On equivalence of two approaches to group decision making with interval multiplicative preference relation based on COWG operator

Abstract

We propose two new approaches to rank all the alternatives in the group decision making (GDM) with interval multiplicative preference relation (IMPR) and point out their equivalence on solutions, based on the continuous ordered weighted geometric (COWG) operator. First we introduced the COWG operator and used it to aggregate the individual IMPR into crisp one, which can be obtained the priority vector by eigenvector method. Then we develop two new approaches to derive the group priority vector. One is the weighted geometric mean method (WGMM) of all individual priority vectors under the condition of α - acceptable consistency of multiplicative preference relation. The other is the relative entropy method (REM), in which an optimization model is constructed to minimize the difference between the group priority vector and all individual priority vectors based on the conception of relative entropy. We find that the REM has the same solution with WGMM, which provides the optimal theory basis of WGMM. Finally, a numerical example is illustrated to rank the given alternatives in the GDM with IMPR and show that the REM is feasible.