Group decision making based on a novel aggregation operator under linguistic interval-valued Atanassov intuitionistic fuzzy information

Abstract

Efficient aggregation methods and order relationships are crucial in solving group decision making (GDM) problems with linguistic interval-valued Atanassov intuitionistic fuzzy information. Based on a novel score function, this paper first presents a new method to rank linguistic interval-valued Atanassov intuitionistic fuzzy numbers (LIVAIFNs). The proposed ranking method overcomes the limitations of existing methods. Then, a new linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (NLIVAIFWA) aggregation operator (AO) is proposed. The NLIVAIFWA AO of LIVAIFNs presented in this paper can overcome the drawbacks of the linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (LIVAIFWA) AO, the linguistic interval-valued Atanassov intuitionistic fuzzy weighted geometric (LIVAIFWG) AO, the linguistic interval-valued Atanassov intuitionistic fuzzy Hamacher weighted averaging (LIVAIFHWA) AO and the improved linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (ILIVAIFWA) AO of LIVAIFNs. Furthermore, some primary properties of the NLIVAIFWA AO are discussed, and a novel GDM method based on the provided NLIVAIFWA AO of LIVAIFNs is constructed. Finally, the effectiveness of the proposed GDM method is demonstrated through numerical examples, highlighting its superiority, and advantages.