The Spherical q-Linear Diophantine Fuzzy Multiple-Criteria Group Decision-Making Based on Differential Measure

Spherical q-linearDiophantine fuzzy sets(Sq-LDFSs)provedmore effective for handling uncertainty and vagueness in multi-criteria decision-making(MADM).It does not only cover the data in two variable parameters but is also beneficial for three parametric data.By Pythagorean fuzzy sets,the difference is calculated only between two parameters(membership and non-membership).According to human thoughts,fuzzy data can be found in three parameters(membership uncertainty,and non-membership).So,to make a compromise decision,comparing Sq-LDFSs is essential.Existing measures of different fuzzy sets do,however,can have several flaws that can lead to counterintuitive results.For instance,they treat any increase or decrease in the membership degree as the same as the non-membership degree because the uncertainty does not change,even though each parameter has a different implication.In the Sq-LDFSs comparison,this research develops the differentialmeasure(DFM).Themain goal of the DFM is to cover the unfair arguments that come from treating different types of FSs opposing criteria equally.Due to their relative positions in the attribute space and the similarity of their membership and non-membership degrees,two Sq-LDFSs formthis preference connectionwhen the uncertainty remains same in both sets.According to the degree of superiority or inferiority,two Sq-LDFSs are shown as identical,equivalent,superior,or inferior over one another.The suggested DFM’s fundamental characteristics are provided.Based on the newly developed DFM,a unique approach tomultiple criterion group decision-making is offered.Our suggestedmethod verifies the novel way of calculating the expert weights for Sq-LDFSS as in PFSs.Our proposed technique in three parameters is applied to evaluate solid-state drives and choose the optimum photovoltaic cell in two applications by taking uncertainty parameter zero.The method’s applicability and validity shown by the findings are contrasted with those obtained using various other existing approaches.To assess its stability and usefulness,a sensitivity analysis is done.

Multi-Attribute Group Decision-Making Method under Spherical Fuzzy Bipolar Soft Expert Framework with Its Application

Spherical fuzzy soft expert set(SFSES)theory blends the perks of spherical fuzzy sets and group decision-making into a unified approach.It allows solutions to highly complicated uncertainties and ambiguities under the unbiased supervision and group decision-making of multiple experts.However,SFSES theory has some deficiencies such as the inability to interpret and portray the bipolarity of decision-parameters.This work highlights and overcomes these limitations by introducing the novel spherical fuzzy bipolar soft expert sets(SFBSESs)as a powerful hybridization of spherical fuzzy set theory with bipolar soft expert sets(BSESs).Followed by the development of certain set-theoretic operations and properties of the proposed model,important problems,including the selection of non-powered dam(NPD)sites for hydropower conversion are discussed and solved under the proposed approach.These problems mainly focus on the need for an efficient tool capable of considering the bipolarity of parameters,complicated ambiguities,and multiple opinions.Supporting the new approach by a detailed comparative analysis,it is concluded that the proposed model is more comprehensive and reliable for multi-attribute group decisionmaking(MAGDM)than the previous tools,particularly considering the bipolarity of parameters under SFSES environment.

Consensus model of social network group decision-making based on trust relationship among experts and expert reliability

Due to people’s increasing dependence on social networks,it is essential to develop a consensus model considering not only their own factors but also the interaction between people.Both external trust relationship among experts and the internal reliability of experts are important factors in decision-making.This paper focuses on improving the scientificity and effectiveness of decision-making and presents a consensus model combining trust relationship among experts and expert reliability in social network group decision-making(SN-GDM).A concept named matching degree is proposed to measure expert reliability.Meanwhile,linguistic information is applied to manage the imprecise and vague information.Matching degree is expressed by a 2-tuple linguistic model,and experts’preferences are measured by a probabilistic linguistic term set(PLTS).Subsequently,a hybrid weight is explored to weigh experts’importance in a group.Then a consensus measure is introduced and a feedback mechanism is developed to produce some personalized recommendations with higher group consensus.Finally,a comparative example is provided to prove the scientificity and effectiveness of the proposed consensus model.

Multi-attribute Group Decision-making Based on Hesitant Bipolar-valued Fuzzy Information and Social Network

Fuzzy sets have undergone several expansions and generalisations in the literature,including Atanasov’s intuitionistic fuzzy sets,type 2 fuzzy sets,and fuzzy multisets,to name a few.They can be regarded as fuzzy multisets from a formal standpoint;nevertheless,their interpretation differs from the two other approaches to fuzzy multisets that are currently available.Hesitating fuzzy sets(HFS)are very useful if consultants have hesitation in dealing with group decision-making problems between several possible memberships.However,these possible memberships can be not only crisp values in[0,1],but also interval values during a practical evaluation process.Hesitant bipolar valued fuzzy set(HBVFS)is a generalization of HFS.This paper aims to introduce a general framework of multi-attribute group decision-making using social network.We propose two types of decision-making processes:Type-1 decision-making process and Type-2 decision-making process.In the Type-1 decision-making process,the experts’original opinion is proces for thefinal ranking of alternatives.In Type-2 decision making processs,there are two major aspects we consider.First,consistency tests and checking of consensus models are given for detecting that the judgments are logically rational.Otherwise,the framework demands(partial)decision-makers to review their assessments.Second,the coherence and consensus of several HBVFSs are established forfinal ranking of alternatives.The proposed framework is clarified by an example of software packages selection of a university.

Multi-Criteria Group Decision-Making Method Based on an Improved Single-Valued Neutrosophic Hamacher Weighted Average Operator and Grey Relational Analysis

This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the limitations of present methods based on aggregation operators. First, the limitations of several existing single-valued neutrosophic weighted averaging aggregation operators (i.e. , the single-valued neutrosophic weighted averaging, single-valued neutrosophic weighted algebraic averaging, single-valued neutrosophic weighted Einstein averaging, single-valued neutrosophic Frank weighted averaging, and single-valued neutrosophic Hamacher weighted averaging operators), which can produce some indeterminate terms in the aggregation process, are discussed. Second, an ISNHWA operator was developed to overcome the limitations of existing operators. Third, the properties of the proposed operator, including idempotency, boundedness, monotonicity, and commutativity, were analyzed. Application examples confirmed that the ISNHWA operator and the proposed MCGDM method are rational and effective. The proposed improved ISNHWA operator and MCGDM method can overcome the indeterminate results in some special cases in existing single-valued neutrosophic weighted averaging aggregation operators and MCGDM methods.

Group decision-making method based on entropy and experts cluster analysis

According to the aggregation method of experts＇ evaluation information in group decision-making,the existing methods of determining experts＇ weights based on cluster analysis take into account the expert＇s preferences and the consistency of expert＇s collating vectors,but they lack of the measure of information similarity.So it may occur that although the collating vector is similar to the group consensus,information uncertainty is great of a certain expert.However,it is clustered to a larger group and given a high weight.For this,a new aggregation method based on entropy and cluster analysis in group decision-making process is provided,in which the collating vectors are classified with information similarity coefficient,and the experts＇ weights are determined according to the result of classification,the entropy of collating vectors and the judgment matrix consistency.Finally,a numerical example shows that the method is feasible and effective.

Method for multi-attribute group decision-making based on the compromise weights

Multi-attribute group decision-making problems are considered where information on both attribute weights and value scores of consequences is incomplete.In group decision analysis,if preference information about alternatives is provided by participants,it should be verified whether there exist compromise weights that can support all the preference relations.The different compromise weight vectors may differ for the ranking of the alternatives.In the case that compromise weights exist,the method is proposed to find out all the compromise weight vectors in order to rank the alternatives.Based on the new feasible domain of attribute weights determined by all the compromise weight vectors and the incomplete information on value scores of consequences,dominance relations between alternatives are checked by a nonlinear goal programming model which can be transformed into a linear one by adopting a transformation.The checked dominance relations uniformly hold for all compromise weight vectors and the incomplete information on value scores of consequences.A final ranking of the alternatives can be obtained by aggregating these dominance relations.

Multi-criteria linguistic interval group decision-making approach

For group decision-making problems with linguistic assessment information, a new method based on two-tuple and WC-OWA operator is proposed, in which the criteria＇s weights and the decision-makers＇ preference information might take the form of linguistic grade, or might be between two continuous linguistic grades, or might be linguistic interval, or might be default. In this method, all linguistic values are transformed into two-tuple, and an aggregative decision-making matrix is obtained by using interval operation. The group aggregative values of each criterion on alternatives are computed by using a WC-OWA operator, the aggregative values on alternatives are worked out, and transformed into two-tuple. And the rank of the alternatives is obtained by using the order property of two-tuple. An example shows the feasibility and effectiveness of the proposed method.

Dynamic programming methodology for multi-criteria group decision-making under ordinal preferences

A method of minimizing rankings inconsistency is proposed for a decision-making problem with rankings of alternatives given by multiple decision makers according to multiple criteria. For each criteria, at first, the total inconsistency between the rankings of all alternatives for the group and the ones for every decision maker is defined after the decision maker weights in respect to the criteria are considered. Similarly, the total inconsistency between their final rankings for the group and the ones under every criteria is determined after the criteria weights are taken into account. Then two nonlinear integer programming models minimizing respectively the two total inconsistencies above are developed and then transformed to two dynamic programming models to obtain separately the rankings of all alternatives for the group with respect to each criteria and their final rankings. A supplier selection case illustrated the proposed method, and some discussions on the results verified its effectiveness. This work develops a new measurement of ordinal preferences’ inconsistency in multi-criteria group decision-making （MCGDM） and extends the cook-seiford social selection function to MCGDM considering weights of criteria and decision makers and can obtain unique ranking result.

Business Blockchain Suitability Determinants: Decision-Making through an Intuitionistic Fuzzy Method

Blockchain is one of the innovative and disruptive technologies that has a wide range of applications in multiple industries beyond cryptocurrency.The widespread adoption of blockchain technology in various industries has shown its potential to solve challenging business problems,as well as the possibility to create new business models which can increase a firm’s competitiveness.Due to the novelty of the technology,whereby many companies are still exploring potential use cases,and considering the complexity of blockchain technology,which may require huge changes to a company’s existing systems and processes,it is important for companies to carefully evaluate suitable use cases and determine if blockchain technology is the best solution for their specific needs.This research aims to provide an evaluation framework that determines the important dimensions of blockchain suitability assessment by identifying the key determinants of suitable use cases in a business context.In this paper,a novel approach that utilizes both qualitative(Delphi method)and quantitative(fuzzy set theory)methods has been proposed to objectively account for the uncertainty associated with data collection and the vagueness of subjective judgments.This work started by scanning available literature to identify major suitability dimensions and collected a range of criteria,indicators,and factors that had been previously identified for related purposes.Expert opinions were then gathered using a questionnaire to rank the importance and relevance of these elements to suitability decisions.Subsequently,the data were analyzed and we proceeded to integrate multi-criteria group decision-making(MCGDM)and intuitionistic fuzzy set(IFS)theory.The findings demonstrated a high level of agreement among experts,with the model being extremely sensitive to variances in expert assessments.Furthermore,the results helped to refine and select the most relevant suitability determinants under three important dimensions:functional suitability of the use case,organizational applicability,and ecosystem readiness.

Consensus intuitionistic fuzzy group decision-making method for aircraft cockpit display and control system evaluation

A novel group decision-making （GDM） method based on intuitionistic fuzzy sets （IFSs） is developed to evaluate the ergonomics of aircraft cockpit display and control system （ACDCS）. The GDM process with four steps is discussed. Firstly, approaches are proposed to transform four types of common judgement representations into a unified expression by the form of the IFS, and the features of unifications are analyzed. Then, the aggregation operator called the IFSs weighted averaging （IFSWA） operator is taken to synthesize decision-makers’ （DMs’） preferences by the form of the IFS. In this operator, the DM’s reliability weights factors are determined based on the distance measure between their preferences. Finally, an improved score function is used to rank alternatives and to get the best one. An illustrative example proves the proposed method is effective to valuate the ergonomics of the ACDCS.

Decision-making approach by employing grey incidence analysis and group negotiation

For the problems of the consistency ranking of the group decision-making scheme,from the view of group negotiation and system coordination,the grey incidence analysis and Nash bargaining model are used to establish a consistency group decision-making method.First,the concepts of the consensus partial decision-making program and the consensus overall ideal decision-making program are defined,and then a multi-object optimization model is constructed based on the satisfaction maximization of group negotiation and deviation minimization of system coordination to determine the consensus partial decision-making program and the consensus overall ideal decision-making program.Moreover,the grey incidence analysis is exploited to measure the close degrees between them.Finally,a real case of the online product evaluation verifies the validity and rationality of the proposed model.

Group Decision-Making Method with Incomplete Intuitionistic Fuzzy Preference Relations Based on a Generalized Multiplicative Consistent Concept

Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative consistent for IFPRs is defined,and a mathematical programming model is constructed to supplement the missing values in incomplete IFPRs.Moreover,in this study,another mathematical programming model is constructed to improve the consistency level of unacceptably multiplicative consistent IFPRs.For group decisionmaking(GDM)with incomplete IFPRs,three reliable sources influencing the weights of experts are identified.Subsequently,a method for determining the weights of experts is developed by simultaneously considering three reliable sources.Furthermore,a targeted consensus process(CPR)is developed in this study with reference to the actual situation of the consensus level of each IFPR.Meanwhile,in response to the proposed multiplicative consistency definition,a novel method for determining the optimal priority weights of alternatives is redefined.Lastly,based on the above theory,a novel GDM method with incomplete IFPRs is developed,and the comparative and sensitivity analysis results demonstrate the utility and superiority of this work.

Group training on the improvement of college students'career decision-making self-efficacy

A group training was conducted on 17 college students to improve their career decision-making self-efficacy (CDMSE). The result showed that there was significant difference between the pre-test and the post-test for the experimental group (n = 17), whereas no significant difference was found between the pre-test and the post- test for the control group (n = 17). In the pre-test, there was no significant difference between the experimental group and the control group, and obvious difference between the two groups was found in the post-test. This indicated that the group training was effective on improving the CDMSE of the college students whose scores of CDMSE were below 27% point of the total students.

Dynamic hesitant fuzzy linguistic group decision-making from a reliability perspective

A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approach is applied to transform the dynamic HFLTSs(DHFLTSs) into a set of proportional linguistic terms to eliminate the time dimension. Second, expert reliability is measured by considering both group similarity and degree of certainty, and an optimization method is employed to quantify the linguistic terms by maximizing the group similarity. Third, through computing the attribute stability as well as its reliability, a combination rule which considers both reliability and weight is proposed to aggregate the information, and then the aggregated grade values and degree of stability are used to make a selection. Finally,the application and feasibility of the proposed method are verified through a case study and method comparison.

Information Aggregation of Group Decision-Making in Emergency Events

Information is a key factor in emergency management, which helps decision makers to make effective decisions. In this paper, aiming at clarifying the information aggregation laws, and according to the characteristic of emergency information, information relative entropy is applied in the information aggregation to establish the information aggregation model of emergency group decision-making. The analysis shows that support and credibility of decision rule are the two factors in information aggregation. The results of four emergency decision-making groups in case study support the analysis in the paper.

Group Decision-Making Model of Renal Cancer Surgery Options Using Entropy Fuzzy Element Aczel-Alsina Weighted Aggregation Operators under the Environment of Fuzzy Multi-Sets

Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their scientifical and reasonable information expression and group decision-making model for renal cancer patients.Fuzzy multi-sets(FMSs)have a number of properties,which make them suitable for expressing the uncertain information of medical diagnoses and treatments in group decision-making(GDM)problems.To choose the most appropriate surgical treatment scheme for a patient with localized renal cell carcinoma(RCC)(T1 stage kidney tumor),this article needs to develop an effective GDM model based on the fuzzy multivalued evaluation information of the renal cancer patients.First,we propose a conversionmethod of transforming FMSs into entropy fuzzy sets(EFSs)based on the mean and Shannon entropy of a fuzzy sequence in FMS to reasonably simplify the information expression and operations of FMSs and define the score function of an entropy fuzzy element(EFE)for ranking EFEs.Second,we present the Aczel-Alsina t-norm and t-conorm operations of EFEs and the EFE Aczel-Alsina weighted arithmetic averaging(EFEAAWAA)and EFE Aczel-Alsina weighted geometric averaging(EFEAAWGA)operators.Third,we develop a multicriteria GDM model of renal cancer surgery options in the setting of FMSs.Finally,the proposed GDM model is applied to two clinical cases of renal cancer patients to choose the best surgical treatment scheme for a renal cancer patient in the setting of FMSs.The selected results of two clinical cases verify the efficiency and rationality of the proposed GDM model in the setting of FMSs.

Extension of Paraconsistent Many-Valued Similarity Method to Group Decision

The Paraconsistent Many-Valued Similarity (PMVS) method for multi-attribute decision making will be incomplete as a decision model if it is not extended to the realm of group decision-making. Therefore, in this article, our primary objective is to show how the paraconsistent many-valued similarity method can be used to solve group decision-making problems involving choice making or ranking of a finite set of decision alternatives. Moreover, since weights are very important parameters in multi-attribute decision-making, we have introduced the Borda rule to calculate the weights of experts and that of every criterion under consideration. To demonstrate how the proposed method works, a numerical example on energy sources of an economy from the points of view of a group of experts is investigated. Further, we compare the results of this new approach with that of fuzzy TOPSIS group decision-making method to illustrate the robustness and effectiveness of the former.

Group Decision-making Models on Determining the Importance Ratings of Technical Characteristics

Determining the importance ratings of technical characteristics is a typical group decision-making process. The linguistic-based approach can effectively manage the imprecise and multi-granularity information i;n quality function deployment and facilitate decision-making in deriving the importance ratings. Based on the linguistic weighted averaging （LWA） operator and the linguistic hybrid averaging （LHA） operator, a practical approach is proposed to first aggregate the individual judgments into a collective value for each technical characteristic under linguistic environment, and then measure the deviation degree of linguistic variables to obtain the importance ratings of technical characteristics. A case study shows the application of the proposed method.

Group Decision-Making Method of Entry Policy During a Pandemic

Omicron,the new mutant coronavirus,has spread rapidly globally,attracting close attention from different stakeholders worldwide.The complex and constantly changing epidemic situation has had a new impact on the world.Therefore,this paper focuses on the characteristics of the rapid spread of the COVID-19 variant strain.Generally,epidemic prevention experts conduct preliminary screening as part of the existing epidemic plan database according to the current local situation,after which they sort the alternatives deemed more suitable for the situation.Then the decision-makers identify the most divergent expert group,plan for consultation and adjustments,and finally obtain the plan with the smallest divergence.This article aims to integrate the experts'opinions with the method of minimizing the differences,which can maximize the expert consensus and help organize the schemes that best meet the epidemic situation.The experts'negotiation and iteration of the differences in the initial plan align with the current complex and dynamic epidemic situation and are of great significance to the rapid formulation of plans to achieve effective prevention and control.