Multi-criteria Group Research Articles

Multi-criteria group decision making approach based on a new type of neutrosophic vague approach is used to select the shares of the companies for purchase

In this paper, we introduce the neutrosophic vague soft set, a combination of vague and neutrosophic soft sets. With the help of aggregated operations, we discuss neutrosophic vague soft sets. Multi-criteria group decision making can be evaluated effectively using the VIKOR approach. In this approach, the score function is generated by aggregating the VIKOR method to a neutrosophic vague soft approach. With the help of closeness values, alternative solutions are presented as optimal ones. To invest some money into the top five companies on the stock exchange, an investment company intends to purchase shares of the companies. Their investment strategy was to allocate some of their cash in percentages of 30 dollars, 25 dollars, 20 dollars, 15 dollars, and 10 dollars according to the top five ranked companies to minimize this effect.

Neutrosophic Fuzzy Score Matrices: A Robust Framework for Advancing Medical Diagnostics

In this paper, we introduce the Single-Valued Neutrosophic Fuzzy Matrix (SVNFM), which consists of entries that are all single-valued neutrosophic fuzzy sets (SVNFS). Our objective is to provide a practical tool for dealing with uncertain and indeterminate input. To achieve this, we first define a neutrosophic fuzzy matrix (NFM) and discuss its fundamental properties. The use of various operations in decision making is a notable characteristic of single-valued neutrosophic fuzzy matrices (SVNFMs). In this paper, we propose a multicriteria group decision-making method that incorporates novel operations on neutrosophic fuzzy matrices. Finally, we present a case study to demonstrate the effectiveness of the proposed strategy.

A Novel Approach to Roughness of Linear Diophantine Fuzzy Sets by Fuzzy Relations and its Application towards Multi-Criteria Group Decision-Making

A Novel Approach to Roughness of Linear Diophantine Fuzzy Sets by Fuzzy Relations and its Application towards Multi-Criteria Group Decision-Making

Interval-valued Pythagorean fuzzy entropy and its application to multi-criterion group decision-making

<abstract><p>Entropy is an important tool of information measurement in the fuzzy set and its inference. The research on information measurement based on interval-valued Pythagorean fuzzy sets mostly involves the distance formula for interval-valued Pythagorean fuzzy numbers, but seldom involves the measurement of fuzziness. In view of this situation, we have aimed to propose new interval-valued Pythagorean fuzzy entropy and weighted exponential entropy schemes. Based on the interval-valued Pythagorean fuzzy weighted averaging operator, a strategy based on weighted exponential entropy is proposed to solve the multi-criteria group decision-making (MCGDM) problem in the interval-valued Pythagorean environment. Two examples illustrate that this paper provides a feasible new method to solve the MCGDM problem in an interval-valued Pythagorean fuzzy (IVPF) environment. Finally, by comparing with the existing methods, it is concluded that the entropy measure of IVPF schemes and the corresponding MCGDM method can select the optimal solution of the practical problem more precisely and accurately. Therefore, the comparative analysis shows that the proposed measurement method has the characteristics of flexibility and universality.</p></abstract>

Evaluation of sustainable cold chain suppliers using a combined multi-criteria group decision-making framework under fuzzy ZE-numbers

Health 4.0 actively focuses on cold supply chains (CSCs) due to digital transformation and technological advancements in refrigeration. With the ill effects of climate change and greenhouse gas emissions, countries globally seek sustainable supply chain management. In this context, integrating sustainability with CSCs becomes crucial. Health sectors actively consider CSC for their activities. In this context, to gain potential suppliers for healthcare management, the present work focuses on grading suppliers from the CSC with sustainability factors. Previous related studies on sustainable cold chain supplier selection (CSSS) (i) have not modeled uncertainty effectively, and (ii) have yet to use any approach under fuzzy Z-numbers information. Therefore, this paper developed an integrated framework, including the Logarithm Methodology of Additive Weights (LMAW) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods based on extended fuzzy Z-numbers. The practicality of the framework is exemplified via a case example within the Indian health sector, and results indicate that job creation, value price, and productivity via renewable resources are the most critical factors. Moreover, regarding the findings, the economic dimension is the foremost pillar for effective selection. Sensitivity and comparison analyses are performed to understand the efficacy of the integrated framework as well. The proposed framework could contribute to the relevant literature due to its capacity to cope with complex decision-making problems and find many application areas in engineering.

Non-uniform allocation of information granularity to improve consistency and consensus in multi-criteria group decision-making: Application to building refurbishment

If a decision depends on the views of a group of people, it is crucial that these views are consistent, in particular if they are represented in terms of fuzzy preference relations. Moreover, before making the decision, the agreement achieved must be as high as possible. In most cases, to achieve it, the initial viewpoint of each group member must be modified during the decision-making process, which causes an information loss. To handle this issue, some conditions have been added to the modification process. Concretely, some approaches have turned to an allocation of information granularity to control it. However, these approaches either allocate the information granularity in a uniform way or not consider the issues of consistency and consensus in a scenario of multi-criteria group decision-making. To enhance these approaches, we elaborate a novel granular-based approach composed of two processes. Firstly, an automatic process based upon a non-uniform allocation of information granularity is developed to maximize both the consensus and the consistency in multi-criteria group decision-making where fuzzy preference relations are used to model the group members’ views. Based upon it, secondly, an interactive process requiring the implication of the group members is introduced, which also intends to maximize both the consensus and the consistency. Some experimental studies are completed to show the essence of this new approach and to demonstrate its performance and flexibility. A case study on building refurbishment is also conducted to validate its effectiveness and feasibility in practical real-world problem-solving.

T-Spherical fuzzy soft rough aggregation operators and their applications in multi-criteria group decision-making

T-Spherical fuzzy soft rough aggregation operators and their applications in multi-criteria group decision-making

A Hybrid DEMATEL and Bayesian Best–Worst Method Approach for Inland Port Development Evaluation

Inland ports are gaining more and more attention as important hubs for inland cities to promote foreign trade. However, studies on the evaluation of inland ports are lacking. In this work, we aim to construct an index system and propose a multi-criteria group decision-making method to comprehensively evaluate the development of inland ports. Unlike previous studies, using pressure–state–response model as a reference, we built up a demand–risk–power–potential framework for the index system proposed in this study. To determine the different weights for each indicator, which is a typical multi-criteria decision-making problem, we innovatively combined the decision-making trial and evaluation laboratory (DEMATEL) and the Bayesian best–worst method (BBWM) based on their distinct advantages in dealing with data coupling and group decision-making. In addition, this work introduces a case study of inland ports in the Huaihai Economy Zone to validate the efficacy of the proposed evaluation model and method. After calculating and obtaining the comprehensive scores and rankings of each inland port in this case, we compared the evaluation results with those under the BBWM, TOPSIS, and CRITIC methodologies, and found that the results under the DEMATEL–BBWM methodology can provide better differentiation for inland port evaluation results. Moreover, based on the evaluation results, a performance–importance matrix is formulated to identify the areas requiring attention in the development process of each inland port. Subsequently, rational managerial insights are put forward to achieve the sustainable development of inland ports in the Huaihai Economy Zone.

Multi-criteria group decision making based on graph neural networks in Pythagorean fuzzy environment

Given that the majority of existing approaches for multi-criteria group decision making (MCGDM) rely solely on the preferences of decision makers (DMs) and fail to consider the various relationships between alternatives, this paper attempts to model the relevant relational structures using graphs and introduce the concept of graph neural networks (GNNs) in the context of group decision-making. By leveraging the powerful expressive capabilities of GNNs, the aim is to mine additional information pertinent to the decision-making process and screen out alternatives for the final decision. To begin, we provide a mapping of MCGDM to the graph domain and construct a corresponding relation graph among alternatives. Additionally, to deal with uncertain or vague information, we transform the group decision-making problem into a Pythagorean fuzzy environment and define a novel measure of entropy specifically designed for Pythagorean fuzzy sets (PFSs) in the entropy weight model to determine the weights of criteria. Simultaneously, we propose a new distance measure for PFSs, which is then applied to the extended Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method to rank alternatives. Furthermore, we develop a GNNs-based Pythagorean fuzzy MCGDM approach that incorporates the aforementioned techniques for group decision-making. Finally, to validate the effectiveness and superiority of this approach, we employ it to address a supplier selection issue. Compared with baseline group decision-making approaches, our approach can indeed capture the relationships among alternatives in complex group decision-making scenarios and outperforms the best-performing baseline by nearly 2.8% in terms of ranking accuracy.

Some T-spherical fuzzy dombi hamy mean operators and their applications to multi-criteria group decision-making process

Renewable energy sources play an influential role in the world’s climate and reduce the rate of harmful gasses such as carbon dioxide, methane, nitrous oxide, and many other greenhouse gasses that contribute to global warming. The theoretical concept of the T-spherical fuzzy (T-SF) set (T-SFS) is the most suitable model to evaluate energy resources under uncertainty. This article illustrates appropriate operations based on Dombi triangular norm and t-conorm. We derived a series of new aggregation approaches, such as T-SF Dombi Hamy mean (T-SFDHM) and T-SF weighted Dombi Hamy Mean (T-SFDWHM) operators. Further authors illustrated a list of new approaches such as T-SF Dual Dombi Hamy mean (T-SFDDHM), and T-SF Dombi weighted Dual Hamy mean (T-SFDWDHM) operators. Some exceptional cases and desirable properties of our derived approaches are also studied. We illustrate an application of renewable energy resources to be evaluated using a multi-attribute group decision-making (MAGDM) method. A case study was also studied to choose appropriate energy resources using our proposed methodology of the T-SFDWHM and T-SFDWDHM operators. To show the effectiveness and validity of our current methods, we compared the existing results with currently developed aggregation operators (AOs).

Assessing the triage and efficacy of strategies of SAARC to improve regional integrity of South Asia using multicriteria group decision making under q-rung orthopair hesitant fuzzy environment

The South Asian Association for Regional Cooperation (SAARC) plays a crucial role in fostering regional integration and cooperation among the countries of South Asia. However, the organization faces various challenges in achieving its objectives due to the complex and dynamic nature of the region. This study aims to assess the triage and efficacy of strategies employed by SAARC in pursuit of regional integrity in South Asia, using a Multi-Criteria Group Decision Making (MCGDM) technique. The assessment process involves several uncertainties which are resolved using q-rung orthopair hesitant fuzzy (q-ROHF) set. A distance measure is developed for q-ROHF sets and is applied to find the best strategy among six well known strategies, viz., SAARC Agreement on Trade in Services (SATIS), SAARC Development Fund (SDF), Establishment of South Asian University (SAU), SAARC Arbitration Council (SARCO), South Asian Preferential Trade Agreement (SAPTA) and South Asian Free Trade Area (SAFTA) through SWARA-TOPSIS based MCGDM technique. The MCGDM method is updated by developing several aggregation operators, viz., Archimedean q-ROHF weighted average, q-ROHF Einstein weighted average, q-ROHF Hamacher weighted average, q-ROHF Frank weighted average along with their geometric forms to combine decision makers’ individual decision. The result shows that the most effective strategy for the economic integration of SAARC is SDF; SATIS comes next as best strategy for economic integration of SAARC. The study reveals that SAU has least impact on the regional economic integration of SAARC. The achieved results reveals the age old proverb that “play on the stomach and sit on the back” – the members of SAARC who are by nature economically poor can afford to take initiative for a successful effective regionalization if it is planned to bring socio economic development of themselves.

Dual Hesitant q-Rung Orthopair Fuzzy Interaction Partitioned Bonferroni Mean Operators and Their Applications

The purpose of this paper is to introduce interaction partitioned Bonferroni mean operators under dual hesitant q-rung orthopair fuzzy environment. Motivated by the idea of q-rung orthopair fuzzy interaction operational laws, partitioned Bonferroni mean, and dual hesitant q-rung orthopair fuzzy sets, for dual hesitant q-rung orthopair fuzzy numbers, we present dual hesitant q-rung orthopair fuzzy interaction operational rules and propose several dual hesitant q-rung orthopair fuzzy interaction partitioned Bonferroni mean aggregation operators, including the interaction partitioned Bonferroni mean operator for dual hesitant q-rung orthopair fuzzy numbers, the weighted interaction partitioned Bonferroni mean operator for dual hesitant q-rung orthopair fuzzy numbers, the interaction partitioned geometric Bonferroni mean operator for dual hesitant q-rung orthopair fuzzy numbers, and the weighted interaction partitioned geometric Bonferroni mean operator for dual hesitant q-rung orthopair fuzzy numbers. Moreover, some properties and special cases associated with these proposed operators are also analyzed. For dual hesitant q-rung orthopair fuzzy numbers, based on the proposed operators, a multicriteria group decision-making method is proposed. Finally, an example for missile purchase problem is illustrated to demonstrate the superiority and feasibility by comparing with other existing multicriteria group decision-making methods.

A Framework for Evaluating Distance Learning of Environmental Science in Higher Education using Multi-Criteria Group Decision Making

A Framework for Evaluating Distance Learning of Environmental Science in Higher Education using Multi-Criteria Group Decision Making

Q-Multi Cubic Pythagorean Fuzzy Sets and Their Correlation Coefficients for Multi-Criteria Group Decision Making

Q-multi cubic Pythagorean fuzzy sets (Q-mCPFSs) are influential, effective and symmetrical for representing uncertain and imprecise information in decision making processes. Q-mCPFSs extend the concept of Q-multi fuzzy sets by introducing the notion of cubic Pythagorean membership functions, which provide a more flexible and accurate representation of uncertainty. First, we will introduce the concepts of Q-mPFSs and Q-mIVPFSs. With the combination of Q-mPFSs and Q-mIVPFSs, we will present the concept of Q-mCPFSs. Then, we propose two correlation coefficients for Q-mCPFSs. Furthermore, multi-criteria GDM methods using Q-mCPFSs will be discussed, highlighting their advantages in handling uncertain and imprecise information. Finally, we will provide an illustrative example, to demonstrate the effectiveness of Q-mCPFSs in decision making processes.The main contributions of the Q-mCPFS information expression, correlation coefficients and GDM methods in the Q-mCPFS setting of both uncertainty and certainty are thus highlighted in this study. These contributions provide valuable insights into the application of Q-mCPFSs in decision making processes, allowing decision makers to make more informed and effective choices. Additionally, the illustrative example serves as a practical demonstration of how these methods can be applied in real-world scenarios, further emphasizing their effectiveness and relevance.

An extended ITARA-TOPSIS method for multi-criteria group decision-making problems based on R-number

With the continuous improvement and development of various decision-making methods, it has led to the widespread use of fuzzy sets and fuzzy numbers. At the same time, the application of decision-making methods in different fuzzy environments has been very effective in addressing the deficiencies in existing research. At present, triangular fuzzy numbers have been widely used in the evaluation aspects of various decision making methods, and the proposed R-number effectively solve the uncertainty involving problems related to future events, but the existing research based on the TOPSIS method in the R-number environment has not yet been clearly applied to the triangular fuzzy number environment, and the indifference threshold-based attribute ratio analysis (ITARA) method in the fuzzy environment has yet to be extended. Therefore, this paper proposes a fuzzy indifference threshold-based attribute ratio analysis (FITARA) method based on triangular fuzzy numbers for solving the problem of determining attribute weights in the multi-attribute decision-making process. Secondly, the various risks of the decision environment and the impact on future events are considered and R-number are used to solve this puzzle. In addition, the incorporation of risk perception factors in the context of the existing RTOPSIS method considering multiple risk factors and the use of Manhattan distances to optimize the large number of operations in the process of the method resulted in the development of the FITARA-RTOPSIS model. Finally, the proposed FITARA-RTOPSIS method is applied to the problem of siting emergency supplies storage depots, and the effectiveness of the proposed method is verified through comparative analysis.

Development of an integrated scenario-based stochastic rolling-planning multistage logistics model considering various risks

In this study, a new integrated scenario-based stochastic rolling-planning multistage logistics model is proposed to reduce overall logistics costs. To achieve this goal, two phases were considered in the model. In the first phase, a multi-criteria group decision-making model was developed to select a trustworthy supplier. In the second stage, the selected suppliers were integrated with other stakeholders to develop a rolling-planning-based logistics model using a variety of risky scenarios. Several risk factors including price variability, demand, and quality risks were considered in the model. By considering these risk factors, a new risk-embedded rolling-planning logistics method was established that regulates inventory, stock-out, and overstock problems by constantly controlling the production volume at the manufacturing site based on actual demands. In this model, the supplier's side material quality, price fluctuation risks, and customer-side demand risks were considered simultaneously. To evaluate the performance of the proposed model, a numerical example was set up, and the obtained results were compared with those of another model where fixed volume production and delivery approach was used instead of the rolling-planning approach. To verify the superiority and robustness of the proposed model, its performance was verified through a sensitivity analysis under different experimental conditions. The findings show that in a risk environment, the proposed model estimates lower logistics costs of 2697648.00 units compared to another model whose costs were 2721843.00 units.

A SPHERICAL FUZZY BASED DECISION MAKING FRAMEWORK WITH EINSTEIN AGGREGATION FOR COMPARING PREPAREDNESS OF SMEs IN QUALITY 4.0

Researchers work hard to embrace technological changes and redefine the quality management as Quality 4.0 (Q 4.0). In this context, the purpose of the current work is twofold. First, it aims to compare the preparedness of the small and medium enterprises (SMEs) for sustaining in Q4. Second, it intends to propose a novel hybrid spherical fuzzy based multi-criteria group decision-making (MAGDM) framework with Einstein aggregation (EA). A real-life case study on six SMEs is carried out with the help of three experts. For aggregating the individual responses (using spherical fuzzy numbers or SFNs), EA is used. Then two very recent models such as Simple Ranking Process (SRP) and Symmetry Point of Criterion (SPC) are extended using SFN to rank the SMEs. Finally, the validation tests and sensitivity analysis are carried out. It is noted that the application of analytical tools, knowledge management and use of technology under the support and mentorship of visionary leadership are the key criteria for building up the capability to embrace Q 4.0. Interestingly, it is noted that medium scale firms are better prepared than small-scale enterprises. This work is apparently a first of its kind that focuses on SMEs for assessing their quality management practices in Industry 4.0 era.

Software systems supporting remote education – Fuzzy assessment using a multi-criteria group decision-making method

During the COVID-19 pandemic, the demand for systems supporting remote education increased significantly, and after the pandemic this form of education remained in place to supplement the stationary education. Among the tools that comprehensively support remote learning, there are two most popular systems, i.e. Google Workspace for Education and Microsoft Office 365, available in several different variants, differing in the functionalities offered. The aim of the article is to analyse the functionality, as well as to compare and evaluate this software. Since the assessment of e-learning systems is based on the subjective judgements of experts, and the assessment criteria are qualitative in nature, a new MCGDM (Multi-Criteria Group Decision Making) method called NEAT F-PROMETHEE GDSS (New Easy Approach To Fuzzy PROMETHEE – Group Decision Support System) was developed for the purposes of the study. This method captures the uncertain and imprecise qualitative assessments expressed by many experts and aggregates them into an overall quantitative assessment. As a result of the assessment, it was found that all variants of Google Workspace for Education and Microsoft Office 365 meet the basic requirements for tools for conducting remote learning. In addition, the use of the NEAT F-PROMETHEE GDSS method made it possible to create a ranking of individual software variants. Based on the group evaluation, it was determined that the best system in terms of the relationship between the offered capabilities and the cost of use is Google Workspace for Education Plus, with other variants of Google Workspace for Education taking subsequent positions in the ranking. In turn, Microsoft Office 365 solutions received a worse group rating, largely due to the higher cost of use and slightly less ability to control student work.

Spherical fuzzy analytic hierarchy process and linear assignment model based MCGDM method with its application in ranking of states for their business climate

Ranking of the states for business climate is often done by survey analysis and hence prejudiced by untrustworthy and instable responses of the participants. In the present study, we integrate spherical fuzzy set (SFS) and linear assignment model (LAM) with analytic hierarchy process (AHP) to develop a multi criteria group decision making (MCGDM) method to rank Indian states for their business climate and potential index. The proposed MCGDM method is developed using state investment potential index (SIPI) published by the National Council of Applied Economic Research (NCAER), New Delhi to analyse the 'ease of doing business' aspects of various states based on six parameters. We take these six parameters, sub parameters as criteria and sub criteria in proposed MCGDM method and find their global weight using AHP method. Advantages of the proposed method are that it uses SFSs which are more efficient than other extensions of fuzzy sets in handling non-determinacy, and applies LAM to avoid subjectivity in the preferences of decision makers. We also do the sensitivity analysis of the ranking by changing the weights of the criteria and sub criteria to confirm the robustness of the proposed MCGDM method.

Multi-criteria group decision-making method based on total distance and BWM with spatial information in Hesitant Pythagorean fuzzy environment

The processing method of fuzzy information is a critical element in multi-criteria group decision-making (MCGDM). The hesitant Pythagorean fuzzy set (HPFS) has a higher capacity in express the uncertainty of human inherent preference. A composite weighted mathematical programming model with prospect theory and best-worst method (BWM) is proposed to solve the uncertainty of criterion weight acquisition and decision-makers (DMs) psychological behavior under the HPF environment. The decision-making process is as follows: Firstly, a novel spatial distance measurement method is designed which considers the extension space of HPFSs space by five parameters under the HPF environment. Secondly, the optimal criteria weights model minimizes the total distance between the alternatives and the HPF positive ideal solution (HPFPIS), as well as minimizes the consistency ratio of BWM. Thirdly, we propose the prospect decision matrix by the prospect theory and optimal weights, then use the ordered weighted average operator under the normal distribution to calculate the weight of DMs and rank the decision alternatives. Finally, an example is illustrated here, sensitivity and reliability, and comparative analysis are conducted to verify the effectiveness of the proposed method.