Abstract
Let H is an H v -group and \(\mathcal{U}\) the set of all finite products of elements of H. The relation β* is the smallest equivalence relation on H such that the quotient H/ β* is a group. The relation β* is transitive closure of the relation β, where β is defined as follows: x β y if and only if \(\{ x,y \} \subseteq u\) for some \(u \in \mathcal{U}\). Based on the relation β, we define a neighborhood system for each element of H, and we presents a general framework for the study of approximations in H v -groups. In construction approach, a pair of lower and upper approximation operators is defined. The connections between H v -groups and approximation operators are examined.
Similar content being viewed by others
References
Biswas R, Nanda S (1994) Rough groups and rough subgroups. Bull Polish Acad Sci Math 42:251–254
Bonikowaski Z (1995) Algebraic structures of rough sets. In: Ziarko WP (eds) Rough sets, Fuzzy sets and Knowledge Discovery. Springer, Berlin Heidelberg New York, pp 242–247
Comer SD (1993) On connections between information systems, rough sets and algebraic logic. Algebraic Meth Logic Comput Sci 28:117–124
Corsini P, Leoreanu V (2003) Applications of hyperstructure theory. In: Advanced in mathematics, vol 5. Kluwer, Dodrecht
Corsini P (1993) Prolegomena of hypergroup theory, 2nd ed, Aviani Editor, pp 1–26
Corsini P (1999–2000) Hypergroups and rough sets. In: Honorary volume dedicated to Professor Emeritus Ioannis Mittas, Aristotle University of Thessaloniki
Davvaz B (1999) Lower and Upper Approximations in H v -groups. Ratio Math 13:71–86
Davvaz B (1998) Rough sets in a fundamental ring. Bull Iranian Math Soc 24(2):49–61
Davvaz B (2002) Approximations in H v -modules. Taiwanese J Math 6(4):499–505
Freni D (1991) Una nota sul cuore di un ipergruppo e sulla chiusura transitive β* di β. Rivista Mat Pura Appl 8:53–156
Iwinski T (1987) Algebraic approach to rough sets. Bull Polish Acad Sci Math 35:673–683
Koskas M (1970) Groupoids, demi-hypergroupes et hypergroupes. J Math Pure Appl 49(9):155–162
Kuroki N (1997) Rough ideals in semigroups. Inf Sci 100:139–163
Leoreanu V (1999–2000) Direct limits and products of join spaces associated with rough sets. Honorary volume dedicated to Professor Emeritus Ioannis Mittas, Aristotle University of Thessaloniki
Lin TY, Yao YY (1996) Mining soft rules using rough sets and neighborhoods. In: Proceedings of the symposium on modelling, analysis and simulation, computational engineering in systems applications (CESA’96). IMASCS Multiconference, Lille, France, July 9–12 pp 1095–1100
Pawlak Z (1982) Rough sets. Int J Inf Comp Sci 11:341–356
Pawlak Z (1991) Rough sets - theoretical aspects of reasoning about data. Kluwer, Dordrecht
Pomykala J, Pomykala JA (1988) The stone algebra of rough sets. Bull Polish Acad Sci Math 36:495–508
Vougiouklis T (1994) Hyperstructures and their representations. Hadronic, Florida
Vougiouklis T (1995) A new class of hyperstructures. J Combin inform Syst Sci 20:229–235
Vougiouklis T (1991) The fundamental relation in hyperrings. The general hyperfield. In: Proc of the 4th int. congress on algebraic hyperstructures and appl. (A.H.A 1990). World Sientific, Xanthi, Greece, pp 203–211
Wu W-Z, Zhang W-X (2002) Neighborhood operator systems and applications. Inform Sci 144:201–217
Yao YY (1998) Relational interpretation of neighborhood operators and rough set approximation operators. Inf Sci 111:239–259
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Davvaz, B. A New view of the approximations in H v -groups. Soft Comput 10, 1043–1046 (2006). https://doi.org/10.1007/s00500-005-0031-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-005-0031-9