Multiattribute decision making based on the improved intuitionistic fuzzy Einstein weighted averaging operator of intuitionistic fuzzy values

Abstract

Abstract This paper proposes the improved intuitionistic fuzzy Einstein weighted averaging (IIFEWA) operator of intuitionistic fuzzy values (IFVs). The proposed IIFEWA operator can overcome the drawbacks of the intuitionistic fuzzy Einstein improved weighted averaging (IFEIWA) operator, the intuitionistic fuzzy Hamacher improved weighted averaging (IFHIWA) operator, the intuitionistic fuzzy Hamacher weighted averaging (IFHWA) operator, the intuitionistic fuzzy Einstein weighted averaging ( I F W A ω e ) operator, the intuitionistic fuzzy weighted averaging (IFWA) operator and the intuitionistic fuzzy Hamacher interactive ordered weighted averaging (IFHIOWA) operator of IFVs, where they have the drawbacks that (1) the membership grades and the non-membership grades of their obtained aggregating IFVs are indeterminated in some situations and (2) if there is only one IFV whose membership grade is equal to 1, then the membership grade of the aggregated IFV of n IFVs becomes 1; if there is only one IFV whose non-membership grade is equal to 0, then the non-membership grade of the aggregated IFV of n IFVs becomes 0. Based on the proposed IIFEWA operator, we propose a new multiattribute decision making (MADM) method. The proposed MADM method overcomes the drawbacks of the existing MADM methods, where they cannot distinguish the ranking orders of alternatives in some situations.