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.

Spherical Functions on Fuzzy Lie Group

Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Helgason-spherical function on G is then established on .

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.

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.

金融保险集团一体化战略的A-FUZZY分析模型及实证研究

随着金融体系深化改革的持续推进,保险业、证券业和银行业的混业经营变得越来越普遍,为了在全球化市场上获得持久竞争优势,金融机构跨行业经营方式也开始向集团化和一体化趋势发展,金融保险集团的一体化成为全球保险业经营体制的最大创新,对于深化金融改革的中国保险行业来说越发重要。文章基于AHP模糊综合量化评价方法构建科学的金融保险集团一体化战略评价模型,采用专家打分数据进行实证分析,发现在一体化战略中组织能力的权重最高,业务创新和资源整合是金融保险集团一体化战略的重要助推器。

Novel combinatorial algorithm for the problems of fuzzy grey multi-attribute group decision making

To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.

Group Decision Making Based Fuzzy Pattern Recognition Model for Lectotype Optimization of Offshore Platforms 1

This paper develops a fuzzy pattern recognition model for group decision making to solve the problem of lectotype optimization of offshore platforms. The lack of data and the inexact or incomplete information for criteria are the main cause of uncertainty in the evaluation process, therefore it is necessary to integrate the judgments from different decision makers with different experience, knowledge and preference. This paper first uses a complementary principle based pairwise comparison method to obtain the subjective weight of the criteria from each decision maker. A fuzzy pattern recognition model is then developed to integrate the judgments from all the decision makers and the information from the criteria, under the supervision of the subjective weights. Finally a case study is given to show the efficiency and robustness of the proposed model.

Fuzzy Logic Based Group Maturity Rating for Software Performance Prediction

Driven by market requirements, software services organizations have adopted various software engineering process models （such as capability maturity model （CMM）, capability maturity model integration （CMMI）, ISO 9001：2000, etc.） and practice of the project management concepts defined in the project management body of knowledge. While this has definitely helped organizations to bring some methods into the software development madness, there always exists a demand for comparing various groups within the organization in terms of the practice of these defined process models. Even though there exist many metrics for comparison, considering the variety of projects in terms of technology, life cycle, etc., finding a single metric that caters to this is a difficult task. This paper proposes a model for arriving at a rating on group maturity within the organization. Considering the linguistic or imprecise and uncertain nature of software measurements, fuzzy logic approach is used for the proposed model. Without the barriers like technology or life cycle difference, the proposed model helps the organization to compare different groups within it with reasonable precision.

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.

Fuzzy interval linguistic sets with applications in multi-attribute group decision making

Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets(HFLTSs), an effective linguistic computational tool in modeling and eliciting such information, have hence aroused many scholars’ interests and some extensions have been introduced recently.However, these methods are based on the discrete linguistic term framework with the limited expression domain, which actually depict qualitative information using several single values. Therefore,it is hard to ensure the integrity of the semantics representation and the accuracy of the computation results. To deal with this problem, a semantics basis framework called complete linguistic term set(CLTS) is designed, which adopts a separation structure of linguistic scale and expression domain, enriching semantics representation of decision makers. On this basis the concept of fuzzy interval linguistic sets(FILSs) is put forward that employs the interval linguistic term with probability to increase the flexibility of eliciting and representing uncertain and hesitant qualitative information. For practical applications, a fuzzy interval linguistic technique for order preference by similarity to ideal solution(FILTOPSIS) method is developed to deal with multi-attribute group decision making(MAGDM) problems. Through the cases of movie and enterprise resource planning(ERP) system selection, the effectiveness and validity of the proposed method are illustrated.

Group Decision Making With Consistency of Intuitionistic Fuzzy Preference Relations Under Uncertainty

Intuitionistic fuzzy preference relation(IFPR) is a suitable technique to express fuzzy preference information by decision makers(DMs). This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR,by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly,a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.

Homomorphic Properties of Fuzzy Rough Groups

This paper is devoted to the discussion of homomorphic properties of fuzzy rough groups.The fuzzy approximation space was generated by fuzzy normal subgroups and the fuzzy rough approximation operators were discussed in the frame of fuzzy rough set model.The basic properties of fuzzy rough approximation operators were obtained.

A hybrid heterogeneous Pythagorean fuzzy group decision modelling for crowdfunding development process pathways of fintech‑based clean energy investment projects

This study aims to evaluate the crowdfunding alternatives regarding new service development process pathways of clean energy investment projects.In this framework,a new model has been generated by considering the consensus-based group decisionmaking with incomplete preferences,Pythagorean fuzzy decision-making trial and evaluation laboratory(DEMATEL)and technique for order preference by similarity to ideal solution(TOPSIS).Moreover,a comparative evaluation has been performed with Vise Kriterijumska Optimizacija I.Kompromisno Resenje methodology and sensitivity analysis has been made by considering 4 different cases.The main contribution is to identify appropriate crowdfunding-based funding alternatives for the improvement of the clean energy investments with a novel MCDM model.By considering the iteration technique and consensus-based analysis,the missing parts in the evaluations can be completed and opposite opinion problems can be reduced.Furthermore,with the help of hybrid MCDM model by combining DEMATEL and TOPSIS,more objective results can be reached.It is concluded that the analysis results are coherent and reliable.The findings indicate that the full launch is the most significant criterion for equity and debt-based crowdfunding alternatives.On the other side,the analysis has the highest weight for reward and donation-based alternatives whereas design is the most essential item regarding the royalty-based alternative.Additionally,it is also defined that equity-based crowdfunding alternative is the most significant for the service development process of clean energy investment projects.In this way,it will be possible to provide a continuous resource for clean energy investment projects.On the other hand,by providing financing with equity,there will be no fixed financing cost for clean energy investors.If these investors make a profit,they distribute dividends with the decision of their authorized bodies.

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.

Stability and stabilization of discrete T-S fuzzy time-delay system based on maximal overlapped-rules group

The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal overlapped-rules group（MORG）,a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function（CLKF） approach and the fuzzy Lyapunov-Krasovskii function（FLKF） approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.

A study on distributive and modular lattice ordered fuzzy soft group and its duality

Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.

Transfer theorems for fuzzy semi-groups

Discusses the use of the notion of fuzzy point to study some basic algebraic structures, such as group, semi group and ideal and then clarifies the links between the fuzzy point approach and the classical fuzzy approach.

Improved Group Fuzzy Preference Programming Method Based on Fuzzy Random Theory

A new prioritization method in the analytic hierarchy process （AHP）, which improves the group fuzzy preference programming （GFPP） method, is proposed. The fuzzy random theory is applied in the new prioritization method. By modifying the principle of decision making implied in the GFPP method, the improved group fuzzy preference programming （IGFPP） method is formulated as a fuzzy linear programming problem to maximize the average degree of the group satisfaction with all possible group priority vectors. The IGFPP method inherits the advantages of the GFPP method, and solves the weighting trouble existed in the GFPP method. Numerical tests indicate that the IGFPP method performs more effectively than the GFPP method in the case of very contradictive comparison judgments from decision makers.

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.