Consensus Model In Group Decision Making

The main aim of this dissertation is to study the consensus model in group decision making (GDM). In GDM, consensus models are decision aid tools and help experts modify their individual opinions to reach a closer agreement. We have proposed different consensus approaches to reach consensus in GDM problems. Our main results are summarized as follows.1. Based on the concept of minimum-cost consensus, we propose a novel framework to achieve minimum-cost consensus under aggregation operators. Analytical results indicate that the proposed framework reduces to the consensus model of Ben-Arieh et al. when the selected aggregation operator is the ordered weighted averaging (OWA) operator with weight vector (1/2,...,0,...1/2)T. Furthermore, this paper closely examines the minimum-cost consensus models with a linear cost function under the common aggregation operators (e.g., the weighted veraging operator and the OWA operator) Linear-programming-based approaches are also developed to solve these models.2. For consensus models of group decision making using preference relations, the consistency measure includes two subproblems:individual consistency measure and consensus measure. In the analytic hierarchy process (AHP), the decision makers express their preferences using judgement matrices (i.e., multiplicative preference relations). Also, the geometric consistency index is suggested to measure the individual consistency of judgement matrices, when using row geometric mean prioritization method (RGMM), one of the most extended AHP prioritization procedures. This paper further defines the consensus indexes to measure consensus degree among judgement matrices (or decision makers) for the AHP group decision making using RGMM. By using Chiclana et al.’s consensus framework, and by extending Xu and Wei’s individual consistency improving method, we present two AHP consensus models under RGMM. Simulation experiments show that the proposed two consensus models can improve the consensus indexes of judgement matrices to help AHP decision makers reach consensus. Moreover, our proposal has two desired features:(1) in reaching consensus, the adjusted judgement matrix has a better individual consistency index (i.e., geometric consistency index) than the corresponding original judgement matrix;(2) this proposal satisfies the Pareto principle of social choice theory.3. We propose linear optimization models for solving some issues on consistency of fuzzy preference relations, such as individual consistency construction, consensus model and management of incomplete fuzzy preference relations. Our proposal optimally preserves original preference information in constructing individual consistency and reaching consensus (in Manhattan distance sense), and maximizes the consistency level of fuzzy preference relations in calculating the missing values of incomplete fuzzy preference relations. Linear optimization models can be solved in very little computational time using readily available softwares. Therefore, the results in this paper are also of simplicity and convenience for the application of consistent fuzzy preference relations in GDM problems.4. By introducing the concept of the interval numerical scale and by defining a generalized inverse operation of the interval numerical scale, we propose an interval version of2-tuple fuzzy linguistic representation model and develop the corresponding computational model to deal with the linguistic2-tuples. The interval version of2-tuple fuzzy linguistic representation model uses interval numbers to match the terms in a linguistic terms set, and generalizes the existing2-tuple fuzzy linguistic representation models. Further, by defining the interval consistency of the transitive calibration matrix,this paper proposes a consistency-based approach to derive the interval numerical scale from the transitive calibration matrix. Under established interval numerical scale, the transitive calibration matrix is of perfect consistency in terms of the interval sense.5. We propose the concept of distribution assessments in a linguistic term set, and study the operational laws of linguistic distribution assessments. The weighted averaging operator and the ordered weighted averaging operator for linguistic distribution assessments are presented. We also develop the concept of distribution linguistic preference relations, whose elements are distribution assessments. Further, we study the consensus measures for group decision making based on distribution linguistic preference relations. Two desirable properties of the proposed consensus measures are shown. A consensus model also has been developed to help decision makers improve the consensus level among distribution linguistic preference relations. Finally, illustrative numerical examples are given. The results in this paper provide a theoretic basis for the application of linguistic preference relations based on distribution assessment in group decision making.