Neutrosophic Hyperideals of Г-Semihyperrings
Abstract
The purpose of this paper is to introduced neutrosophic hyperide-als of a Г-semihyperring and consider some operations on them to investigate some of its basic properties.
References
[1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87 - 96.
[2] P. Corsini, Prolegomena of Hypergroup Theory", Second edition, Aviani Editore, Italy, 1993.
[3] P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory" Adv. Math., Kluwer Academic Publishers, Dordrecht, 2003.
[4] M. Krasner, A class of hyperrings and hyperfields, Internat. J. Math. Math. Sci. 6(2)(1983), 307-312.
[5] B. Davvaz, Isomorphism theorems of hyperrings, Indian J. Pure Appl. Math. 35(3)(2004), 321-331.
[6] B. Davvaz, Rings derived from semihyperrings, Algebras Groups Geom. 20 (2003), 245-252.
[7] B. Davvaz, Some results on congruences in semihypergroups, Bull. Malays. Math. Sci. Soc. 23(2) (2000), 53-58.
[8] B. Davvaz, Polygroup Theory and Related Systems", World scientific publishing Co. Pte. Ltd., Hackensack, NJ, 2013.
[9] B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications", International Academic Press, Palm Harbor, USA, 2007.
[10] B. Davvaz and S. Omidi, Basic notions and ptoperties of ordered semihyperrings, Categories and General Algebraic Structure with Applications, 4(1) (2016), In press.
[11] S.O. Dehkordi and B. Davvaz, Г-semihyperrings: Approximations and rough ideals, Bulletin of the Malaysian Mathematical Sciences Society (2), (32)(3) (2009) 375- 390.
[12] F. Marty, Sur une generalisation de la notion de groupe, 8iem Congress Math. Scandinaves, Stockholm (1934), 45-49.
[13] J. Mittas, Hypergroupes canoniques, Math. Balkanica 2(1972), 165-179.
[14] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35(1971), 512-517.
[15] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math. 24(2005) 287 - 297.
[16] S. Spartalis, A class of hyperrings, Rivista Mat. Pura Appl. 4(1989), 56-64.
[17] D. Stratigopoulos, Hyperanneaux, hypercorps, hypermodules, hyperspaces vectoriels et leurs proprietes elementaires, C. R. Acad. Sci., Paris A (269)(1969), 489-492.
[18] H.S. Vandiver, Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer. Math. Soc. 40(1934), 914-920.
[19] T. Vougiouklis, On some representations of hypergroups, Ann. Sci. Univ. Clermont Ferrand II Math. 26(1990), 21-29.
[20] T. Vougiouklis, Hyperstructures and Their Representations", Hadronic Press Inc., Florida, 1994.
[21] L. A. Zadeh, Fuzzy sets, Information and Control 8(1965) 338 - 353.
[2] P. Corsini, Prolegomena of Hypergroup Theory", Second edition, Aviani Editore, Italy, 1993.
[3] P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory" Adv. Math., Kluwer Academic Publishers, Dordrecht, 2003.
[4] M. Krasner, A class of hyperrings and hyperfields, Internat. J. Math. Math. Sci. 6(2)(1983), 307-312.
[5] B. Davvaz, Isomorphism theorems of hyperrings, Indian J. Pure Appl. Math. 35(3)(2004), 321-331.
[6] B. Davvaz, Rings derived from semihyperrings, Algebras Groups Geom. 20 (2003), 245-252.
[7] B. Davvaz, Some results on congruences in semihypergroups, Bull. Malays. Math. Sci. Soc. 23(2) (2000), 53-58.
[8] B. Davvaz, Polygroup Theory and Related Systems", World scientific publishing Co. Pte. Ltd., Hackensack, NJ, 2013.
[9] B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications", International Academic Press, Palm Harbor, USA, 2007.
[10] B. Davvaz and S. Omidi, Basic notions and ptoperties of ordered semihyperrings, Categories and General Algebraic Structure with Applications, 4(1) (2016), In press.
[11] S.O. Dehkordi and B. Davvaz, Г-semihyperrings: Approximations and rough ideals, Bulletin of the Malaysian Mathematical Sciences Society (2), (32)(3) (2009) 375- 390.
[12] F. Marty, Sur une generalisation de la notion de groupe, 8iem Congress Math. Scandinaves, Stockholm (1934), 45-49.
[13] J. Mittas, Hypergroupes canoniques, Math. Balkanica 2(1972), 165-179.
[14] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35(1971), 512-517.
[15] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math. 24(2005) 287 - 297.
[16] S. Spartalis, A class of hyperrings, Rivista Mat. Pura Appl. 4(1989), 56-64.
[17] D. Stratigopoulos, Hyperanneaux, hypercorps, hypermodules, hyperspaces vectoriels et leurs proprietes elementaires, C. R. Acad. Sci., Paris A (269)(1969), 489-492.
[18] H.S. Vandiver, Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer. Math. Soc. 40(1934), 914-920.
[19] T. Vougiouklis, On some representations of hypergroups, Ann. Sci. Univ. Clermont Ferrand II Math. 26(1990), 21-29.
[20] T. Vougiouklis, Hyperstructures and Their Representations", Hadronic Press Inc., Florida, 1994.
[21] L. A. Zadeh, Fuzzy sets, Information and Control 8(1965) 338 - 353.
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2017-01-01
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