Multi-attribute Group Decision-making Approach Research Articles

Neutrality geometric aggregation operators based on cubic q-rung orthopair fuzzy sets and their applications in multiple attribute group decision-making problems

Cubic q-rung orthopair fuzzy set (Cq-ROFS) is a hybrid set that can hold much more information to handle data uncertainties. It provides more space for decision makers (DMs) to describe their opinion in the multi-attribute group decision-making (MAGDM). In order to involve neutral character to discuss the neutral values assigned by decision-makers, in this paper, some cubic q-rung orthopair fuzzy aggregation operators based on neutrality operation are proposed, such as the cubic q-rung orthopair fuzzy weighted neutrality geometric (Cq-ROFWNG) operator, the cubic q-rung orthopair fuzzy ordered weighted neutrality geometric (Cq-ROFOWNG) operator, the cubic q-rung orthopair fuzzy hybrid neutrality geometric (Cq-ROFHNG) operator. Meanwhile, some properties of these operators are discussed. Further, we develop a novel MAGDM approach based on the proposed operators in a cubic q-rung orthopair fuzzy environment. Finally, numerical examples are provided to demonstrate the effectiveness and superiority of the proposed method through a detailed comparison with existing methods.

Effective multi-attribute group decision-making approach to study astronomy in the probabilistic linguistic q-rung orthopair fuzzy VIKOR framework

This study employs a novel fuzzy logic-based framework to address multi-attribute group decision-making problems commonly encountered in modern astronomy. Our approach utilizes the probabilistic linguistic q-rung orthopair fuzzy set (PLq-ROFS) to handle the inherent uncertainties associated with astronomical data. The PLq-ROFS offers significant advantages over existing fuzzy sets like probabilistic hesitant, linguistic intuitionistic, and linguistic Pythagorean fuzzy sets, which comprise both stochastic and non-stochastic uncertainties simultaneously. To aggregate the probabilistic linguistic decision information effectively, we propose two novel operators: the PLq-ROF weighted power average (PLq-ROFWPA) and the PLq-ROF weighted power geometric (PLq-ROFWPG). These operators form the foundation of a novel method within the PLq-ROF environment. Furthermore, this study integrates the PLq-ROF framework with the VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) model, a widely used decision-making (DM) tool known for its ability to balance group utility maximization with individual regret minimization. This integration leads to the PLq-ROF-VIKOR model, a novel approach for ranking alternative solutions based on the subjective preferences of decision-makers. The effectiveness of the proposed method is demonstrated through a real-world case study in astronomy, accompanied by both parameter and comparative analyses. These analyses highlight the efficiency and accuracy of the PLq-ROF-VIKOR model, ultimately leading to the conclusion that cosmology is the most optimal key finding in this case study.

Sustainable mining method selection by a multi-stakeholder collaborative multi-attribute group decision-making method

How to protect the ecological environment during mineral resource exploitation is a crucial issue for the survival and development of human society. In this context, mining method selection requires simultaneous achieving environmental protection and resource exploitation, while involving the coordination of multi-agent interests. Therefore, this study develops a multi-stakeholder collaborative multi-attribute group decision-making approach for mining method selection. This method enables multiple stakeholders and experts from different fields to make decisions together. First, a conflict resolution model is proposed to resolve cognitive conflict and interest conflict among multi-stakeholders. Then, the 2-tuple linguistic representation model is used to deal with the decision maker's fuzzy preference. Next, the comprehensive attribute weights are calculated and the alternatives are prioritized. A case study for mining method selection in a gold mine in Shandong Province, China, is presented to verify the validity of the proposed method. This method considers not only the coordination between mineral resource exploitation and ecological environment protection but also the conflicting views of stakeholders. The proposed method is a useful tool for the assessment and selection of development schemes involving multiple stakeholders.

A MAGDM approach for evaluating the impact of artificial intelligence on education using 2-tuple linguistic q-rung orthopair fuzzy sets and Schweizer-Sklar weighted power average operator.

The impact of artificial intelligence (AI) in education can be viewed as a multi-attribute group decision-making (MAGDM) problem, in which several stakeholders evaluate the advantages and disadvantages of AI applications in educational settings according to distinct preferences and criteria. A MAGDM framework can assist in providing transparent and logical recommendations for implementing AI in education by methodically analyzing the trade-offs and conflicts among many components, including ethical, social, pedagogical, and technical concerns. A novel development in fuzzy set theory is the 2-tuple linguistic q-rung orthopair fuzzy set (2TLq-ROFS), which is not only a generalized form but also can integrate decision-makers quantitative evaluation ideas and qualitative evaluation information. The 2TLq-ROF Schweizer-Sklar weighted power average operator (2TLq-ROFSSWPA) and the 2TLq-ROF Schweizer-Sklar weighted power geometric (2TLq-ROFSSWPG) operator are two of the aggregation operators we create in this article. We also investigate some of the unique instances and features of the proposed operators. Next, a new Entropy model is built based on 2TLq-ROFS, which may exploit the preferences of the decision-makers to obtain the ideal objective weights for attributes. Next, we extend the VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) technique to the 2TLq-ROF version, which provides decision-makers with a greater space to represent their decisions, while also accounting for the uncertainty inherent in human cognition. Finally, a case study of how artificial intelligence has impacted education is given to show the applicability and value of the established methodology. A comparative study is carried out to examine the benefits and improvements of the developed approach.

An extended multi-expert concept lattice-based heterogeneous multi-attribute group decision-making approach

In practical multi-attribute group decision-making (MAGDM) problems, it is common to utilize heterogeneous representation forms to express distinct preference information for different experts, primarily due to their diverse backgrounds. To address the problem of reducing information loss from the aggregation of experts' opinions in heterogeneous MAGDM as well as improving the interpretability of the decision-making process, this paper introduces a concept lattice-based heterogeneous MAGDM approach. The heterogeneous multi-expert formal context is first proposed to capture the heterogeneous evaluation information of alternatives provided by different experts. Then, extended multi-expert concept lattices are constructed to aggregate evaluation information of alternatives by different experts. In this case, all concepts are considered to minimize information loss during the aggregation process. Second, to obtain more reasonable decision results, the distance between the concept intents and the heterogeneous positive and negative ideal solutions is considered, and the alternatives are ranked based on this measure. In addition, the MAGDM process for each alternative is visualized using the extended multi-expert concept lattices. This representation aids in identifying key concepts, their interdependencies, and the overall impact on the decision result. Finally, numerical examples and comparative analysis validate the validity and rationality of the proposed approach in heterogeneous MAGDM.

A novel group decision-making approach based on partitioned Hamy mean operators in q-rung orthopair fuzzy context

In multi-attribute group decision-making (MAGDM), the attributes can be placed into independent groups based on their properties through partitioning. First, the partitioned dual Hamy mean (PDHM) operator is introduced, along with its essential properties. This operator integrates these separate groups while preserving the relationships between the attributes within each group. Furthermore, the partitioned Hamy mean (PHM) and the PDHM operators are also constructed in the generalized orthopair fuzzy environment, namely the q-rung orthopair fuzzy PHM (q-ROFPHM), the q-rung orthopair fuzzy PDHM (q-ROFPDHM), and their weighted forms. Their essential properties are verified to ensure the validity of the proposed aggregation operators (AOs). Subsequently, a new MAGDM approach is developed, employing the proposed AOs. The MAGDM problem of selecting the best person is examined. Moreover, the research includes a sensitivity analysis in three directions and a comparative analysis of the proposed MAGDM approach with five different approaches. The findings indicate that applying attribute partitioning in the proposed approach mitigates the adverse impact of irrelevant attributes, leading to more feasible and reliable outcomes. Additionally, a practical case study focuses on selecting a suitable industry for investment among the five available options. This case study demonstrates the approach’s effectiveness by considering five distinct qualities and results that make the Internet industry the best place to invest. Furthermore, a comparative analysis with four similar papers is also performed, indicating that the developed method’s results are more reliable and consistent.

A concept lattice-based expert opinion aggregation method for multi-attribute group decision-making with linguistic information

During the multi-attribute group decision-making (MAGDM) processing, the individuals often hold different opinions about the alternatives. It is necessary to aggregate the different individual opinions into a unified group opinion. In the real world, experts sometimes use linguistic expressions to evaluate attributes in uncertain environments. To address the problem of reducing the information loss of expert opinion aggregation in MAGDM, this paper proposes a MAGDM approach based on linguistic concept lattices in the context of uncertain linguistic expression. A linguistic concept lattice for multi-expert linguistic formal context is first constructed based on linguistic truth-valued lattice implication algebra, which can express both comparable and incomparable linguistic information in the decision-making process. Different expert opinions are aggregated via the extent of fuzzy linguistic concepts, which can reduce information loss in the aggregation process. Second, meet-irreducible elements in the linguistic concept lattice are introduced to reduce the computational complexity of obtaining all fuzzy linguistic concepts in the decision-making process. the distance between the intents of different fuzzy linguistic concepts is considered to enhance the rationality of linguistic decision results. In addition, the expert’s decision-making process for each alternative is visualized via linguistic concept lattices. Finally, the case study and comparative analysis illustrate the validity and rationality of the proposed approach in MAGDM with linguistic information.

Possibilistic simulation based interactive fuzzy MAGDM under discrimination q-rung picture linguistic information. Application in educational programs efficiency evaluation

In certain Multi-Attribute Group Decision-Making (MAGDM) approaches an aggregation of decision-making matrices of experts’ evaluations/ratings of possible alternatives by their attributes into an etalon decision-making matrix is an important task. Based on possible great experience and deep knowledge of the subject, the expert tries to dominate other experts in the decision-making process. Besides, every expert has a possibility of a certain degree to influence on the decision-making process. In such cases experts’ evaluations aggregation into an etalon matrix by the additive or linear aggregation instruments is unacceptable. We present a new two-stage MAGDM approach to solve this task. On the first stage: In the evidence theory environment the connection between experts’ pair interaction indexes and possibility levels of their influence on decision-making process is constructed. For this, a Monte-Carlo simulation algorithm is created, the result of which is the estimated class of associated probabilities of the possibility distribution. Experts’ evaluations in decision-making matrixes are represented by the q-rung orthopair fuzzy numbers (q-ROFNs). Before aggregation of experts’ data into an etalon decision-making matrix, evaluations are transformed into discrimination q-rung picture linguistic numbers (q-RPLNs). New definitions are introduced for the Score and Accuracy functions of the q-rung picture linguistic numbers. q-rung picture linguistic numbers contain as well quantitative as qualificative information on experts’ reflections on objects, while discrimination q-rung picture linguistic numbers describe interactive phenomena between arguments. Based on constructed possibility distribution on the experts’ group, the ordered weighted averaging (OWA) and Choquet averaging (CA) aggregation operators under q-rung picture linguistic environment are extended (q-RPLOWA and q-RPLCA, respectively). By the q-RPLOWA and q-RPLCA operators decision-making matrices of experts’ evaluations/ratings are condensed into an etalon decision-making matrix. On the second stage: The concept of Euclidean distance and the entropy of De Luca–Termini are defined for q-rung picture linguistic set. The new relative closeness parameter for the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) approach under q-rung picture linguistic information is also defined. The technique for the TOPSIS approach for the ranking of possible alternatives in MAGDM by aggregating discrimination q-rung picture linguistic data of etalon matrix is developed. For illustration of the obtained results, Educational Programs Efficiency Evaluation problem is considered. Our constructed MAGDM approach complies with the principle of expertise in educational programs evaluation commission. The numerical results obtained for the q-RPLNs environment and the ranking of alternatives are compared with the numerical results and the ranking of alternatives obtained by the same approach for the initial expert data in q-ROFNs environment. A comparison with the results obtained by other existing methods is given.

MAGDM approach using the hyperbolic sine similarity measure of confidence neutrosophic number credibility sets in a fuzzy credibility multi-valued circumstance

Group decision-making is that individuals collectively make a choice from a set of alternatives. Then, in complex decision-making problems, the decision-making process is no longer subject to a single individual, but group decision-making. Hence, the decision reliability and credibility of the collective evaluation information become more critical. However, current decision-making methods lack the confidence level and credibility measure of group evaluation information. To ensure the confidence level and credibility measure of small-scale group decision-making problems, the aim of this paper is to propose a Multi-Attribute Group Decision-Making (MAGDM) approach using a hyperbolic sine similarity measure between Confidence Neutrosophic Number Credibility Sets (CNNCSs) in the circumstance of Fuzzy Credibility Multi-Valued Sets (FCMVSs). To achieve this aim, this paper contains the following works. First, we present FCMVS to represent the mixed information of fuzzy sequences and credibility degree sequences with different and/or identical fuzzy values. Second, according to the normal distribution and confidence level of fuzzy values and credibility degrees in FCMVS, FCMVS is transformed into CNNCS to avoid the operational issue between different fuzzy sequence lengths in FCMVSs and to ensure the confidence neutrosophic numbers/confidence intervals of fuzzy values and credibility degrees. Third, a hyperbolic sine similarity measure of CNNCSs is established in the circumstance of FCMVSs. Fourth, a MAGDM approach is developed based on the weighted hyperbolic sine similarity measure in the circumstance of FCMVSs. Fifth, the proposed MAGDM approach is applied to an actual example of the equipment supplier choice problem to illustrate the efficiency and rationality of the proposed MAGDM approach in a FCMVS circumstance. In general, this study reveals new contributions in the representation, transformation method, and similarity measure of small-scale group assessment information, as well as the proposed MAGDM method subject to the normal distribution and confidence levels in small-scale MAGDM scenarios.

Incomplete intuitionistic fuzzy behavioral group decision-making based on multigranulation probabilistic rough sets and MULTIMOORA for water quality inspection

Water quality inspection (WQI) is one of the primary ways to ensure the safe utilization of water resources, and complicated data modeling, fusion and analysis play a significant role in seeking the resource with the best water quality. Nevertheless, the challenges of missing data, relatively large differences in decision results and bounded rationality owned by decision-makers (DMs) in terms of WQI still exist nowadays. Thus, from the aspect of stable and behavioral decision-making in multi-granularity incomplete intuitionistic fuzzy information systems (MG-IIFISs), the paper investigates a comprehensive multi-attribute group decision-making (MAGDM) approach for the application of WQI. First, the concept of MG-IIFISs is built by modeling MAGDM problems with intuitionistic fuzzy numbers (IFNs), then a new transformation scheme is constructed for transforming MG-IIFISs into multi-granularity intuitionistic fuzzy information systems (MG-IFISs) based on the similarity principle. Second, three types of multigranulation intuitionistic fuzzy probabilistic rough sets (MG IF PRSs) are developed by referring to the MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) method. Afterwards, attribute weights are objectively calculated based on the best-worst method (BWM), and a new stable and behavioral MAGDM approach is constructed by means of the TODIM (an acronym in Portuguese for interactive multi-criteria decision-making) method. At last, a case study in the setting of WQI is conducted with the support of a UCI data set, and sensitivity analysis, comparative analysis and experimental analysis are investigated to display the validity of the proposed approach. In general, the proposed approach improves the stability of decision results via MULTIMOORA and BWM, and also fully considers the bounded rationality of DMs’ psychological behaviors from the aspect of the TODIM method, which has certain advantages in the community of MAGDM studies.

EDAS METHOD FOR MULTIPLE ATTRIBUTE GROUP DECISION MAKING WITH PROBABILISTIC DUAL HESITANT FUZZY INFORMATION AND ITS APPLICATION TO SUPPLIERS SELECTION

Probabilistic dual hesitant fuzzy set (PDHFS) is a more powerful and important tool to describe uncertain information regarded as generalization of hesitant fuzzy set (HFS) and dual HFS (DHFS), not only reflects the hesitant attitude of decision-makers (DMs), but also reflects the probability information of DMs. Score function of fuzzy number and weighting method are very important in multi-attribute group decision-making (MAGDM) issues. In many fuzzy environments, the score function and entropy measure have been proposed one after another. Firstly, based on the detailed analysis of the existed score function of PDHF element (PDHFE) and with the help of previous references, we build a novel score function for PDHFE. Secondly, a combined weighting method is built based on the minimum identification information principle by fusing PDHF entropy and Criteria Importance Through Intercriteria Correlation (CRITIC) method. Thirdly, a novel PDHF MAGDM approach (PDHF-EDAS) is built by extending evaluation based on distance from average solution (EDAS) approach to the PDHF environment to solve the issue that the decision attribute information is PDHFE. Finally, the practicability and effectiveness of the PDHF MAGDM technique is verified by suppliers selection (SS) and comparing analysis with existing methods.

Decision Support System Based on Complex Fractional Orthotriple Fuzzy 2-Tuple Linguistic Aggregation Operator

In this research, we provide tools to overcome the information loss limitation resulting from the requirement to estimate the results in the discrete initial expression domain. Through the use of 2-tuples, which are made up of a linguistic term and a numerical value calculated between [0.5,0.5), the linguistic information will be expressed. This model supports continuous representation of the linguistic data within its scope, permitting it to express any information counting received through an aggregation procedure. This study provides a novel approach to develop a linguistic multi-attribute group decision-making (MAGDM) approach with complex fractional orthotriple fuzzy 2-tuple linguistic (CFOF2TL) assessment details. Initially, the concept of a complex fractional orthotriple fuzzy 2-tuple linguistic set (CFO2TLS) is proposed to convey uncertain and fuzzy information. In the meantime, simple aggregation operators, such as CFOF2TL weighted average and geometric operators, are defined. In addition, the CFOF2TL Maclaurin’s symmetric mean (CFOF2TLMSM) operators and their weighted shapes are presented, and their attractive characteristics are also discussed. A new MAGDM approach is built using the developed aggregation operators to address managing economic crises under COVID-19 with the CFOF2TL information. As a result, the effectiveness and robustness of the developed method are accompanied by an empirical example, and a comparative study is carried out by contrasting it with previous approaches.

A novel approach on spherical fuzzy rough set based-EDA𝒮 method for group decision support system

In daily life, the decision making problem is a complicated work related to uncertainties and vagueness. To overcome this vagueness and uncertainties, many fuzzy sets and theories have been presented by different scholars and researchers. EDA𝒮 (Evaluation based on distance from average solution) method plays a major role in decision-making problems. Especially, when multi-attribute group decision-making (MAGDM) problems have more conflicting attribute. In this paper, a new approach known as Spherical fuzzy rough-EDA𝒮 (SFR-EDA𝒮) method is used to handle these uncertainties in the MAGDM problem. The aggregation operators have the ability to combine different sources of information, which plays an essential role in decision making (DM) problem. Keeping in view the increasing complexity of the DM problem, it will be useful to combine the aggregation operators with the fuzzy sets in solving DM problem. Therefore, an aggregation operator known as SFR-EDA𝒮 method is utilized. For this propounded some new averaging and geometric aggregation is investigated. Moreover, the essential and desirable properties with some particular cases are deliberated and discussed detail. To evaluate the emergency program, a MAGDM approach is used based on the new introduced operators. Later on, the viability and applicability the proposed method is certified by a detailed analysis with the other existing approaches.

An Integrated Multiattribute Group Decision-Making Approach for Risk Assessment in Aviation Emergency Rescue

An effective risk assessment approach for assessing the risk level of aviation emergency rescue is essential to aviation emergency management. Therefore, this study is aimed at extending a novel integrated multiattribute group decision-making (MAGDM) approach to conduct risk assessment in aviation emergency rescue. First, a combined improved Swiss cheese model and fault tree analysis method are used to build the index system for risk assessment. Next, the weight vector for risk assessment is calculated using the consensus-based improved analytic hierarchy process (IAHP). Then, based on the traditional technique for order preference by similarity to the ideal solution (TOPSIS) method, we improve the definition express of ideal solution and the standardized formula of indexes, thereby providing a consensus-based improved TOPSIS method to compute the evaluation matrix for risk assessment. Finally, the weight vector and evaluation matrix are combined to estimate the risk level of aviation emergency rescue. As aviation emergency rescue in a sudden natural disaster an example, we illustrate the feasibility of the proposed method and demonstrate its effectiveness by comparative analysis with some similar approaches. The proposed approach can evaluate the safety status of aviation emergency rescue operations, which provides a starting point for the improvement of aviation emergency rescue.

A New Multi-Attribute Group Decision-Making Approach Based on Fermatean Fuzzy Power Hamy Mean Operator and Novel Score Function

A New Multi-Attribute Group Decision-Making Approach Based on Fermatean Fuzzy Power Hamy Mean Operator and Novel Score Function

Multiattribute Group Decision‐Making Method in terms of Linguistic Neutrosophic Z‐Number Weighted Aggregation Operators

To make a fuzzy value more reliable, Zadeh presented the notion of Z‐number, which reflects a fuzzy value related to its reliability measure. Since linguistic expression conforms to human thinking habits, linguistic neutrosophic decision‐making is one of the key research topics in linguistic indeterminate and inconsistent setting. In order to ensure the reliability of multiattribute group decision‐making (MAGDM) problems in the linguistic environment of truth, falsehood, and indeterminacy, we require a new linguistic neutrosophic framework that combines the decision‐maker’s linguistic neutrosophic judgment with its reliability measure. Inspired by the linguistic Z‐numbers of the truth, falsehood, and indeterminacy, this article first proposes a linguistic neutrosophic Z‐number (LNZN) to make the truth, falsehood, and indeterminacy linguistic values more reliable. Then, we define the operational relations, score and accuracy functions, and sorting laws of LNZNs. Next, we establish the LNZN weighted arithmetic mean (LNZNWAM) and LNZN weighted geometric mean (LNZNWGM) operators and indicate their properties. Furthermore, an MAGDM approach is developed based on the two aggregation operators and the score and accuracy functions of LNZNs in the LNZN setting. Lastly, an MAGDM example of industrial robot selection and comparison with existing related methods are provided to verify the applicability and efficiency of the developed MAGDM method in the setting of LNZNs. In general, the developed MAGDM approach not only makes the MAGDM information more reliable but also solves MAGDM problems under the environment of LNZNs.

The Evaluation on Development Quality of Open Education Based on Dempster-Shafer With Multigranularity Unbalanced Hesitant Fuzzy Linguistic Information for Chinese Case

Multi-granularity unbalanced hesitant fuzzy linguistic term set (MGUHFLTS) is an effective expression of linguistic information, which applied in multi-attribute group decision-making (MAGDM), meanwhile Dempster-Shafer evidence theory (DSET) is profound method of representing and aggregating uncertain information. In order to combine the advantages from both, a new MAGDM approach based on Dempster-Shafer with MGUHFLTSs is proposed. The initial MGUHFLTSs decision matrix is transformed to evidence matrix, and a novel weight determination model of MAGDM problem with MGUHFLTSs is established in this approach. In additional, in order to combine evidence with MGUHFLTSs, a new MAGDM combination algorithm is proposed by means of DSET combination rules, which reduces the loss of MGUHFLTSs information for. An example is applied with this method about evaluation on the development quality of open education. Finally, this paper proves the validity and superiority of the proposed method.

A novel multi-granularity three-way decision making approach in q-rung orthopair fuzzy information systems

The notion of q-rung orthopair fuzzy sets (q-ROFSs) enables decision makers to record diverse uncertain information in a larger scope by easing the limitation of membership and non-membership degrees. The paper introduces q-ROFSs into the framework of multi-granularity three-way decisions (MG-3WD) and explores a novel multi-attribute group decision making (MAGDM) approach in q-rung orthopair fuzzy (q-ROF) information systems. After reviewing some fundamental issues on q-ROFSs and MG-3WD, we first propose different types of multigranulation q-ROF probabilistic models and discuss some of their theoretical properties. Afterwards, a q-ROF MAGDM approach is constructed in light of the proposed multigranulation q-ROF probabilistic models and decision making-based 3WD methods. Then, we provide an example of corporate financial quality matching (CFQM) to show the practicability of the established q-ROF MAGDM approach. At last, corresponding sensitivity analysis, validity tests, comparative analysis and experimental analysis are arranged to reveal the applicability of the established approach from the aspect of MG-3WD.

Pythagorean fuzzy multiattribute group decision making based on risk attitude and evidential reasoning methodology

Two aspects of problems including selection of aggregation operator for extreme fuzzy evaluation value and risk attitude of decision makers cannot be well solved in Pythagorean fuzzy (PF) multiattribute group decision making (MAGDM). This paper extends the evidential reasoning aggregation method in the intuitionistic fuzzy environment, expands the dictionary ranking method by constructing interval-valued numbers through the proposed credibility functions of PF values and the concept of closeness degree, widens the continuous generalized ordered weighted average ( C - GOWA ) operator to establish a risk attitude ranking measure, and puts forward a PF MAGDM approach based on risk attitude and evidence reasoning methodology (ERM). First, the proposed method utilizes the ERM to aggregate each decision maker's decision matrix and the weights of the attributes to get his/her aggregated decision matrix. Then, it incorporates the obtained aggregated decision matrices of the experts, the weights of the experts and the ERM to accomplish the aggregated PF value of each alternative. Finally, the ranking measure value of risk attitude on each alternative's PF value is calculated, and the sensitivity analysis on the ranking measure function is carried out. The proposed method has overcome the drawbacks of the existing methods for fuzzy MAGDM in PF environments.

Multi-attribute group decision-making for online education live platform selection based on linguistic intuitionistic cubic fuzzy aggregation operators

The purpose of this study is to propose a multi-attribute group decision-making (MAGDM) method for online education live platform selection based on proposed novel aggregation operators (AOs) under linguistic intuitionistic cubic fuzzy set (LICFS). First, the Archimedean copula and co-copula are extended to handle linguistic intuitionistic cubic fuzzy information (LICFI) and the operational law of linguistic intuitionistic cubic fuzzy variables (LICFVs) based on extended copula (EC) and extended co-copula (ECC) are given. In addition, linguistic intuitionistic cubic fuzzy copula weighted average (LICFCWA) operator and linguistic intuitionistic cubic fuzzy copula weighted geometric (LICFCWG) operator are proposed based on EC and ECC under LICFI; meanwhile, some special forms of LICFCWA and LICFCWG have been obtained by different types generators of ECs and ECCs. Third, a novel MAGDM approach based on proposed LICFCWA (LICFCWG) is constructed to solve the selection problem of the online education live platform in the period of the COVID-19, and a detailed parameter analysis was carried out. Fourthly, LICFS will degenerate into linguistic intuitionistic fuzzy set and intuitionistic cubic fuzzy set, respectively, in different cases. Finally, some comparisons are carried out with other existing proposed MAGDM approaches. By comparing different types of experiments, the effectiveness and flexibility of the proposed approach are also showed.