Approximations in hyperrings. (English) Zbl 1236.16044

Davvaz, Bijan

J. Mult.-Val. Log. Soft Comput. 15, No. 5-6, 471-488 (2009).

Summary: This paper considers a relationship between rough sets and hyperrings. It is devoted to approximation operators within approximation spaces based on Krasner hyperrings. These approximation spaces consist of universes of hyperrings and various equivalence relations on these universes. It investigates approximation operators determined by equivalence relations defined by means of normal hyperideals of hyperrings. It considers also approximation spaces connected with strong homomorphisms between hyperrings where equivalence relations are defined by homomorphisms kernels, homomorphism images and counter images of hyperideals by which, in most cases, they are also hyperideals.

MSC:

16Y99	Generalizations
20N20	Hypergroups
20N25	Fuzzy groups

Keywords:

Krasner hyperrings; normal hyperideals; prime hyperideals; rough sets; lower approximations; upper approximations; approximation spaces; strong homomorphisms