. To do so, two ratios for the remaining DMs are calculated: (i) Overlap Ratio, which shows the relative value of overlap between the confidence interval (CI) of each DM and the maximum possible overlap value. (ii) Relative confidence interval CI which reflects the relative value of CI for each DM compared to the confidence interval CI of all DMs. The final step is assigning weight to each DM, considering the two values Overlap Ratio and Relative confidence interval. DMs with closer opinions to the aggregated opinion of all DMs, or those with an adequate level of discrimination in their judgments gain more weight. The framework addresses and prescribes possible actions for all possible cases in GDM including without outliers, cases with partial outliers, and extreme cases with complete disagreement among DMs, or when none of the DMs show an adequate level of discrimination power. The moderate version preassigns a minimum weight to all unbiased DMs and then follows the weighting step for the remaining total weight. However, the soft version follows the preassignmnet of weights to all DMs in the initial pool, meaning there is no elimination in this setting. The proposed approach is tested for several scenarios with different sizes. Four performance measures are introduced to evaluate the effectiveness of the proposed method. The resulted performance measures show the reliability of the outcomes.

A comparison between intuitionistic and hesitant fuzzy applied to supplier selection group decision making problem

Supplier selection and evaluation is approached in the literature as a multi-criteria decision problem in which usually more than one decision-maker has to judge the importance of criteria and the performance of suppliers. Fuzzy techniques are commonly applied to deal with the uncertainty in the evaluation process. Intuitionistic and hesitant fuzzy representations have been applied to group decision problems. However, none of the studies in the literature presents a comparison of these two fuzzy representations when applied to multi-criteria group decision-making (MCGDM) problems. Thus, this paper presents the results of a comparative study of the intuitionist fuzzy and the hesitant fuzzy representations applied to supplier selection problem. The techniques were implemented and tested in a pilot application to a textile manufacturing company. The comparison was based on congruency of results, adequacy to group decision, data collection effort and flexibility of judgement, computational complexity and modelling of uncertainty.

A Novel Approach Toward Roughness of Bipolar Soft Sets and Their Applications in MCGDM

The uncertainty in the data is an obstacle in decision-making (DM) problems. In order to solve problems with a variety of uncertainties a number of useful mathematical approaches together with fuzzy sets, rough sets, soft sets, bipolar soft sets have been developed. The rough set theory is an effective technique to study the uncertainty in data, while bipolar soft sets have the ability to handle the vagueness, as well as bipolarity of the data in a variety of situations. This study develops a new methodology, which we call the theory of dominance-based bipolar soft rough sets (DB-BSRSs), which will be used to propose a new technique to solve decision-making problems. The idea introduced in this study has never been discussed earlier. Furthermore, this concept has been explored by means of a detailed study of the structural properties. Moreover, some important measures like the accuracy measure , the measure of precision , and the measure of quality for DB-BSRSs are also provided. Finally, an application of the DB-BSRSs in multi-criteria group decision-making (MCGDM) problem is presented and an algorithm for this application is proposed, supported by an example, which yields the best decision, as well as, the worst decision between some objects. In comparison with some existing results, we also present some advantages of our proposed method.

Weighted Parameterized Correlation Coefficients of Indeterminacy Fuzzy Multisets and Their Multicriteria Group Decision Making Method with Different Decision Risks

Real-life data introduce noise, uncertainty, and imprecision to statistical projects; it is advantageous to consider strategies to overcome these information expressions and processing problems. Neutrosophic (indeterminate) numbers can flexibly and conveniently represent the hybrid information of the partial determinacy and partial indeterminacy in an indeterminate setting, while a fuzzy multiset is a vital mathematical tool in the expression and processing of multi-valued fuzzy information with different and/or same fuzzy values. If neutrosophic numbers are introduced into fuzzy sequences in a fuzzy multiset, the introduced neutrosophic number sequences can be constructed as the neutrosophic number multiset or indeterminate fuzzy multiset. Motivated based on the idea, this study first proposes an indeterminate fuzzy multiset, where each element in a universe set can be repeated more than once with the different and/or identical indeterminate membership values. Then, we propose the parameterized correlation coefficients of indeterminate fuzzy multisets based on the de-neutrosophication of transforming indeterminate fuzzy multisets into the parameterized fuzzy multisets by a parameter (the parameterized de-neutrosophication method). Since indeterminate decision-making issues need to be handled by an indeterminate decision-making method, a group decision-making method using the weighted parameterized correlation coefficients of indeterminate fuzzy multisets is developed along with decision makers’ different decision risks (small, moderate, and large risks) so as to handle multicriteria group decision-making problems in indeterminate fuzzy multiset setting. Finally, the developed group decision-making approach is used in an example on a selection problem of slope design schemes for an open-pit mine to demonstrate its usability and flexibility in the indeterminate group decision-making problem with indeterminate fuzzy multisets.

Consensual Group-AHPSort: Applying consensus to GAHPSort in sustainable development and industrial engineering

Multi-Criteria Group Decision Making (MCGDM) deals with the process of taking decisions among a number of decision makers who evaluate different alternatives on several criteria that may be conflicting. In such a type of problems conflicts may are not only related to the criteria but also with the decision makers that could result in unsatisfactory solutions because of disagreements or deadlocks to achieve a decision. To avoid these undesirable results, consensus processes have been applied to group decision. The application of MCGDM has been mainly focused on decision problems for ranking and choice alternatives but, similarly to multi-criteria decision making, other types of problems such as sorting and description can be formulated. Although, a few number of MCGDM-sorting models, comparing with ranking and choice ones, have been proposed their importance and impact is quite significant nowadays. Hence, our aim is to consider the recent proposal on Group-AHPSort that did not consider any disagreement measure across the sorting decision process and study how the use of consensus processes can avoid some misclassifications or disagreements among the group of decision makers taking part in the MCGDM problem. To illustrate our approach, a case study focusing on the sorting of five European Union countries according to their sustainable development performance regarding social issues will show the importance and utility of detecting and smoothing disagreements in Group-AHPSort.

Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices and their application in decision-making

This study aims to propose the concept of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices) and to present several of its basic properties. Therefore, it would be possible to improve the problem-modelling capabilities of the available intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets in the occurrence of a large number of data. Moreover, by using ifpifs-matrices, we suggest a new soft decision-making method, denoted by EA20, and apply it to a multi-criteria group decision-making (MCGDM) problem. We then compare the ranking performance of EA20 for five noise-removal filters with those of ten state-of-the-art soft decision-making methods. The results show that EA20 successfully models performance-based value assignment problems. Finally, we discuss ifpifs-matrices and EA20 for further research.

T-spherical fuzzy TODIM method for multi-criteria group decision-making problem with incomplete weight information

In this paper, we investigate the multi-criteria group decision-making (MCGDM) problems with incomplete weight information under T-spherical fuzzy environment. Firstly, motivated by the idea of the intuitionistic fuzzy interaction method, we propose some operation laws of T-spherical fuzzy numbers (T-SFNs), as well as some T-spherical fuzzy interaction aggregation operators, such as the T-spherical fuzzy weighted averaging interaction (T-SFWAI) operator, the T-spherical fuzzy weighted geometric interaction (T-SFWGI) operator, the T-spherical fuzzy ordered weighted interaction aggregation operators and the generalized T-spherical fuzzy interaction aggregation operators. Then, some desirable properties of the proposed T-SFWAI and T-SFWGI operators and some special cases of the generalized T-spherical fuzzy interaction aggregation operators are discussed in detail. Secondly, for the situations where the information about the weights of criteria is partly known or completely unknown, we establish two optimization models to determine the weights of criteria based on the maximizing deviation method and Lagrange function method, respectively. Thirdly, the traditional TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) approach is extended to solve MCGDM problem under the T-spherical fuzzy environment by defining the distance between T-SFNs, score function and accuracy function of T-spherical fuzzy number. Finally, a numerical example is given to illustrate the application of the extended TODIM approach, and further the sensitivity analysis and comparison analysis are carried out to demonstrate the influence of parameter on the final result and the effectiveness of the extended method.

Distance and Similarity Measures for Octahedron Sets and Their Application to MCGDM Problems

In this paper, in order to apply the concept of octahedron sets to multi-criteria group decision-making problems, we define several similarity and distance measures for octahedron sets. We present a multi-criteria group decision-making method with linguistic variables in octahedron set environment. We give a numerical example for multi-criteria group decision-making problems.

Multigranulation single valued neutrosophic covering-based rough sets and their applications to multi-criteria group decision making

In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).Firstly, a type of SVN covering-based rough set model is proposed.Based on this rough set model, three types of multigranulation SVN covering-based rough set models under the concept of multigranulation SVN $beta$-covering approximation space are proposed, where $beta$ is a SVN number.Moreover, the connections among these four models are investigated.Secondly, some conditions under which different multigranulation SVN $beta$-covering approximation spaces induced the same multigranulation SVN covering approximation operators are presented.Finally, three novel methods are presented to MCGDM problems under the multigranulation SVN covering-based rough set models.Furthermore, the proposed MCGDM methods are compared with other methods through a problem about paper defect diagnosis.

A novel methodology to select sustainable municipal solid waste management scenarios from three-way decisions perspective

Selecting a sustainable municipal solid waste management (MSWM) scenario can reduce greenhouse gas emissions and deal with the energy crisis, effectively. However, traditional decision approaches only rank alternative scenarios but fail to manage them. Implementing effective management for alternative MSWM scenarios can save decision costs and improve efficiency. Thus, this paper aims to construct a novel multi-criteria group decision-making (MCGDM) methodology to manage and rank sustainable scenarios. To evaluate sustainable MSWM scenarios, a comprehensive evaluation index system is constructed from five dimensions including economy, environment, society, technology, and energy. The hesitant fuzzy linguistic term set is employed to articulate evaluation information. Given the importance of experts and the incomplete criteria weight information, an inclusion measure-based approach is proposed to obtain expert weights, and the grey relational analysis linear programming model with incomplete criteria weight information is constructed to determine criteria weights. An inclusion measure-based hesitant fuzzy linguistic multigranulation three-way decisions over two universes approach is developed to manage and rank alternative MSWM scenarios. The feasibility of the proposed methodology is illustrated by a numerical case. Triple sensitivity analysis is performed from the perspectives of decision-makers’ risk appetite, expert weight fluctuations, and criteria weight fluctuations. A comparative analysis is implemented to demonstrate the effectiveness and superiority of the proposed methodology. This study provides a novel insight to solve MSWM scenario selection and can extensively be applied to handle other MCGDM problems.

The adjustable approaches to multi-criteria group decision making based on inverse fuzzy soft matrices

In this paper, we focus on the matrices representing the inverse fuzzy soft sets over both the universal object set and the universal parameter set. Some basic operations and properties of these inverse fuzzy soft matrices are investigated. Moreover, two adjustable approaches to multi-criteria group decision making (MCGDM), namely inverse fuzzy soft sum-product decision making (IFSSPDM) and inverse fuzzy soft distributive If-difference decision making (IFSDIf-dDM), are proposed. The IFSSPDM approach achieves the optimal choice for the MCGDM problem based on the inverse fuzzy soft structures consisting of multiple-discrete parameter sets and common universal object sets. The objective of IFSDIf-dDM approach is to present a solution for the MCGDM problem based on the inverse fuzzy soft structures consisting of a common universal parameter set and two discrete universal object sets. Thus, the solutions can be obtained using the practicality of inverse fuzzy soft matrices for two different types of decision making problems. Besides, the comparisons are presented showing that the proposed approaches produce more convincing outputs than the current fuzzy soft approaches.

Intuitionistic Fuzzy Sets in Multi-Criteria Group Decision Making Problems Using the Characteristic Objects Method

Over the past few decades, several researchers and professionals have focused on the development and application of multi-criteria group decision making (MCGDM) methods under a fuzzy environment in different areas and disciplines. This complex research area has become one of the more popular topics, and it seems that this trend will be increasing. In this paper, we propose a new MCGDM approach combining intuitionistic fuzzy sets (IFSs) and the Characteristic Object Method (COMET) for solving the group decision making (GDM) problems. The COMET method is resistant to the rank reversal phenomenon, and at the same time it remains relatively simple and intuitive in practical problems. This method can be used for both symmetric and asymmetric information. The Triangular Intuitionistic Fuzzy Numbers (TIFNs) have been used to handle uncertain data. This concept can ensure the preference information about an alternative under specific criteria more comprehensively and allows for easy modelling of symmetrical or asymmetrical linguistic values. Each expert provides the membership and non-membership degree values of intuitionistic fuzzy numbers (IFNs). So this approach deals with a different kind of uncertainty than with hesitant fuzzy sets (HFSs). The proposed combination of COMET and IFSs required an adaptation of the matrix of expert judgment (MEJ) and allowed to capture the behaviour aspects of the decision makers (DMs). Therefore, we get more reliable solutions while solving MCGDM problems. Finally, the proposed method is presented in a simple academic example.

Classification of trapezoidal bipolar neutrosophic number, de-bipolarization technique and its execution in cloud service-based MCGDM problem

Neutrosophic set can deal with the uncertainties related to the information of any decision making problem in real life scenarios, where fuzzy set may fail to handle those uncertainties properly. In this study, we present the perception of trapezoidal bipolar neutrosophic numbers and its classification in different frame. We introduce the idea of disjunctive structures of trapezoidal bipolar neutrosophic numbers namely type-1 trapezoidal bipolar neutrosophic number, type-2 trapezoidal bipolar neutrosophic numbers, and type-3 trapezoidal bipolar neutrosophic number based on the perception of dependency among membership functions in neutrosophic set. In any neutrosophic decision-making problem, the decision maker uses the comparison of neutrosophic numbers to choose among alternatives solutions. Here, we introduce a ranking method, i.e., De-bipolarization scheme for trapezoidal bipolar neutrosophic number (TrBNN) using removal area technique. We also describe the utility of trapezoidal bipolar neutrosophic number and its appliance in a multi criteria group decision making problem (MCGDM) for distinct users in trapezoidal bipolar arena which is more ethical, precise and reliable in neutrosophic field.

Multicriteria group decision-making under uncertainty using interval data and cloud models

In this study, we propose a multicriteria group decision-making (MCGDM) algorithm under uncertainty where data is collected as intervals. The proposed MCGDM algorithm aggregates the data, determines the optimal weights for criteria and ranks alternatives with no further input. The intervals give flexibility to experts in assessing alternatives against criteria and provide an opportunity to gain maximum information. We also propose a novel method to aggregate experts’ judgements using cloud models. We introduce an experimental approach to check the validity of the aggregation method. After that, we use the aggregation method for an MCGDM problem. Here, we find the optimal weights for each criterion by proposing a bi-level optimisation model. Then, we extend the technique for order of preference by similarity to ideal solution (TOPSIS) for data based on cloud models to prioritise alternatives. As a result, the algorithm can gain information from decision-makers with different levels of uncertainty and examine alternatives with no more information from decision-makers. The proposed MCGDM algorithm is implemented on a case study of a cybersecurity problem to illustrate its feasibility and effectiveness. The results verify the robustness and validity of the proposed MCGDM using sensitivity analysis and comparison with other existing algorithms.

Towards a Hybrid Evaluation Approach to Chinese Sustainable Drinking Water Source Regions within an Uncertain Decision Environment

Confronted with the increasingly serious water pollution in China, companies are implementing scientific measures to strive for sustainable drinking water source regions (DWSRs). The challenge lies in how to evaluate available DWSRs. Considering the complexity and uncertainty existing in the evaluation process, we deem this process a complicated multi-criteria group decision-making (MCGDM) problem. It involves fuzzy decision information, prioritized relationships among different criteria, and distinctively allocated weights of decision makers regarding different alternatives. By utilizing the asymmetrical weak probabilistic hesitant fuzzy elements (P-HFES) to depict fuzzy data, this paper leads a direction to investigating a data-driven MCGDM approach and its application to evaluate available DWSRs. First, considering the common sense that criteria are not always given symmetrical priority, we propose a series of aggregation operators for integrating weak P-HFEs by including the prioritized relationship of criteria. Moreover, the importance weights of criteria and decision makers are objectively determined through a priority-based basic unit interval and monotonic (P-BUM) function and some novel distance measures, respectively. Finally, an evaluation approach is established. It aims to handle MCGDM problems with incomplete weight information regarding the criteria and decision makers in weak probabilistic hesitant fuzzy circumstance. Practically, focusing on evaluating three DWSRs, a realistic example of application is furnished to verify the feasibility of the proposed approach.

Possibility Degree and Power Aggregation Operators of Single-Valued Trapezoidal Neutrosophic Numbers and Applications to Multi-Criteria Group Decision-Making

Single-valued trapezoidal neutrosophic numbers (SVTNNs) are very useful tools to describe complex cognitive information because of their advantage in maintaining the completeness and accuracy of information. This paper develops a method based on the single-valued trapezoidal neutrosophic power-weighted aggregation operators and possibility degree of SVTNNs for dealing with multi-criteria group decision-making (MCGDM) problems. First, the limitations of the existing operations for SVTNNs are discussed, and then an improved operation is defined. Moreover, the possibility degree of two SVTNNs with consideration of the influence of risk attitudes is proposed, and the comparison rules for SVTNNs are thereby established. Based on the new operation and possibility degree of SVTNNs, the single-valued trapezoidal neutrosophic power average and single-valued trapezoidal neutrosophic power geometric operators are proposed to aggregate the single-valued trapezoidal neutrosophic information. Furthermore, a single-valued trapezoidal neutrosophic MCGDM method is developed. Finally, an example of a company selecting the most suitable green supplier is provided to present a comparative analysis between the proposed approach and other related methods. This example can demonstrate the effectiveness and flexibility of the proposed methodology.

Multiple criteria group decision analysis using a Pythagorean fuzzy programming model for multidimensional analysis of preference based on novel distance measures

The preference concerning criteria or alternatives from decision makers (DMs) is a critical element in multicriteria group decision making (MCGDM). The linear programming technique for the multidimensional analysis of preference (LINMAP) is the most influential technique in adjusting the error between the objective assessments on criteria and subjective preferences on alternatives via optimal programming for MCGDM problems. Considering the higher capacity for expressing the uncertainties of human inherent preferences of the Pythagorean fuzzy (PF) sets, this article explores the LINMAP technique for MCGDM problems under the PF scenario. First, we present a novel (squared) Euclidean distance measure for the PF sets since it possesses captivating characteristics of the PF sets and the distance measure. Second, we define the preference degrees over alternatives that are expressed as PF sets and calculate their magnitudes via relative distances, which are used to calculate the consistency and inconsistency indices. Third, the ordered weighted averaging (OWA) operator under the normal distribution is introduced to obtain the weights of DMs to reduce the influence of unfair arguments. Fourth, we construct the biobjective PF-LINMAP model for minimizing both the error extents and the overall distances to the PF positive ideal solution for the minimum error and global optimum. Then, we obtain the optimal criterion weights and ranks of the candidates via relative closeness indices. Finally, we perform our PF-LINMAP method to choose the optimal green supplier, and we implement the sensitivity analysis and comparative analysis with those of the available PF-LINMAP methods to verify the feasibility and superiority of our approach.

Group decision-making framework using complex Pythagorean fuzzy information

This paper contributes to the expanding literature on VIKOR, a well-known multi-criteria decision-making technique. It is abundantly used to find the compromise solution regarding some significant criteria under different models. The general VIKOR methodology implements the principle that a recommended response must be a feasible solution which is nearest to positive ideal solution having maximum group utility and minimum individual regret. In this article, we propose a new strategy to address multi-criteria group decision-making problems named complex Pythagorean fuzzy VIKOR (CPF-VIKOR) method. It is designed to handle a great deal of vagueness and hesitation which are often present in human decisions. The CPF-VIKOR method allows the linguistic terms to express individual opinions of experts about the performance of alternatives and the weights of the criteria. We combine the individual judgments of experts with the help of complex Pythagorean fuzzy weighted averaging operator. Further, we compute the ranking measure with the help of group utility and regret measures by adjusting the weight of strategy of maximum group utility within the unit interval. We sort the alternatives in an ascending order relative to group utility measure and individual regret measure. Moreover, we demonstrate our proposed method with the help of a flow chart and two numerical examples: one for the selection of the most beneficial renewable energy project in Spain and another for the selection of the most suitable logistic village location in Turkey. Finally, we present the comparative analysis of our proposed method with the CPF-TOPSIS method to prove its validity.

Q-Rung Orthopair Fuzzy Prioritized Aggregation Operators and Their Application Towards Green Supplier Chain Management

Supply management and environmental concerns are becoming increasingly relevant to scientific decision analysis around the world. Several companies have implemented the green supply chain management (GSCM) approach for attaining economic advantages while retaining sustainable growth for the environment. Green supplier selection has also been analyzed in many literary works as an important part of GSCM, which is considered an important multi-criteria group decision making (MCGDM) problem. The lack of consideration of the relationships of alternatives to the uncertain environment will be the main reason for weak conclusions in some MCGDM problems. To address these drawbacks, we introduce a new approach for selecting green suppliers with the q-rung orthopair fuzzy information, in which the input assessment is considered by using q-rung orthopair fuzzy numbers (q-ROFNs). A q-ROFN is extremely valuable in representing vague information that occurs in these real-world circumstances. The priority relationship of the alternatives to q-rung orthopair fuzzy information is very helpful to deal with GSCM. Consequently, we develop some prioritized operators with q-ROFNs named the q-rung orthopair fuzzy prioritized weighted average (q-ROFPWA) operator and q-rung orthopair fuzzy prioritized weighted geometric (q-ROFPWG) operator. Several important characteristics of these operators such as idempotents, boundary, and monotonicity are also well proven. Finally, an application of the proposed operators is presented for green supplier selection in GSCM. The scientific nature of the proposed methodology is illustrated by a numerical example to validate its rationality, symmetry, and superiority.