Journal
JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY
Volume 73, Issue 11, Pages 2572-2590Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/01605682.2021.2004947
Keywords
Multi-criteria decision making; interval fuzzy reciprocal preference relation; additive consistency; normalized interval fuzzy utility; goal programming
Funding
- National Natural Science Foundation of China [72171209, 71671160]
- Natural Science Foundation of Zhejiang Province of China [Y22G014460, LY19G010004]
Ask authors/readers for more resources
This paper proposes a parametric approach to define additive consistency of IFRPRs, develops important properties of consistent IFRPRs, establishes computational formulas and a goal programming model to address the additive consistency issue.
The interval fuzzy reciprocal preference relation (IFRPR) is one of commonly used frameworks characterizing decision-makers' indeterminate preferences in multi-criteria decision making. Existing additive consistency frameworks and methods of generating additively consistent IFRPRs from interval fuzzy utility vectors as well as interval utility derivation methods often fail to obtain a satisfactory solution. To settle these challenging issues, this paper devises parametric transitivity equations to define additive consistency of IFRPRs. The parameter values are then determined and an equivalent definition is proposed for additively consistent IFRPRs. Important properties of consistent IFRPRs are developed and an additive consistency index is designed. A notion of equivalent interval fuzzy utility vectors is introduced and a novel framework is presented to normalize interval fuzzy utility vectors. Computational formulas are established for the generation between additively consistent IFRPRs and normalized interval fuzzy utility vectors. A goal programming model is built and converted into a linear program for deriving normalized interval fuzzy utility vectors from IFRPRs. Three illustrations including comparative analysis are provided to expose how the proposed models are utilized to identify whether an IFRPR is additively consistent and determine unknown preferences in an incomplete IFRPR as well as obtain normalized interval fuzzy utility vectors from IFRPRs.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available