A Method for Aggregating Group Preference Based on Pair-wise Comparison with Random Binary Relations under Interval Belief Structures

Received: 13 Mar. 2012; Revised 21 Jul. 2012; Accepted 11 Aug. 2012e ceived: Jul 8, 2011; RevisedAccepted Jan. 6, Abstract: The aim of this paper is to develop an approach to solve the random lattice order group decision-making problem, where the preference information on alternatives pair provided by experts is in the form of uncertain binary preference relations. In this paper, firstly, the preference characterization of decision makers is extended from four various binary relations to seven various binary relations. We give the definition and properties of significance degree, interval belief and interval-valued distribution preference vector. Then, to process uncertain binary preference relations, a comparison matrix about interval significance degree of preference relations is constructed. Based on the interval-valued comparison matrix, the interval significance degree by approximation models is driven, so we need to aggregate group preference to interval-valued distribution preference vector of decision group. Furthermore, the comparison principle of interval number and the method to determine the binary relation are presented. Finally, example is used to illustrate the use of the proposed approach.