Define a ratio-based similarity index for a pair of interval-valued cross ratios.Develop new similarity measures for interval reciprocal preference relations (IRPRs).Devise an induced interval-valued cross ratio ordered weighted geometric operator.Develop a consensus model to solve group decision making problems with IRPRs. Similarity analysis and preference information aggregation are two important issues for consensus building in group decision making with preference relations. Pairwise ratings in an interval reciprocal preference relation (IRPR) are usually regarded as interval-valued And-like representable cross ratios (i.e., interval-valued cross ratios for short) from the multiplicative perspective. In this paper, a ratio-based formula is introduced to measure similarity between a pair of interval-valued cross ratios, and its desirable properties are provided. We put forward ratio-based similarity measurements for IRPRs. An induced interval-valued cross ratio ordered weighted geometric (IIVCROWG) operator with interval additive reciprocity is developed to aggregate interval-valued cross ratio information, and some properties of the IIVCROWG operator are presented. The paper devises an importance degree induced IRPR ordered weighted geometric operator to fuse individual IRPRs into a group IRPR, and discusses the derivation of its associated weights. By employing ratio-based similarity measurements and IIVCROWG-based aggregation operators, a soft consensus model including a generation mechanism of feedback recommendation rules is further proposed to solve group decision making problems with IRPRs. Three numerical examples are examined to illustrate the applicability and effectiveness of the developed models.
['Zhou-Jing Wang', 'Jian Lin']
Ratio-based similarity analysis and consensus building for group decision making with interval reciprocal preference relations