Affiliations: Department of Mathematics, Yazd University, 89195-741
Yazd, Iran | Dipartimento di Matematica e Informatica, Via delle
Scienze 206, 33100 Udine, Italy
Abstract: The hypernear-rings generalize the concept of near-rings, in the
sense that instead of the operation + the hyperoperation + is defined
on the set R, that is a R× R→ p* (R), where p*(R) is the set of all
the non-empty subsets of R. The study of hypernear-rings is extremely
challenging, effering curiously beautiful results to one who is willing to look
for structure where symmetry is not so abundant. In this paper, using the
notion of "belongingness (∈)" and "quasi-coincidence (q)" of fuzzy points
with fuzzy sets, the concept of (∈, ∈∨ q)-fuzzy sub-hypernear-ring
(hyperideal) is introduced. Characterization and some of the fundamental
properties of such fuzzy sub-hypernear-rings (hyperideals) are obtained.
(∈, ∈ ∨ q)-fuzzy cosets determined by (∈, ∈ ∨
q)-fuzzy sub-hypernear-rings are discussed. Finally, we give the definition of
a fuzzy sub-hypernear-ring (hyperideal) with thresholds which is a
generalization of an ordinary fuzzy sub-hypernear-ring (hyperideal) and an
(∈, ∈, ∨ q)-fuzzy sub-hypernear-ring (hyperideal).
