Multi-criteria decision making process using complex cubic interval valued intuitionistic fuzzy set

Abstract

This paper presents a new notion of complex cubic interval valued intuitionistic fuzzy set (CCIVIFS) which is an extension from the innovative concept of a cubic interval valued intuitionistic fuzzy set (CIVFS). The novelty of CCIVIFS is to achieve more range of values with the combination of interval-valued membership, interval-valued non-membership and fuzzy membership. We define some basic operations namely complement, union, intersection and notions of α-internal, β-internal, α-external and β-external complex cubic interval valued intuitionistic fuzzy set are introduced. Also P-union, P-intersection, R-union and R-intersection of α -internal and β-external complex cubic IVIF sets are discussed. Furthermore, a group decision-making method is discussed to illustrate the applicability and validity of the proposed approach.