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Binary relations, interval structures and join spaces. (English) Zbl 1015.20052

An interval structure can be represented by a binary relation. A hyperoperation is defined on a set equipped with a binary relation. In this paper the hyperstructures based on the related interval structures are studied. Some necessary and sufficient conditions on these hyperstructures to be hypergroups, join spaces and \(H_v\)-groupoids are obtained.

MSC:

20N20 Hypergroups
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[1] J. Chvalina,Commutative hypergroups in the sense of Marty and ordered sets, Proceedings of the Summer School on General Algebra and Ordered Sets 1994, Olomouc (Czech Republic) 19-30. · Zbl 0827.20085
[2] P. Corsini,Rought Sets, Fuzzy Sets and Join Spaces, Honorary Volume dedicated to Prof. Emeritus Ioannis Mittas, 1999, Greece.
[3] P. Corsini,Prolegomena of Hypergroup Theory, Aviani Editore (1993). · Zbl 0785.20032
[4] P. Corsini,Hypergraphs and hypergroups, Algebra Universalis35 (1996). · Zbl 0858.05081
[5] Corsini, P., On the hypergroups associated with binary relations, Multi. Val. Logic vol., 5, 407-420 (2000) · Zbl 0999.20055
[6] P. Corsini and V. Leoreanu,Hypergroups and binary relations, Algebra Universalis43 (2000). · Zbl 1016.20056
[7] V. Leoreanu,Direct limils and products of join spaces associated with rough sets, Honorary Volume dedicated to Prof. Emeritus Ioannis Mittas, 1999, Greece.
[8] Leoreanu, V., Direct limits and products of join spaces associated with rough sets, II (2001), Iran: Kashan University, Iran
[9] Leoreanu, V.; Leoreanu, L., Hypergroups associated with hypergraphs, Italian Journal of Pure and Applied Math., 4, 119-126 (1998) · Zbl 0966.20033
[10] Z. Pawlak,Rough Sets, Kluwer Academic Publisher (1991). · Zbl 0758.68054
[11] W. Prenowitz, and J. Jantosciak,Geometries and Join Spaces, J. reine und angewandte Math.257 (1972). · Zbl 0264.50002
[12] Rosenberg, I. G., Hypergroups and join spaces determined by relations, Italian Journal of Pure and Applied Mathematics, 4, 93-101 (1998) · Zbl 0962.20055
[13] T. Vougiouklis,Hyperstructures and Their Representations, Monographs, Hadronic Press (1994). · Zbl 0828.20076
[14] S.K.M. Wong, and Nie Xiapin,Rough Sets: a special case of Interval Structures, Proceedings of the International Workshop on Rough Sets, Fuzzy Sets and Knowledge Discovery (RSKD ’93) Banf, Alberta Canada 1993/W.P. Zarko (ed.) Springer 1994. · Zbl 0819.04011
[15] S.K.M. Wong, L.S. Wang and Y.Y. Yao,Interval structures, a framework for representing uncertain information, Proc. Eighth Conf. Uncert. in Artiff. Intelligence.
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