(ᾶ, α)-crossing cubic QS-ideal of QS-algebra

Abstract

As an extension of bipolar-valued fuzzy sets, the notion of $(\widetilde{\alpha},\alpha)$- crossing cubic $QS$-ideals of a $QS$-algebra is introduced, and several related properties are investigated. Characterizations of $(\widetilde{\alpha},\alpha)$-crossing cubic $QS$-ideal in $QS$-algebras are established. The relations between $(\widetilde{\alpha},\alpha)$-crossing cubic subalgebras and $(\widetilde{\alpha},\alpha)$ crossing cubic $QS$-ideals of a $QS$-algebras are studied. Moreover, the homomorphic image (pre-image) of $(\widetilde{\alpha},\alpha)$-crossing cubic $QS$-ideal of a $QS$-algebra under a homomorprhism of $QS$-algebras is discussed.