A new multi-criteria weighting and ranking model for group decision-making analysis based on interval-valued hesitant fuzzy sets to selection problems

The multi-criteria group decision-making methods under fuzzy environments are developed to cope with imprecise and uncertain information for solving the complex group decision-making problems. A team of some professional experts for the assessment is established to judge candidates or alternatives among the chosen evaluation criteria. In this paper, a novel multi-criteria weighting and ranking model is introduced with interval-valued hesitant fuzzy setting, namely IVHF-MCWR, based on the group decision analysis. The interval-valued hesitant fuzzy set theory is a powerful tool to deal with uncertainty by considering some interval-values for an alternative under a set regarding assessment factors. In procedure of the proposed IVHF-MCWR model, weights of criteria as well as experts are considered to decrease the errors. In this regard, optimal criteria’ weights are computed by utilizing an extended maximizing deviation method based on IVHF-Hamming distance measure. In addition, experts’ judgments are taken into account for computing the criteria’ weights. Also, experts’ weights are determined based on proposed new IVHF technique for order performance by similarity to ideal solution method. Then, a new IVHF-index based on Hamming distance measure is introduced to compute the relative closeness coefficient for ranking the candidates or alternatives. Finally, two application examples about the location and supplier selection problems are considered to indicate the capability of the proposed IVHF-MCWR model. In addition, comparative analysis is reported to compare the proposed model and three fuzzy decision methods from the recent literature. Comparing these approaches and computational results shows that the IVHF-MCWR model works properly under uncertain conditions.     

A linguistic modeling of consensus in group decision making basedon OWA operators

In this paper, a model for group decision-making is proposed and defined in a linguistic context. A multiperson multicriteria decision problem is considered, in which a group of experts is involved in the evaluation of the performances of a set of alternatives with respect to a predefined set of criteria. The objective is to evaluate a consensual judgement and a consensus degree on each alternative. Both the experts' evaluations of the alternatives and the degree of consensus are expressed linguistically. A “soft” consensus degree referred to a fuzzy majority of the experts is proposed based on the concept of linguistic quantifier. The entire process is defined in a linguistic domain and modeled within fuzzy set theory by ordered weighted average (OWA) operators     

A CASE-BASED DECISION SUPPORT SYSTEM FOR INDIVIDUAL STRESS DIAGNOSIS USING FUZZY SIMILARITY MATCHING

Stress diagnosis based on finger temperature (FT) signals is receiving increasing interest in the psycho-physiological domain. However, in practice, it is difficult and tedious for a clinician and particularly less experienced clinicians to understand, interpret, and analyze complex, lengthy sequential measurements to make a diagnosis and treatment plan. The paper presents a case-based decision support system to assist clinicians in performing such tasks. Case-based reasoning (CBR) is applied as the main methodology to facilitate experience reuse and decision explanation by retrieving previous similar temperature profiles. Further fuzzy techniques are also employed and incorporated into the CBR system to handle vagueness, uncertainty inherently existing in clinicians reasoning as well as imprecision of feature values. Thirty-nine time series from 24 patients have been used to evaluate the approach (matching algorithms) and an expert has ranked and estimated similarity. On average goodness-of-fit for the fuzzy matching algorithm is 90% in ranking and 81% in similarity estimation that shows a level of performance close to an experienced expert. Therefore, we have suggested that a fuzzy matching algorithm in combination with CBR is a valuable approach in domains, where the fuzzy matching model similarity and case preference is consistent with the views of domain expert. This combination is also valuable, where domain experts are aware that the crisp values they use have a possibility distribution that can be estimated by the expert and is used when experienced experts reason about similarity. This is the case in the psycho-physiological domain and experienced experts can estimate this distribution of feature values and use them in their reasoning and explanation process.     

Group decision-making based on pythagorean fuzzy TOPSIS method

Group decision-making is a process wherein multiple individuals interact simultaneously, analyze problems, evaluate the possible available alternatives, characterized by multiple conflicting criteria, and choose suitable alternative solution to the problem. Technique for establishing order preference by similarity to the ideal solution (TOPSIS) is a well-known method for multiple-criteria decision-making. The purpose of this study is to extend the TOPSIS method to solve multicriteria group decision-making problems equipped with Pythagorean fuzzy data, in which the assessment information on feasible alternatives, provided by the experts, is presented as Pythagorean fuzzy decision matrices having each entry characterized by Pythagorean fuzzy numbers. A revised closeness index is utilized to obtain the ranking of alternatives and to identify the optimal alternative. The developed Pythagorean fuzzy TOPSIS (PF-TOPSIS) is illustrated by a flow chart. At length, practical examples interpreting the applicability of our proposed PF-TOPSIS are solved.     

A cumulative belief degree approach for group decision‐making problems with heterogeneous information

In some complex group decision‐making (GDM) problems, the information needing to be processed may be heterogeneous. This may involve consideration of objective and subjective criteria by experts who have their own particular set of criteria, their own preference format for assessing alternatives under these criteria, and who may themselves be assigned differing importance weights as experts. This paper presents a cumulative belief degree approach to cope with heterogeneous information in multiple attribute GDM problems. The proposed approach focuses to aggregate subjective expert assessments and objective criteria that are presented in various representation formats and scales. The methodology employs transformation formulae for several preference representation scales to belief structure, including 2‐tuple representation, classical fuzzy sets, hesitant fuzzy sets, and intuitionistic fuzzy sets. Aggregation formulae are proposed to combine expert criteria evaluations and find a collective preference. A consensus degree is calculated for measuring the agreement between the experts. An illustrative example is presented to clarify the steps of the methodology, and validity of the approach is assured through comparative analysis with the existing methods.     

A new integrated methodology using modified Delphi-fuzzy AHP-PROMETHEE for Geospatial Business Intelligence selection

Geospatial Business Intelligence (Geospatial BI) is a system that combines multidimensional analysis and cartographic visualization. It plays an important role in decision making process for enterprises. Adopting such a comprehensive solution may result in the great investment decision for them, so great deal of attention should be given in the selection of the optimal system. As there are many impacting factors in the selection of Geospatial BI system, the same process is considered as a complex multi-criteria decision making problem. In this paper, we explore the application of an integrated methodology for the evaluation of various Geospatial BI alternatives. The proposed methodology integrates the three well-known decision-making techniques, namely Modified Delphi, fuzzy analytic hierarchical process (fuzzy-AHP), and preference ranking organization method for enrichment evaluations (PROMETHEE). In this respect, the modified Delphi is used to select the most impacting factors by a few decision-makers. The fuzzy-AHP is employed to analyze the structure of the problem and to obtain the weights of the qualitative and quantitative criteria, by incorporating the uncertainty values. Then, the PROMETHEE technique is used for optimal ranking of the alternative system choices. A step-by-step, numerical study is illustrated by using the proposed methodology on the decision making problem of a company that is faced to five Geospatial BI solutions. The results demonstrate that the proposed methodology can successfully accomplish our goal of this study.     

基于犹豫模糊语言的多阶段多属性决策方法

针对不确定语言条件下的决策问题,考虑专家偏好的阶段性差异,提出基于犹豫模糊语言的多阶段多属性决策方法。首先为了更准确地表达专家在决策过程中的犹豫性,采用犹豫模糊语言来表达专家的评估信息;其次考虑阶段权重的波动性,运用基于专家阶段性偏好的信息熵方法构建阶段权重优化模型确定阶段权重;然后利用最大化偏差法来求解属性权重,并采用基于平均解距离评价(EDAS)方法对备选方案进行排序;最后以某企业选取物流商问题为例,验证该方法的有效性和可行性。     

A measurement model for experts knowledge-based systems algorithm using fuzzy analytic network process

This study proposes an experts knowledge-based systems measurement model, the model using fuzzy analytic network process (FANP) to resolve the uncertainty and imprecision of evaluations during pre-negotiation stages, where the comparison judgments of a decision maker are represented as fuzzy triangular numbers. A novel fuzzy prioritization method, which derives crisp priorities (criteria weights and scores of alternatives) from consistent and inconsistent fuzzy comparison matrices, is also proposed. The applicability of the proposed model is demonstrated in a government purchase digital video recorder (DVR) system project study. The stability tests indicate the advantages of the proposal model in determining the value of model. Importantly, the proposed model can provide decision makers a reference material, making it highly applicable for academic and commercial purposes.     

Linguistic-labels aggregation and consensus measure for autocratic decision making using group recommendations

Group decision making is a common and important activity in everyday life. In many cases, due to inherent uncertainty, experts cannot express their score or preference using exact numbers. The use of linguistic labels makes expert judgment more reliable and informative for decision-making. One of the problems of group decision making in fuzzy domains is aggregating experts' opinions, expressed using linguistic labels, into a group opinion. This aggregation allows the group to select the most "preferred" alternative from a finite set of candidates. The aggregation of individual judgments into a group opinion requires a measured level of consensus. In this paper, by introducing a new linguistic-labels aggregation operation, we present a procedure for handling an autocratic group decision-making process under linguistic assessments. The methodology presented results in two consequent outcomes: a group-based recommendation, and a score for each expert, reflecting the expert's contribution towards the group recommendation. By changing the weights of the experts based on their contributions, we increase the consensus and reinforce the common decision, without forcing the experts to modify their opinions. This methodology allows an autocratic decision maker to use a diversified group of consultants for a succession of decisions reaching a high level of consensus.     

Applying fuzzy hierarchy multiple attributes to construct an expert decision making process

The main objective of this paper is to propose an approach within the AHP framework for tackling the uncertainty and imprecision of service evaluations during pre-negotiation stages, where the expert’s comparison judgments are represented as fuzzy triangular numbers. A fuzzy prioritization method, which derives crisp priorities from consistent and inconsistent fuzzy comparison matrices, is described. The fuzzy analytic hierarchy process (FAHP)-based decision-making method can provide decision makers or buyer a valuable reference for evaluating software quality. A case study demonstrates the effectiveness of the proposed scheme. Importantly, the proposed scheme can assist decision makers in assessing the feasibility of digital video recorder system to management public space, making it highly applicable for academic and commercial purposes.     

Multiple attribute group decision-making methods with unknown weights in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting

To better solve the corresponding multiple attribute group decision-making problem with unknown weights, multiple attribute group decision-making methods with completely unknown weights of decision-makers and incompletely known weights of attributes are proposed in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting. In the group decision-making method, two weight models are proposed based on the score function to determine the weights of both experts and attributes from the intuitionistic fuzzy decision matrices and the interval-valued intuitionistic fuzzy decision matrices. Then, overall evaluation formulas of weighted scores for each alternative are introduced in the intuitionistic fuzzy setting and the interval-valued intuitionistic fuzzy setting to obtain the ranking order of alternatives and the most desirable one(s). Finally, two numerical examples demonstrate the applicability and benefit of the proposed methods.     

信任网络下的TODIM群体决策方法

针对在群体决策中如何利用专家之间的社会关系和决策专家的有限理性的问题,提出一种信任网络下的TODIM群体决策方法。首先,根据专家讨论次数,在每一次讨论中,每个专家会根据信任接受程度参考信任者的决策矩阵,并通过信息交互和协商修改决策矩阵;其次,当达到设定的专家讨论次数时,计算最终的群体决策矩阵;最后,分别运用信任网络下的TODIM群体决策方法和TODIM群体决策方法计算各方案排序。对所得结果进行对比分析,并对专家讨论次数和信任接受程度进行灵敏度分析。案例分析结果表明,信任网络下的TODIM群体决策方法能充分结合信任网络,保证了决策过程中的多阶段信息交互和反馈过程,并在对比分析和灵敏度分析上优于对比方法。     

A method for large group decision-making based on evaluation information provided by participators from multiple groups

Large group decision-making (LGDM) is a special group decision-making (GDM) problem, in which a large number of persons take part in decision process, while research concerning this issue is still relatively scarce. The objective of this paper is to develop a method to solve the LGDM problem, in which a large number of persons from multiple groups take part in the decision process and express their personal evaluations on the alternatives according to the pre-established identifier set. In the method, the percentage distribution on evaluations of each group concerning each alternative is determined. The decision weight of each group concerning each alternative is obtained by aggregating the subjective weight, which is provided by the organizer, and the objective weight, determined according to the level of consensus among participators' evaluations. According to the percentage distributions and decision weights, the dominance degrees on pairwise comparisons of alternatives are calculated, and a ranking of alternatives can be determined using the PROMETHEE II method. Finally, an example is given to illustrate the use of the proposed method.     

基于直觉模糊集和证据理论的群决策方法

针对属性值和权重均为直觉模糊数的多属性决策问题,提出一种基于直觉模糊集和证据理论的群决策方法.首先,对专家给出的每个方案的属性值和属性权重进行证据合成,在此基础上合成每个方案的所有属性值;然后,基于直觉模糊集相似度确定专家的相对权重,修正方案证据,并合成所有专家证据,得到方案的信任区间,根据信任区间的大小对方案进行排序;最后,通过数值案例验证了所提出方法的有效性和合理性.     

Pythagorean fuzzy TOPSIS for multicriteria group decision-making with unknown weight information through entropy measure

In this study, a new technique for order preference by similarity to ideal solution (TOPSIS)-based methodology is proposed to solve multicriteria group decision-making problems within Pythagorean fuzzy environment, where the information about weights of both the decision makers (DMs) and criteria are completely unknown. Initially, generalized distance measure for Pythagorean fuzzy sets (PFSs) is defined and used to initiate a new Pythagorean fuzzy entropy measure for computing weights of the criteria. In the decision-making process, at first, weights of DMs are computed using TOPSIS through the geometric distance model. Then, weights of the criteria are determined using the entropy weight model through the newly defined entropy measure for PFSs. Based on the evaluated criteria weights, TOPSIS is further applied to obtain the score value of alternatives corresponding to each decision matrix. Finally, the score values of the alternatives are aggregated with the calculated DMs’ weights to obtain the final ranking of the alternatives to avoid the loss of information, unlike other existing methods. Several numerical examples are considered, solved, and compared with the existing methods.     

Enhancing decision-making flexibility by introducing a new last aggregation evaluating approach based on multi-criteria group decision making and Pythagorean fuzzy sets

Uncertainty is an important factor in any decision-making process. Different tools and approaches have been introduced to handle the uncertain environment of group decision making. One of the latest tools in dealing with uncertainty is Pythagorean fuzzy sets (PFSs). These sets extend the concept of intuitionistic fuzzy sets. To show the advantages of these new sets, this paper offers a novel last aggregation group decision-making process for weighting and evaluating. The methodology employs a new approach in computing the weight of decision makers. Moreover, the concept of entropy is applied to address the fuzziness of weights of evaluation criteria in the process. The method develops a new index in ranking the alternatives. Finally, the proposed method is last aggregation, which means it will be more precise in situations with high variations in decision makers’ judgments. To show the applicability of the method, an example from the literature is adopted and solved for internet companies.     

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 the final 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 for final ranking of alternatives. The proposed framework is clarified by an example of software packages selection of a university.     

A Probability-Based Approach to Comparison of Fuzzy Numbers and Applications to Target-Oriented Decision Making

In this paper, we introduce a new comparison relation on fuzzy numbers based on their alpha-cut representation and comparison probabilities of interval values. Basically, this comparison process combines a widely accepted interpretation of fuzzy sets together with the uncertain characteristics inherent in the representation of fuzzy numbers. The proposed comparison relation is then applied to the issue of ranking fuzzy numbers using fuzzy targets in terms of target-based evaluations. Some numerical examples are used to illuminate the proposed ranking technique as well as to compare with previous methods. More interestingly, according to the interpretation of the new comparison relation on fuzzy numbers, we provide a fuzzy target-based decision model as a solution to the problem of decision making under uncertainty, with which an interesting link between the decision maker's different attitudes about target and different risk attitudes in terms of utility functions can be established. Moreover, an application of the proposed comparison relation to the fuzzy target-based decision model for the problem of fuzzy decision making with uncertainty is provided. Numerical examples are also given for illustration.     

A new linguistic MCDM method based on multiple-criterion data fusion

Multiple-criteria decision-making (MCDM) is concerned with the ranking of decision alternatives based on preference judgements made on decision alternatives over a number of criteria. First, taking advantage of data fusion technology to comprehensively consider each criterion data is a reasonable idea to solve the MCDM problem. Second, in order to efficiently handle uncertain information in the process of decision making, some well developed mathematical tools, such as fuzzy sets theory and Dempster Shafer theory of evidence, are used to deal with MCDM. Based on the two main reasons above, a new fuzzy evidential MCDM method under uncertain environments is proposed. The rating of the criteria and the importance weight of the criteria are given by experts’ judgments, represented by triangular fuzzy numbers. Then, the weights are transformed into discounting coefficients and the ratings are transformed into basic probability assignments. The final results can be obtained through the Dempster rule of combination in a simple and straight way. A numerical example to select plant location is used to illustrate the efficiency of the proposed method.     

Fuzzy MCDM approach for selecting the best environment-watershed plan

In the real word, the decision-making problems are very vague and uncertain in a number of ways. Most of the criteria have interdependent and interactive features, so they cannot be evaluated by conventional measure method. Such as the feasibility, thus, to approximate the human subjective evaluation process, it would be more suitable to apply a fuzzy method in the environment-watershed plan topic. This paper describes the design of a fuzzy decision support system in multi-criteria analysis approach for selecting the best plan alternatives or strategies in environment watershed. The fuzzy analytic hierarchy process (FAHP) method is used to determine the preference weightings of criteria for decision makers by subjective perception (natural language). A questionnaire was used to find out from three related groups comprising 15 experts, including 5 from the university of expert scholars (include Water Resources Engineering and Conservation, Landscape and Recreation, Urban Planning, Environment Engineering, Architectural Engineering, etc.), 5 from the government departments, and 5 from industry. Subjectivity and vagueness analysis is dealt with the criteria and alternatives for selection process and simulation results by using fuzzy numbers with linguistic terms. It incorporated the decision-makers’ attitude towards the preference; overall performance value of each alternative can be obtained based on the concept of fuzzy multiple-criteria decision-making (FMCDM). This research also gives an example of evaluation consisting of five alternatives, solicited from an environment-watershed plan work in Taiwan, is illustrated to demonstrate the effectiveness and usefulness of the proposed approach. The result is useful for destination planning and the sustainability of watershed tourism resources as well.