FUZZY GRADE OF THE COMPLETE HYPERGROUPS

Document Type : Research Paper

Authors

1 Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014 Bucharest, Romania

2 Center for Systems and Information Technologies, University of Nova Gorica, Vipavska 13, SI-5000, Nova Gorica, Slovenia

Abstract

This paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. The classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. Finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number

Keywords


[1] R. Ameri and M. M. Zahedi,typergroup and join space induced by a fuzzy subset, PU.M.A.,8(1997).
[2] R. Ameri and O. R. Dehghan,Dimension of fuzzy hypervector spaces, Iranian Journal of Fuzzy Systems,8(5) (2011), 149-166.
[3] C. Angheluta and I. Cristea,On Atanassov's intuitionistic fuzzy grade of complete hyper-groups, J. Mult.-Valued Logic Soft Comput., 20 (2013), 55-74.
[4] P. Corsini,Prolegomena of Hypergroups Theory, Aviani Editore, Tricesimo, 1993.
[5] P. Corsini,Join spaces, power sets, fuzzy sets , Proc. Fifth International Congress on A.H.A.,1993, Iasi, Romania, Hadronic Press, (1994), 45-52.
 
[6] P. Corsini,A new connection between hypergroups and fuzzy sets, Southeast Asian Bull.Math.,27(2003), 221-229.
[7] P. Corsini and I. Cristea,Fuzzy grade of i.p.s. hypergroups of order 7, Iranian Journal of Fuzzy Systems,1(2) (2004), 15-32.
[8] P. Corsini and I. Cristea,Fuzzy sets and non complete 1-hypergroups, An. St. Univ. vidiusConstanta,13(1)(2005), 27-54.
[9] P. Corsini and V. Leoreanu,Join spaces associated with fuzzy sets, J. Combin. Inform. Syst.Sci.,20(1-4) 1995), 293-303.
[10] P. Corsini and V. Leoreanu,Applications of hyperstructure theory, Kluwer Academic Pub-lishers, Advances in Mathematics, 2003.
 
[11] P. Corsini and V. Leoreanu-Fotea,On the grade of a sequence of fuzzy sets and join spacesdetermined by a hypergraph, Southeast Asian Bull. Math., 34(2) (2010), 231-242.
[12] P. Corsini, V. Leoreanu-Fotea and A. Iranmanesh,On the sequence of hypergroups and mem-bership functions determined by a hypergraph, J. Mult.-Valued Logic Soft Comput., 14(6)(2008), 565-577.
[13] P. Corsini and R. Mahjoob,Multivalued functions, fuzzy subsets and join spaces, Ratio Math.,20(2010), 1-41.
[14] I. Cristea,Complete hypergroups, 1-Hypergroups and fuzzy sets, An. St. Univ. Ovidius Constanta,10(2) (2002), 25-38.
[15] I. Cristea,A property of the connection between fuzzy sets and hypergroupoids, Ital. J. Pure Appl. Math.,21 (2007), 73-82.
[16] I. Cristea,About the fuzzy grade of the direct product of two hypergroupoids, Iranian Journal of Fuzzy Systems,7(2) (2010), 95-108.
[17] I. Cristea and B. Davvaz,Atanassov's intuitionistic fuzzy grade of hypergroups, Information Sciences,180 (2010), 1506-1517.
[18] I. Cristea, M. Jafarpour and S. S. Mousavi,On fuzzy preordered structures and (fuzzy) hy-perstructures, Acta Math. Sin. (Engl. Ser.), 28(9) (2012), 1787-1798.
[19] B. Davvaz and M. Karimian,On the n-complete hypergroups, European J. Combin., 28(1)(2007), 86-93.[20] B. Davvaz and M. Karimian,On the n-complete hypergroups and K(H) hypergroups, ActaMath. Sin. (Engl. Ser.),24(11) (2008), 1901-1908.
[21] B. Davvaz, E. Hassani Sadrabadi and I. Cristea,Atanassov's intuitionistic fuzzy grade of the complete hypergroups of order less than or equal to6, submitted.
[22] B. Davvaz, E. Hassani Sadrabadi and I. Cristea,Atanassov's intuitionistic fuzzy grade of i.p.s. pergroups of order less than or equal to6, Iranian Journal of Fuzzy Systems,9(4)(2012), 71-97.
[23] B. Davvaz, E. Hassani Sadrabadi and I. Cristea,Atanassov's intuitionistic fuzzy grade of i.p.s.hypergroups of order7, J. Mult.-Valued Logic Soft Comput., accepted.
[24] H. Hedayati,Generalized fuzzy k-ideals of semirings with interval-valued membership func-tions, Bull.Malays.Math.Sci.Soc., 32(3) (2009), 409-424.
[25] J. Jantosciak,Homomorphism, equivalence and reductions in hypergroups, Riv. Mat. PuraAppl.,9(1991), 23-47.
[26] V. Leoreanu Fotea,t hypermodules, Comput. Math. Appl., 57(3) (2009), 466-47.
[27] V. Leoreanu Fotea and B. Davvaz,Fuzzy hyperrings, Fuzzy Sets and Systems, 160(16)(2009), 2366-2378.[28] F. Marty,Sur une generalization de la notion de groupe, Eight Congress Math. Scandenaves,Stockholm, (1934), 45-49. 
[29] R. Migliorato,On the complete hypergroups, Riv. Mat. Pura Appl., 14 (1994), 21-31.
[30] W. Prenowits and J. Jantosciak,Geometries and join spaces, J. Reind und Angew Math.,257(1972), 100-128.
[31] A. Rosenfeld,Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
[32] M. Shabir, Y. B. Yun and M. Bano,On prime fuzzy bi-ideals of semigroups, Iranian Journal of Fuzzy Systems,7(3) (2010), 115-128.
[33] M. Stefanescu and I. Cristeon the fuzzy grade of the hypergroup, Fuzzy Sets and System159((2008), 1097-1106.
[34] Y. Yin, J. Zhan and X. Huang,A new way to fuzzy h-ideals of hemirings, Iranian Journal of Fuzzy Systems,8(5) (2011), 81-101.
[35] L. A. Zadeh,Fuzzy sets, Information and Control, 8 (1965), 338-353.
[36] J. Zhan and B. Davvaz,Study of fuzzy algebraic hypersystems from a general viewpoint, Int.J. Fuzzy Syst.,12(1) (2010), 73-79.