ATANASSOV'S INTUITIONISTIC FUZZY GRADE OF I.P.S. HYPERGROUPS OF ORDER LESS THAN OR EQUAL TO 6

Document Type: Research Paper

Authors

1 Department of Mathematics, Yazd University, Yazd, Iran

2 University of Udine, Via delle Scienze 206, 33100 Udine, Italy

Abstract

In this paper we determine the sequences of join spaces and Atanassov's
intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than
or equal to 6, focusing on the calculation of their lengths.

Keywords


[1] R. Ameri and H. Hedayati, Fuzzy isomorphism and quotient of fuzzy subpolygroups, Quasi-
groups and Related Systems, 13 (2005), 175-184.
[2] R. Ameri and H. Hedayati, On fuzzy closed, invertible and re
exive subsets of hypergroups,
Italian J. Pure Appl. Math., 22 (2007), 95-114.
[3] R. Ameri and M. M. Zahedi, Hypergroup and join space induced by a fuzzy subset, Pure
Math. App., 8 (1997), 155-168.
[4] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
[5] G. Chowdhury, Fuzzy transposition hypergroups, Iranian Journal of Fuzzy Systems, 6(3)
(2009), 37-52.
[6] P. Corsini, Prolegomena of hypergroups theory, Aviani Editore, 1993.
[7] P. Corsini, Sugli ipergruppi canonici niti con identita parziali scalari, Rend. Circolo Mat.
di Palermo, Serie II, Tomo, XXXVI (1987), 205-219.
[8] P. Corsini, (i:p:s:) Ipergruppi di ordine 6, Ann. Sc. de I'Univ. Blaise Pascal, Clermont-Ferrand
II, 24 (1987), 81-104.
[9] P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Asian Bull.
Math., 27 (2003), 221-229.
[10] P. Corsini, Join spaces, power sets, fuzzy sets, In: Proc. Fifth International Congress on
A.H.A. 1993, Iasi, Romania, Hadronic Press, (1994), 45-52.
[11] P. Corsini and I. Cristea, Fuzzy grade of i:p:s: hypergroups of order less or equal to 6, Pure
Math Appl., 14(4) (2003), 275-288.
[12] P. Corsini and I. Cristea, Fuzzy grade of i:p:s: hypergroups of order 7, Iranian Journal of
Fuzzy Systems, 1 (2004), 15-32.
[13] P. Corsini and V. Leoreanu, Join spaces associated with fuzzy sets, J. Combin. Inform. Syst.
Sci., 20 (1995), 293-303.
[14] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Advances in Mathematics,
Kluwer Academic Publishers, Dordercht, 2003.
[15] P. Corsini and V. Leoreanu-Fotea, On the grade of a sequence of fuzzy sets and join spaces
determined by a hypergraph, Southeast Asian Bull. Math., 34 (2010), 231-242.
[16] 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 (2008)
565-577.
[17] I. Cristea, About the fuzzy grade of the direct product of two hypergroupoids, Iranian Journal
of Fuzzy Systems, 7 (2010), 95-108.
[18] I. Cristea and B. Davvaz, Atanassov's intuitionistic fuzzy grade of hypergroups, Information
Sciences, 180 (2010), 1506-1517.

[19] B. Davvaz, Fuzzy hyperideals in ternary semihyperrings, Iranian Journal of Fuzzy Systems,
6(4) (2009), 21-36.
[20] B. Davvaz, Fuzzy Hv-groups, Fuzzy Sets and Systems, 101 (1999), 191-195.
[21] B. Davvaz and P. Corsini, On ( ; )-fuzzy Hv-ideals of Hv-rings, Iranian Journal of Fuzzy
Systems, 5(2) (2008), 35-47.
[22] B. Davvaz and V. Leoreanu-Fotea, Hyperring theory and applications, Hadronic Press, Inc,
115, Palm Harber, USA, 2007.
[23] B. Davvaz, P. Corsini and V. Leoreanu-Fotea, Atanassov's intuitionistic (S; T)-fuzzy n-ary
subhypergroups and their properties, Information Sciences, 179 (2009), 654-666.
[24] M. Horry and M. M. Zahedi, Hypergroups and general fuzzy automata, Iranian Journal of
Fuzzy Systems, 6(2) (2009), 61-74.
[25] O. Kazanc, S. Yamak and B. Davvaz, On n-ary hypergroups and fuzzy n-ary homomorphism,
Iranian Journal of Fuzzy Systems, 8(1) (2011), 1-17.
[26] J. Mittas, Hypergroupes canoniques, values et hypervalues. Hypergroupes fortement et su-
perieurement canoniques, Bull. Soc. Math. Greece, 23 (1982), 55-88.
[27] F. Marty, Sur une generalization de la notion de group, 8th Congress Math. Scandenaves,
Stockholm, (1934), 45-49.
[28] W. Prenowitz and J. Jantosciak, Geometries and join spaces, J. Reine und Angew Math.,
257 (1972), 100-128.
[29] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
[30] M. Stefanescu and I. Cristea, On the fuzzy grade of hypergroups, Fuzzy Sets and Systems,
159 (2008), 1097-1106.
[31] T. Vougiouklis, Hyperstructures and their Representations, Hadronic Press, Inc, 115, Palm
Harber, USA, 1994.
[32] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.