(a, b)-Fuzzy subrings and (a, b)-fuzzy ideals of a ring

As an extension of the concept of a fuzzy subring and a fuzzy ideal, a new kind of a fuzzy subring and a fuzzy ideal calledan (a, b)-fuzzy subring and an (a, b)-fuzzy ideal of a ring is defined and their properties are studied. We also investigate the preimage of an (a, b)-fuzzy subring and an (a, b)-fuzzy ideal under a ring homomorphism. Also, (a, b)-level fuzzy subrings (fuzzy ideals) are studied. A necessary and sufficient condition for two (a, b)-level fuzzy subrings (fuzzy ideals) to be equal is proved. We show that the set of cosets of an (a, b)-fuzzy ideal forms a ring.

Keywords:

b)-fuzzy subring , b)-fuzzy ideal , (a , b)-fuzzy level subset