Group decision making based on incomplete intuitionistic multiplicative preference relations

The incomplete intuitionistic multiplicative preference relation (incomplete IMPR), whose elements are intuitionistic multiplicative numbers, is suitable for describing the asymmetric preference information and allows the decision makers to skip some dubious comparisons flexibly. In this paper, the concept of incomplete IMPR is introduced and the approaches for group decision making (GDM) with incomplete IMPRs is investigated. To do this, the consistency property of an IMPR is discussed, especially the acceptable consistency. Based on it, two approaches to complement all missing elements of incomplete IMPRs are presented, which involve two steps: estimating step and adjusting step. Firstly, a geometric mean method is given for estimating initial values of the missing elements. Then two different methods are developed for adjusting those initial values: one adopts the local optimization models, which is time-saving; the other utilizes an iterative method which can operate the whole optimization process conveniently and flexibly. After that, two procedures for GDM with incomplete IMPRs are proposed and illustrated by a problem of venue selection for communication drills. Compared with the previous work, the proposed methods have better performance on the computational complexity and the speed for processing a large amount of data. (C) 2014 Published by Elsevier Inc.