Novel concepts of doubt bipolar fuzzy H-ideals of BCK/BCI-algebras

Abstract

In this paper, we introduce the notion of doubt bipolar fuzzy H-ideals of BCK/BCI-algebras and investigate some interesting properties. We characterize strong doubt positive t-level cut set, strong doubt negative s-level cut set, homomorphism and equivalence relation by considering doubt bipolar fuzzy H-ideals of BCK/BCI-algebras. Characterization theorem of characteristic doubt bipolar fuzzy H-ideals is also discussed. Particularly, the notion of Cartesian product of two doubt bipolar fuzzy H-ideals by using max-min operations is introduced, and some related properties are studied. Ordinary H-ideals are linked with doubt bipolar fuzzy H-ideals by means of doubt level cut set of Cartesian product of two bipolar-valued fuzzy sets.