Multiperson Decision Making Under Linguistic Environment

The main aim of this dissertation is to study multiperson decision making problem under linguistic entironment. On the basis of the newly proposed version of 2-tuple fuzzy linguistic representation model for computing with words, we constructed a linguistic multiperson decision making model (LMDMM) and develpe a consensus approach for LMDMM. At last, applying the linguistic approach, we detailedly study the choice of the numerical scales and prioritization methods in AHP. This dissertation is helpful to complete Chiclana et al.'s multiperson decision making model and Saaty's analytic hierarchy process.The main results of the paper are summarized as follows.1. We proposes a linguistic multiperson decision making model (LMDMM) based on linguistic preference relations, integrating fuzzy preference relations, different types of multiplicative preference relations and multigranular linguistic preference relations. In the LMDMM, several transformation functions are first obtained to relate fuzzy preference relations and different types of multiplicative preference relations with multigranular linguistic preference relations. Then, we design the select process of LMDMM, based on the use of fuzzy majority and the extended ordered weighted operator (or the 2-tuple ordered weighted averaging operator), and discuss conditions under which the proposed select process satisfies the established social choice axioms. At last, we analyze the internal consistency of the proposed transformation functions. The results in this paper are helpful to complete Chiclana et al.'s fuzzy decision model [Fuzzy Sets and Systems 97 (1998) 33; 2003(137): 71] and Herrera et al.'s multiplicative decision model [European Journal of Operational Research 129 (2001) 372].2. Inspired by the concept of deviation measure between two linguistic preference relations [Omega, 2005 (33): 249], this paper further defines the deviation measure of a linguistic preference relation to the set of consistent linguistic preference relations. Based on this, we present a consistency index of linguistic preference relations and develop a consistency measure method for linguistic preference relations. Using this consistency measure, we discuss how to deal with inconsistency in linguistic preference relations, and also investigate the consistency properties of collective linguistic preference relations. We also propose an OWA-based consensus operator to aggregate linguistic variables. Some desired properties of the consensus operator have been shown. In particular, the consensus operator provides a theoretic basis for constructing an alternative consensus model for mutiperson group decision making under linguistic environment. This consensus model can preserve the original linguistic information given by the decision makers as much as possible, and support consensus process automatically, without moderator.3.This paper provides a method to compute canonical characteristic values (CCVs) of linguistic labels, when the semantics of the elements in the linguistic term set, which is often charactered by fuzzy numberes, are unknowned. Based on this, we develop a new 2-tuple fuzzy linguistic representation model for computing with words (CW). Comparing with Herrera-Martínez model [IEEE Transactions on Fuzzy Systems, 2000(8): 746] and Wang-Hao model [IEEE Transactions on Fuzzy Systems, 2006 (14): 435], the newly proposed 2-tuple fuzzy linguistic representation model can easily deals with linguistic labels, which do not have to be symmetrically distributed around a medium label and without the traditional requirement of having"equal distance"between them.4.The choice of the numerical scales and prioritization methods is an open problem in the analytic hierarchy process [Management Science, 1987(33): 1383]. By introducing a set of concepts regarding the linguistic variables and linguistic preference relations, and by appying the deviation measures of linguistic preference relations, we present two performance measure algorithms to evaluate the numerical scales and the prioritization methods. Using these performance measure algorithms, we compare the most common numerical scales (the Saaty scale, the geometrical scale, the Ma-Zheng scale and the Salo-H(?)am(?)al(?)ainen scale) and the prioritization methods (the eigenvalue method and the logarithmic least squares method). In addition, we also discuss the parameter of the geometrical scale, develop a new prioritization method, and construct an optimization model to select the appropriate numerical scales for the AHP decision makers. The findings in this paper can help the AHP decision makers select suitable numerical scales and prioritization methods.