An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations

In this paper, we define the concept of uncertain multiplicative linguistic preference relation, and introduce some operational laws of uncertain multiplicative linguistic variables. We propose some new aggregation operators including the uncertain linguistic geometric mean (ULGM) operator, uncertain linguistic weighted geometric mean (ULWGM) operator, uncertain linguistic ordered weighted geometric (ULOWG) operator, and induced uncertain linguistic ordered weighted geometric (IULOWG) operator. The IULOWG operator is a more general type of aggregation operator, which is based on the ULGM and ULOWG operators. Moreover, based on the ULOWG and IULOWG operators and the formula for the comparison between two uncertain multiplicative linguistic variables, we develop an approach to group decision making with uncertain multiplicative linguistic preference relations, and, finally, an application of the approach to group decision-making problem with uncertain multiplicative linguistic preference relations is pointed out.