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Pairwise comparisons between criteria/alternatives are a well-established methodology for group decision making. Both in the literature and in real-world applications, it is common practice to average the opinions of various experts expressed as pairwise comparisons to find a compromise solution. This paper dwells on the inverse problem: given a decision maker who knows his own preferences and the aggregate ones, we introduce and study some optimization problems to help him estimate, in the form of intervals, the preferences of the other decision makers. Since the possibility of estimating the other participants’ preferences violates the requirement of anonymity, this paper also reports the results of some numerical simulations examining the relation between the number of participants in the decision process and their anonymity. In addition to numerical simulations with randomly generated data, this manuscript reports the results of experiments on a dataset of preferences collected in a real-world survey.

Multiple attribute decision making (MADM) problems often include quantitative and qualitative attributes which can be assessed by numerical values and subjective judgements respectively. The evidential reasoning (ER) rule provides a process for dealing with this type of MADM problems of both a quantitative and qualitative nature of uncertainty. In this paper, the ER rule is generalized to dealing with MADM problems in group decision making circumstance where the weights and reliabilities of both experts and attributes are considered. Specifically, the result and process aggregation based ER rules for MADM in group decision making are given respectively, followed by the comparative analysis on the given aggregations. The ER analytical rule for group MADM problems is also provided for the generalization of the ER analytical approach where group decision making is not considered. It is also a development of Yang's ER rule which is a recursive calculation process. Due to the fact that uncertainty and ambiguity are always existent in group decision making, interval weights and reliabilities of experts and attributes should be taken into account in the process of experts’ judgment aggregation. In this paper, several ER based programming models under interval weights and reliabilities are constructed for the generation of global belief degrees in a consistent way. A case study is conducted on the life cycle assessment of electric vehicles to illustrate the applicability of the proposed method and the potential in supporting MADM in group decision making.

Constrained matrix games with payoffs of triangular fuzzy numbers (TFNs) are a type of matrix games with payoffs expressed by TFNs and sets of players’ strategies which are constrained. So far as we know, no study have yet been attempted for constrained matrix games with payoffs of TFNs since there is no effective way to simultaneously incorporate the payoffs’ fuzziness and strategies’ constraints into classical and/or fuzzy matrix game methods. The aim of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of TFNs. In this methodology, we introduce the concepts of Alpha-constrained matrix games for constrained matrix games with payoffs of TFNs and the values. By the duality theorem of linear programming, it is proven that players’ gain-floor and loss-ceiling always have a common interval-type value and hereby any Alpha-constrained matrix game has an interval-type value. Moreover, using the representation theorem for the fuzzy set, it is proven that any constrained matrix game with payoffs of TFNs always has a TFN-type fuzzy value. The auxiliary linear programming models are derived to compute the lower and upper bounds of the interval-type value and optimal strategies of players for any Alpha-constrained matrix game. In particular, the mean and the lower and upper limits of the TFN-type fuzzy value of any constrained matrix game with payoffs of TFNs can be directly obtained through solving the derived three linear programming models with data taken from only 1-cut and 0-cut of payoffs. Hereby the TFN-type fuzzy value of any constrained matrix game with payoffs of TFNs are easily computed. The proposed method in this paper is compared with other methods and its validity and applicability are illustrated with a numerical example.

The authors would like to acknowledge the Spanish State Research Agency support under the Project PID2019-103880RB-I00/ AEI/10.13039/501100011033., An important aspect to be considered in Group Decision Making problems is the study of consensus. Since in these problems it is desirable that the final decision is widely accepted, improving the consensus degree in a fair way is a very interesting task. This paper analyses the improvement in the consensus degrees -obtained by applying Manhattan distance-when the experts' preferences are slightly modified using one of the properties of the Uniform distribution. We carry out an experimental study that shows the enhancement in different cases to which Uniform extension has been applied, with different number of both, experts and alternatives., Spanish Government PID2019-103880RB-I00/ AEI/10.13039/501100011033

In Group Decision Making processes, experts debate about how to rank a set of alternatives. It is usual that, at a certain point of the discussion, the debate gets stuck. In this paper, a novel Group Decision Making method for environments with a high number of alternatives is presented. Fuzzy Ontologies are used in order to represent the alternatives and their characteristics. Moreover, a novel stagnation analysis is used in order to determine if the debate gets stuck. If it does, the method modifies the alternatives set in order to introduce new options and remove the least popular ones. This way, the debate can revive since that the new alternatives provide different points of view. The presented method helps experts to conduct long and thorough debates in order for them to be able to make effective and reliable decisions., MCIN/AEI PID2019-103880RB-I00, FEDER/Junta de Andalucia-Consejeria de Transformacion Economica, Industria, Conocimiento y Universidades B-TIC-590-UGR20, Andalusian government P20_00673, Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia IFPHI-049-135-2020, Universidad de Granada/CBUA

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Consensus in group decision making requires discussion and deliberation between the group members with the aim to reach a decision that reflects the opinions of every group member in order for it to be acceptable by everyone. Traditionally, the consensus reaching problem is theoretically modelled as a multi stage negotiation process, i.e. an iterative process with a number of negotiation rounds, which ends when the consensus level achieved reaches a minimum required threshold value. In real world decision situations, both the consensus process environment and specific parameters of the theoretical model can change during the negotiation period. Consequently, there is a need for developing dynamic consensus process models to represent effectively and realistically the dynamic nature of the group decision making problem. Indeed, over the past few years, static consensus models have given way to new dynamic approaches in order to manage parameter variability or to adapt to environment changes. This paper presents a systematic literature review on the recent evolution of consensus reaching models under dynamic environments and critically analyse their advantages and limitations.

One of the main challenges that the appearance of Web 2.0 and the overall spreading of the Internet have generated is how to tackle with the high number of users and information available. This problem is also inherited by the group decision making problems that can be carried out over the Web. In this article, to solve this issue, a group decision making support system that allows the use of a high number of participants and alternatives is presented. This method allows any number of participants to join the decision making process at any time. Furthermore, they let them provide information only about a certain subset of alternatives. The high participation rate can provide enough information for the decision process to be carried out even if the participants do not provide information about all the high number of available alternatives., This paper has been developed with the financing of FEDER funds in the project TIN2016-75850-R.

Hesitant linguistic term sets have been introduced to capture the human way of reasoning using linguistic expressions involving different levels of precision. In this paper, a lattice structure is provided to the set of hesitant fuzzy linguistic term sets by means of the operations intersection and connected union. In addition, in a group decision making framework, hesitant fuzzy linguistic descriptions are defined to manage situations in which decision makers are assessing different alternatives by means of hesitant fuzzy linguistic term sets. Based on the introduced lattice structure, two distances between hesitant fuzzy linguistic descriptions are defined. These metric structures allow distances between decision makers to be computed. A centroid of the decision making group is proposed for each distance to model group representatives in the considered group decision making framework.

Display Omitted An extended TODIM method is proposed to handle multi-criteria group decision making under triangular intuitionistic fuzzy environment.A weighted arithmetic interaction averaging operator of TIFNs is designed to aggregate information.A novel distance measure of the TIFNs is developed.A decision making problem of selecting renewable energy alternatives is applied to illustrate the validity and practicality of the proposed method. TODIM (an acronym in Portuguese of interactive and multicriteria decision making), which can capture the decision-makers (DMs) psychological behavior, is a recently developed multiple criteria decision making (MCDM) method. The classical TODIM method is introduced to handle information in the form of crisp numbers, but it has no capability to deal with fuzzy information such as triangular intuitionistic fuzzy numbers (TIFNs), which are flexible in reflecting the uncertainty and hesitation associated with the DMs opinions. In this paper, an extended TODIM method is proposed to solve multi-criteria group decision making (MCGDM) problems in a triangular intuitionistic fuzzy environment where weights of both DMs and criteria are completely unknown. First, the definition and characteristics of the classical TODIM and the comparative TIFNs are introduced. Then, novel operation laws considering the interaction between membership and non-membership values of different intuitionistic fuzzy sets are defined, and a weighted arithmetic interaction averaging operator of TIFNs is derived. In addition, an improved distance measure of TIFNs is proposed. From the perspective of similarity, we can obtain the weight of the evaluation value provided by each decision-maker, and aggregate individual decision matrices into a group decision matrix. The classical TODIM method is extended to deal with MCGDM problems with TIFNs, and detailed decision steps are given. Finally, a decision making problem to select renewable energy alternatives is applied to illustrate the validity and practicality of the proposed method.

We investigate the problem of green supplier development program evaluation.The approach can be applied under limited or no quantitative data.Program evaluation uses linguistic ratings (fuzzy numbers) obtained from experts.An integrated approach based on NGT and fuzzy VIKOR is proposed.Sensitivity analysis is performed. Developing environmental performance of suppliers is critical for green supply chain management. Organizations are nowadays investing in various green supplier development programs to enhance their supplier performances. The decision to select the right program for green supplier development is often a challenging decision due to lack of prior experience, limited quantitative information, specific context of the organization, and varying supplier backgrounds. This paper addresses the problem of evaluating green supplier development programs and proposes a fuzzy NGT (Nominal Group Technique)-VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) based solution approach. NGT is used to identify criteria for evaluating green supplier development programs. Fuzzy theory is used to address qualitative (linguistic) ratings for the alternatives and the selected criteria used under lack of quantitative information. VIKOR is used to generate green supplier development program rankings and recommend the best program(s) for implementation. Sensitivity analysis is performed to determine the influence of modeling parameters on ranking results of alternatives. A numerical application is provided.

Usually, at the beginning of the group decision making (GDM) problem, experts’ opinions may differ substantially. Therefore, the consensus reaching process is often a necessity in GDM, and numerous approaches for modeling the consensus process have been proposed. This paper provides an analysis for several novel consensus frameworks and models, investigated by our group. They are the consensus models with minimum adjustments, the consensus models based on consistency and consensus measures, and the direct consensus framework for GDM with different preference representation structures. The advantages of these consensus frameworks and models are analyzed. Meanwhile, the drawbacks and future researches are discussed.

In this paper, a method based on Choquet integral is proposed to solve the interval intuitionistic fuzzy multiple attribute group decision making problems. Firstly, some concepts about interval intuitionistic fuzzy measure are defined, through the strict mathematical reasoning to prove the measure we proposed satisfying the axiomatic system of fuzzy measure. Then, on the basis of fuzzy measure and game theory, we propose two models to determine fuzzy measure based on interval intuitionistic fuzzy entropy and weight information matrix. By calculating the Shapely value to determine expert weights, we establish a linear programming model based on relative entropy to determine the fuzzy measure of attribute weights to reflect the interactive characteristics among the criteria, using the Choquet integral to aggregate the decision-making information. Finally, we give the process of decision making in details.

Data Envelopment Analysis (DEA) is a mathematical model that evaluates the relative efficiency of Decision Making Units (DMUs) with multiple input and output. In some applications of DEA, ranking of the DMUs are important. For this purpose, a number of approaches have been introduced. Among them is the cross-efficiency method. The method utilizes the result of the cross-efficiency matrix and averages the cross-efficiency scores of each DMU. Ranking is then performed based on the average efficiency scores. In this paper, we proposed a new way of handling the information from the cross-efficiency matrix. Based on the notion that the ranking order is more important than individual efficiency score, the cross-efficiency matrix is converted to a cross-ranking matrix. A cross-ranking matrix is basically a cross-efficiency matrix with the efficiency score of each element being replaced with the ranking order of that efficiency score with respect to the other efficiency scores in a column. By so doing, each DMU assume the role of a decision maker and how they voted or ranked the other DMUs are reflected in their respective column of the cross-ranking matrix. These votes are then aggregated using a preference aggregation method to determine the overall ranking of the DMUs. Comparison with an existing cross-efficiency method indicates a relatively better result through usage of the proposed method.

Highlights? We show an expected utility approach to decision-making for group decisions. ? We test the model on a hypothetical context for the disposal of animal carcasses. ? We model expert judgements and supporting evidence within regulatory decisions. ? This approach reflects risk, uncertainty, and conflicts for multiple stakeholders. ? The model uses simplifying assumptions and static group decision making processes. Recent changes in the assessment and management of risks has had the effect that greater importance has been placed on relationships between individuals and within groups to inform decision making. In this paper, we provide the theoretical underpinning for an expected utility approach to decision-making. The approach, which is presented using established evidence support logic (TESLA?), integrating the expected utilities in the forming of group decisions. The rationale and basis are described and illustrated through a hypothetical decision context of options for the disposal of animal carcasses that accumulate during disease outbreaks. The approach forms the basis for exploring the richness of risk-based decisions, and representing individual beliefs about the sufficiency of evidence they may advance in support of hypotheses.

The aim of this paper is to present a new model of decision support system for group decision making problems based on a linguistic approach and dynamic sets of alternatives. The model incorporates a mechanism that allows to manage dynamic decision situations in which some information about the problem is not constant in time. We assume that the set of alternatives can change during the decision making process. The model is presented in a mobile and dynamic context where the experts' preferences can be incomplete. The linguistic approach is used to represent both the experts' preferences about the alternatives and the agreement degrees to manage the change of some alternatives. A prototype of such mobile decision support system in which the experts use mobile devices to provide their linguistic preferences at anytime and anywhere has been implemented. In such a way, we provide a new linguistic group decision making framework that is mobile and dynamic.

The importance of technology management is a vital determinant of long-run success or failure of organizations in today's world. Since technology is a major driver of the global economic development, business professionals seek more effective ways to manage existing and emerging technology. This study proposes a model to understand the links between competitive advantages, competitive priorities and competencies of a firm in the context of the technology management. We use the fuzzy analytical hierarchy process (AHP) to analyze these links. Moreover, we examine the perception of a group of managers from different Turkish firms regarding the technology management. The main result of this paper is that the concept of the management of technology arises to be much more important than both the product technology and the process technology. (C) 2005 Elsevier Inc. All rights reserved.

This paper presents a laboratory experiment to measure the effect of group membership on individual behavior in modified dictator games. The results suggest that this effect is influenced by the degree of group membership saliency. A within-subject design is employed: in stage 1, each subject decides individually; in stage 2, the subjects are divided into groups of three and one person is selected at random from each group to make the decision (the 'hierarchical decision rule'). In stage 3, additional pre-play communication in the group is allowed before the decision and, in stage 4, the decisions are again made on an individual basis. Interestingly, the dictators behave more selfishly when group members are not allowed to communicate. However, if groups are allowed to communicate, decisions do not differ from individual choices. Chat content shows that groups are concerned with reaching a consensus, even though talk is 'cheap' and only one group member will make the binding decision.