On Bipolar Anti Fuzzy h-ideals in Hemi-rings

In this work, we present notions of bipolar anti fuzzy h-ideals and bipolar anti fuzzy interior h-ideals in hemi-rings. Investigating some of their properties, we characterize hemi-rings by means of positive anti β-cut and negative anti α-cut. Meanwhile, some results of homomorphisms, anti images and anti pre-images are given to show the rationality of the definitions introduced in the present paper. Also, we define an equivalence relation on bipolar anti fuzzy h-ideals. In particular, we investigate translations, extensions and multiplications of bipolar anti fuzzy h-ideals. Finally, we present characterizations of h-hemi-regular and h-semi-simple hemi-rings in terms of bipolar anti fuzzy h-ideals.