Imprecise set theory applied to BCK/BCI-algebras

Abstract

Using the imprecise set by Baruah, subalgebras and (closed) ideals of BCK/BCI-algebras are addressed. Concepts of imprecise subalgebras and (closed) imprecise ideals in BCK/BCI-algebras are introduced, and several properties are investigated. Imprecise subalgebras are made by using the BCK-part of a BCI-algebra and the initial section of a BCK-algebra. The membership $t$-cut and reference $s$-cut are used to form the characterization of imprecise subalgebras and imprecise ideals. By presenting examples, it is found that the two concepts imprecise subalgebras (resp. imprecise ideals) and intuitionistic fuzzy subalgebras (resp. intuitionistic fuzzy ideals) are independent of each other. A relationship is established between imprecise subalgebras and imprecise ideals. We explore imprecise subalgebras and (closed) imprecise ideals in relation to homomorphism. The imprecise subalgebras and (closed) imprecise ideals are explored with respect to homomorphisms.