A Subjective and Objective Integrated Method for MAGDM Problems with Multiple Types of Exact Preference Formats
Group decision making with preference information on alternatives has become a very active research field over the last decade. Especially, the investigation on the group decision making problems based on different preference formats has attracted great i
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Abstract. Group decision making with preference information on alternatives has become a very active research field over the last decade. Especially, the investigation on the group decision making problems based on different preference formats has attracted great interests from researchers recently and some approaches have been developed for dealing with these problems. However, the existing approaches can only be suitable for handling the subjective preference information. In this paper, we investigate the multiple attribute group decision making (MAGDM) problems, in which the attribute values (objective information) are given as non-negative real numbers, the information about attribute weights is to be determined, and the decision makers have their subjective preferences on alternatives. The provided subjective preference information can be represented in three well-known exact preference formats: 1) utility values; 2) fuzzy preference relations; and 3) multiplicative preference relations. We first set up three constrained optimization models integrating the given objective information and each of three preference formats respectively, and then based on these three models, we establish an integrated constrained optimization model to derive the attribute weights. The obtained attribute weights contain both the subjective preference information given by all the decision makers and the objective information. Thus, a straightforward and practical method is provided for MAGDM with multiple types of exact preference formats.
1 Introduction Decision making is a common activity in everyday life. In many real-world situations, such as economic analysis, strategic planning, medical diagnosis, and venture capital, etc. [1], multiple decision makers are usually involved in the process of decision making, and needed to provide their preference information over a finite set of feasible alternatives. Due to that each decision maker has his/her unique characteristics with regard to knowledge, skills, experience and personality, the different decision makers may express their preferences by means of different preference representation formats, such as utility values [2], fuzzy preference relation [3], multiplicative preference relation [3], etc. The issue has attracted great attention from researchers recently, and a variety of approaches have been developed to dealing with various group H. Yin et al. (Eds.): IDEAL 2007, LNCS 4881, pp. 145–154, 2007. © Springer-Verlag Berlin Heidelberg 2007
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Z. Xu and J. Chen
decision making problems with nonhomogeneous preference information. In [4], some representation models were established for group decision making problems based on the concept of fuzzy majority for the aggregation and exploitation of the information represented by means of preference orderings, utility functions, and fuzzy preference relations. For the group decision making problem, where the information about the alternatives provided by the decision makers can be presented by means of preference orderings, utilit
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