A group decision making method with preference analysis to re-build the Global Entrepreneurship Index.

Consistency and consensus study for group decision making (GDM) with fuzzy preference relations (FPRs) are necessary, which have a decisive impact on the quality of decision results. Consistency can prevent self-contradictory judgments, and consensus limits the deviation among individual judgments within the preset threshold. Because acceptably multiplicative consistency still cannot avoid self-contradictory judgments, this paper considers the ordinal consistency and acceptably multiplicative consistency simultaneously. In view of these aspects, we introduce a new optimal model-based method for GDM with FPRs. As minimum total adjustment and minimum individual adjustment may be inconsistent, we introduce the Solidarity consistency and consensus adjustment mechanism (So-CCAM) to allocate the minimum total adjustment, which fully considers the cooperation and solidarity among decision makers. When the So-CCAM does not exhibit stability, we present the nucleolus consistency and consensus adjustment mechanism (Nu-CCAM), which is the best element in the core according to lexicographical order. After that, an algorithm is offered. To demonstrate the application and efficiency of the new method, an illustrative example is offered, and a comparison is carried out. It offers the first optimization models-based method for GDM with FPRs in view of ordinal consistency, acceptably multiplicative consistency, and consensus analysis. Further, it provides two rational consistency and consensus adjustment mechanisms by cooperative game theory.

The selection of a waste-to-energy (WTE) plant site is the core issue that determines whether the WTE project can effectively treat municipal solid waste, reduce environmental pollution, and promote the development of a circular economy, and is often determined through group decision-making. The complexity of this group decision problem makes the opinions of decision makers often with uncertainty. The single-valued neutrosophic set (SVNS) can reduce the loss of information that contains uncertainty by quantitatively describing the information through three functions. In addition, existing studies on group decision-making for WTE plant siting suffer from the problem that decision maker weights do not change in concert with those decision makers’ decision information. Therefore, this study proposes a group decision-making method based on SVNSs. First, a group consensus strategy is proposed to improve group consensus by removing the evaluation value of the corresponding solution for decision makers who do not reach consensus and are unwilling to modify their preferences. Second, a decision maker weight determination and adjustment method is proposed to readjust the decision maker weights from the solution level according to their respective consensus degree when the decision makers’ preference information changes. This method enables the decision makers’ preferences and weights to be changed jointly. An illustrative example and a comparative analysis of WTE plant siting decisions demonstrate the feasibility and superiority of the method. The experimental results show that the method is effective in helping decision makers to select the optimal WTE plant site more accurately.

Optimization-based group decision making using interval-valued intuitionistic fuzzy preference relations

A doubly extended TOPSIS method for group decision making based on ordered fuzzy numbers

Multi criteria decision making (MCDM) and group decision making (GDM) are two well practiced approaches to solve decision making problems. Group decision making combines opinions from Decision makers (DMs) into a coherent group decision. The aim of this paper is to develop a new fuzzy group decision making algorithm and apply it to a real-world groundwater development problem to select the most preferred alternative. Five decision makers (DMs) are selected to express their judgments about relative importance of 3 criteria (water pumped, cost, and risk) and have given their preferences as ordinal preferences, utility values, fuzzy preference relations and multiplicative preference relations. Decision makers' opinions are aggregated based on a fuzzy group decision making. Ordered weighted averaging (OWA) operator has been used to aggregate decision makers' opinions. Consensus measure is also defined to evaluate convergence between group and individual opinions. The outcomes of the proposed algorithm show that proposed fuzzy group decision making process is a relevant approach to aggregate the individual expert's opinion and is a desirable tool to reach consensus among DMs.

An automatic approach to reaching consensus in multiple attribute group decision making

Explosive Ordnance Risk Education Messages (EORE) is a multi-criteria decision-making problem (MCDM) based on three steps, namely, the identification of distinct evolution criteria, the significance criteria, and the variation of data. Because it makes use of a more sophisticated classification technique, the group decision method (GDM) based on weighted arithmetic mean (AM) to prioritize (EORE) messages is the proper approach. In contrast to GDM, which explicitly weights each criterion, GDM implicitly weights each alternative's criterion values. With the help of the new hybrid method weighting technique, we can overcome this theoretical difficulty by providing explicit weights for criteria generated with zero inconsistencies and combined with the new distance-based weighting method. SFS (spherical fuzzy set) is used in hybrid methods, although it can only be used to solve the ambiguity associated with the theoretical concerns outlined above.

Visualizing preferences on spheres for group decisions based on multiplicative preference relations

Group decision making based on the modified probability calculation method and DEA cross-efficiency with probabilistic hesitant fuzzy preference relations

Affordable and reliable energy is not only central to prosperity, but also to poverty reduction, local development, environmental integrity, quality of life, growth, and progress. Given the importance and wide scale of energy generation all around the world, its ever growing economic, social and environmental aspects need to be taken into better consideration. The sustainability performance of energy operations shall be assessed on a project basis, as energy generation projects may significantly vary, depending on the needs and circumstances. This chapter introduces a novel approach for evaluating energy projects from a sustainability point of view and estimates their sustainability performance as a decision-making support tool. Decision environments can sometimes be complicated for an individual decision maker (DM) to consider every aspect of the problem. Group decision making (GDM) can be advantageous to reduce the impact of biased and personal opinions on the decision process. Moreover, DMs’ judgments are mostly far from being completely certain, making it more difficult to put their ratings into numerical forms. In such circumstances, the fuzzy set theory can be applied to better represent DMs’ preferences. This chapter applies GDM together with the fuzzy set theory to find the importance of the selected evaluation criteria. Then, GDM and the fuzzy set theory are combined with VIKOR (Vlse Kriterijumska Optimizacija Kompromisno Resenje) technique to rank the energy project alternatives. This approach is particularly useful for its strength in dealing with actual energy projects so that it can support both researchers and business managers to compare the sustainability performance of planned or realized power plants in a balanced manner. The usability of the proposed approach is shown in a case study from Turkey, where different energy projects are evaluated for their overall sustainability performance.

Group decision processes: MOLP procedures facilitating group and individual decision orientations

A method for group decision-making based on determining weights of decision makers using TOPSIS

We introduce the principle of robust ordinal regression to group decision. We consider the main multiple criteria decision methods to which robust ordinal regression has been applied, i.e., UTAGMS and GRIP methods, dealing with choice and ranking problems, UTADISGMS, dealing with sorting (ordinal classification) problems, and ELECTREGMS, being an outranking method applying robust ordinal regression to well known ELECTRE methods. In this way, we obtain corresponding methods for group decision: UTAGMS-GROUP, UTADISGMS-GROUP and ELECTREGMS-GROUP.KeywordsRobust ordinal regressionMultiple criteria choicesorting and rankingAdditive value functionsOutranking methodsMultiple criteria group decision

This article aims to present a case study of a real decision problem, with the main objective of assisting an animal production company, on the installation of a new factory. When evaluating the various alternatives, organizations seek clear, objective and, if possible, mathematically represented criteria. However, decision-making involves a cognitive mental process resulting from the selection of the most appropriate course of action, based on various tangible and intangible criteria (Saaty, 2000) arbitrarily chosen by decision makers. In addition to the various criteria, we also have the participation of several decision makers with the common objective of choosing of the best place to guarantee the highest growth of the company. Several methods have been developed to aid decision-making in this scenario. In the described case, we used one of those methods, namely AHP (Analytic Hierarchy Process), to hierarchize the possible location for the installation of the new factory, being the alternatives the following: Carregado, Benavente and Covilha. In 1980, Professor L. Saaty of the University of Pittsburgh, created AHP, which allows using qualitative and/or quantitative criteria in the evaluation process. This method starts with the construction of a decision tree where the criteria, sub-criteria and the various alternatives are detailed. In a second step, those criteria are compared among the various elements at the same level of hierarchy, using a matrix created by the author - Fundamental Ratio Scale in pair-wise comparison of Saaty -, with values from 1 to 9, depending on their relevance, being 1 of equal importance and the 9 of absolute importance. The third step in the model is to calculate the relative priority of each criteria and to analyze the consistency of the judgments of the decision makers (i.e. the consistency of their responses/ comparisons). At final step, the composite priority matrix for the various alternatives is obtained, reflecting the alternatives hierarchy. According to Forman and Peniwati (1998), the behavior of a decision makers’ group is a factor that will determine how the information will be analyzed and aggregated. Should the group acts as a unit (when individuals in a group essentially desire the best for the organization they represent, regardless of their own preferences, values and goals, acting in tune and making their judgments so that the group behaves as a new individual), a variant of the AHP known as Individual Judgment Aggregation (IJA) is used. For groups that prefer to maintain individual analysis, there is Individual Priority Aggregation (IPA) alternative. In both cases it is possible to assign different weights to the decision makers in the process or to consider them with same degree of importance in terms of the decision. In both cases, the group decision is treated mathematically. In the application of the AHP to our case, two decision makers considered 3 criteria subdivided into several sub-criteria: implementation (sub-criteria: suppliers, cost of installation and distance to current clients), labor (sub-criteria: availability and qualification) and incentives (sub-criteria: social security, and taxes). In this case study, decision-makers' consensus was chosen, using IJA. The application of this method to this real case allowed us to create a model of analysis and support decision, contributing with another tool for this complex decision process.

Linguistic preference relations (LPRs) can indicate the decision makers (DMs)' qualitative pairwise judgments regarding a set of alternatives in uncertain multicriteria decision-making problems. This paper examines several goal programming models for managing the additive consistency and consensus of LPRs and then develops an additive-consistency- and consensus-based method for group decision making (GDM) with LPRs. First, this paper offers a consistency index to quantify the consistency level for LPRs and define acceptable consistent LPRs. For an LPR that is unacceptably additive consistent, several additive-consistency-based programming models are developed to address the inconsistency and to establish an acceptably consistent LPR. Then, an additive-consistency-based procedure to generate the priority weight vector from the LPR is offered. An additive-consistency-based algorithm for decision making with an LPR is presented. Subsequently, considering the consensus in GDM, a consensus index is proposed for gauging the agreement degree among individual LPRs. Regarding individual LPRs that do not exhibit acceptably additive consistency or acceptable consensus, several goal programming models to derive new LPRs with acceptable consistency and consensus are provided. Afterward, the DMs' weights are determined objectively, and individual LPRs are integrated into a collective LPR. An additive-consistency- and consensus-based GDM method with a group of LPRs is developed. Finally, two practical numerical examples are offered, and a comparative analysis is presented.