Cubic Interval-Valued Intuitionistic Fuzzy Sets and Their Application in BCK/BCI-Algebras

Abstract

As a new extension of a cubic set, the notion of a cubic interval-valued intuitionistic fuzzy set is introduced, and its application in BCK/BCI-algebra is considered. The notions of alpha-internal, beta-internal, alpha-external and beta-external cubic IVIF set are introduced, and the P-union, P-intersection, R-union and R-intersection of alpha-internal and alpha-external cubic IVIF sets are discussed. The concepts of cubic IVIF subalgebra and ideal in BCK/BCI-algebra are introduced, and related properties are investigated. Relations between cubic IVIF subalgebra and cubic IVIF ideal are considered, and characterizations of cubic IVIF subalgebra and cubic IVIF ideal are discussed.