Some Hesitant Multiplicative Aggregation Operators and Their Application in Group Decision Making with Hesitant Multiplicative Preference Relations

The hesitant multiplicative preference relation (HMPR) is a newly developed preference structure that uses an unsymmetrical scale (Saaty's 1-9 scale) to express the decision makers' (DMs') preferences instead of the symmetrical scale (0.1-0.9 scale) in a hesitant fuzzy preference relation. This new preference relation is suitable for describing the situation in which the DMs are hesitant about several possible multiplicative values for the preference degrees over paired comparisons of alternatives. In this paper, we first define some new operational laws for hesitant multiplicative elements. Then, based on these operational laws, we develop two types of hesitant multiplicative aggregation operators for aggregating the hesitant multiplicative preference information, which we call the independent hesitant multiplicative aggregation operators and the correlative hesitant multiplicative aggregation operators. The independent hesitant multiplicative aggregation operators are based on the assumption that the aggregated arguments are independent, and the operators can be used to address situations where the preferences of the DMs are independent. The correlative hesitant multiplicative aggregation operators are developed to reflect the correlations of the aggregated arguments based on the Choquet integral and the power average, and the operators can be used to address the situation where the preferences of DMs are dependent on each other. We further give some desirable properties and special cases of the developed operators and apply these operators to develop several approaches to group decision making based on HMPRs. Finally, several practical examples are provided to illustrate the developed operators and approaches.