Methods for ranking intuitionistic multiplicative numbers by distance measures in decision making

• Two novel methods for ranking IMNs by distance measures are proposed.
• The normalized and weighted normalized Manhattan distances between IMSs are given.
• The distance and accuracy functions of IMNs are introduced into decision making.

Intuitionistic multiplicative number (IMN) is the basic component of intuitionistic multiplicative set (IMS) and intuitionistic multiplicative preference relation, which is suitable for describing the preference information in the unbalance distribution. In this paper, we propose two methods of ranking IMNs by distance measures for applications in decision making. To do it, we first develop the normalized and weighted normalized Manhattan distances between IMSs by analyzing the correlations of IMSs and intuitionistic fuzzy sets quantitatively. As a specific case, we also present the normalized Manhattan distance between IMNs, based on which, we introduce the distance and accuracy functions of IMNs and give a comparison law for them. After that, we propose a method for ranking IMNs in decision making. Furthermore, considering the characteristics of the distance measures, we extend the distance and accuracy functions into IMSs and give the extended distance and accuracy functions of IMSs. Then we apply them to the decision making, especially group decision making, and propose another ranking method for IMNs based on an extended comparison law. Our methods can not only overcome the shortages of the existing method that uses the score and accuracy functions for ranking IMNs which may occur contradiction with our intuition, but also reduce the amount and time of computation.