Iterative algorithms for improving consistency of intuitionistic preference relations

Abstract

Consistency of preference relations is an important research topic in decision making with preference information. The existing research about consistency mainly focuses on multiplicative preference relations, fuzzy preference relations and linguistic preference relations. Intuitionistic preference relations, each of their elements is composed of a membership degree, a non-membership degree and a hesitation degree, can better reflect the very imprecision of preferences of decision makers. There has been little research on consistency of intuitionistic preference relations up to now, and thus, it is necessary to pay attention to this issue. In this paper, we first propose an approach to constructing the consistent (or approximate consistent) intuitionistic preference relation from any intuitionistic preference relation. Then we develop a convergent iterative algorithm to improve the consistency of an intuitionistic preference relation. Moreover, we investigate the consistency of intuitionistic preference relations in group decision making situations, and show that if all individual intuitionistic preference relations are consistent, then the collective intuitionistic preference relation is also consistent. Moreover, we develop a convergent iterative algorithm to improve the consistency of all individual intuitionistic preference relations. The practicability and effectiveness of the developed algorithms is verified through two examples.

Keywords:

• group decision making
• intuitionistic preference relation
• consistency
• iterative algorithm

Acknowledgements

The authors would like to thank the anonymous reviewers for their insightful and constructive comments and suggestions that have led to an improved version of this article. The work was supported by the National Natural Science Foundation of China (No.71071161 and No.61273209), and the China Postdoctoral Science Foundation (No. 2012M520311).