Exponential operational laws and new aggregation operators for intuitionistic multiplicative set in multiple-attribute group decision making process

Abstract

The intuitionistic multiplicative preference set is one of the replacements to the intuitionistic fuzzy preference set, where the preferences related to the object is asymmetrical distribution about 1. In it, Saaty’s 1–9 scale has been used to represent the uncertain and imprecise information. Meanwhile, an aggregation operator by using general operational laws for some fuzzy sets is an important task to aggregate the different numbers. Motivated by these primary characteristics, it is interesting to present the concept of exponential operational laws, which differs from the traditional laws by the way, in which bases are real numbers while exponents are the intuitionistic multiplicative numbers. In this paper, we develop a methodto solve the Multiple Attribute Group Decision Making (MAGDM) problem under the Intuitionistic Multiplicative Sets (IMS) environment. To do it, firstly, we define some new exponential operational laws and a score function for IMS and studied their properties. Secondly, based on this, we develop some averaging and geometric aggregation operators and characterize their various properties. Thirdly, a novel approach is promoted to solve MAGDM problems with IMS information. Finally, some numerical illustrations are given with a comparative study to verify the approach.