Some ILOWA operators and their applications to group decision making with additive linguistic preference relations

The aim of this paper is to present some cases of the induced linguistic ordered weighted averaging (ILOWA) operator which are very suitable to deal with group decision making (GDM) problems with additive linguistic preference relations. We propose the relative consensus degree ILOWA (RCD-ILOWA) operator which uses the relative consensus degree (RCD) variable as the order inducing variable, and the compatibility index ILOWA (CI-ILOWA) operator which uses the compatibility index (CI) variable as the order inducing variable. We also investigate some desired properties of RCD-lLOWA operator and the CI-ILOWA operator which provide theoretic basis for the application of the additive linguistic preference relations in GDM. A general formulation and a nonlinear model to determine experts' weights and two approaches based on the RCD-ILOWA operator and the CI-ILOWA operator for GDM involving additive linguistic preference relations are developed respectively. A numerical example for comprehensive evaluation is given to illustrate the applications of the new operators.