Distributed preference relations for multiple attribute decision analysis

Abstract

In this paper, we propose a new pairwise comparison approach called distributed preference relation (DPR) to simultaneously signify preferred, non-preferred, indifferent, and uncertain degrees of one alternative over another on a set of grades, which is more versatile for elicitation of preference information from a decision maker than multiplicative preference relation, fuzzy preference relation (FPR) and intuitionistic FPR. In a DPR matrix on a set of alternatives, each element is a distribution recording the preferred, non-preferred, indifferent, and uncertain degrees of one alternative over another using a set of grades. To facilitate the comparison of alternatives, we define a score matrix based on a DPR matrix using the given score values of the grades. Its additive consistency is constructed, analysed, and compared with the additive consistency of FPRs between alternatives. A method for comparing two interval numbers is then employed to create a possibility matrix from the score matrix, which can generate a ranking order of alternatives with possibility degrees. A problem of evaluating strategic emerging industries is investigated using the approach to demonstrate the application of a DPR matrix to modelling and analysing a multiple attribute decision analysis problem.

Keywords:

• decision analysis
• multiple attribute decision analysis
• distributed preference relation
• score matrix
• consistency of score matrix
• evaluation of strategic emerging industries

Acknowledgements

The research is supported by the State Key Programme of National Natural Science Foundation of China (No. 71131002), the National Key Basic Research Programme of China (No. 2013CB329603), the National Natural Science Foundation of China (Nos. 71331002, 71201043 and 71571060), and the Humanities and Social Science Foundation of Ministry of Education in China (No. 12YJC630046). The constructive comments provided by the anonymous referees and the editor have helped improve the quality of this paper.