Goal programming approach to derive intuitionistic multiplicative weights based on intuitionistic multiplicative preference relations

The intuitionistic multiplicative preference relation (IMPR) was introduced by Xia et al. [25] to deal with situations in which the decision makers (DMs) exhibit the characteristics of affirmation, negation and hesitation for the preference degrees over paired comparisons of alternatives. The IMPR can reflect the preference information of the DMs over alternatives more comprehensively than the multiplicative preference relation (MPR). In this paper, a new method for decision making is proposed to derive normalized intuitionistic multiplicative weights on the basis of the order consistent IMPR and the consistent IMPR. We first define the concepts of order consistent IMPR, consistent IMPR and normalized intuitionistic multiplicative weights, and then discuss some properties of the consistent IMPR. After that, we investigate a transformation formula to convert the normalized intuitionistic multiplicative priority weights into a consistent IMPR. An optimization model is constructed to generate the normalized intuitionistic multiplicative weights of IMPR, and the optimal deviation values obtained from the model enable us to improve the consistency of the given IMPR, such that the repaired IMPR is consistent. In the end, a numerical example is provided, and comparative analysis with Xu’s approach [26] is performed to demonstrate the validity and applicability of the proposed method.