NEW TYPES OF FUZZY n-ARY SUBHYPERGROUPS OF AN n-ARY HYPERGROUP

Document Type : Research Paper

Authors

1 College of Mathematics and Information Sciences, East China Insti- tute of Technology, Fuzhou, Jiangxi 344000, China

2 Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province 445000, China

3 Department of Mathematics, Yazd University, Yazd, Iran

Abstract

In this paper, the new notions of ``belongingness ($in_{gamma}$)"
and ``quasi-coincidence ($q_delta$)"  of a fuzzy point with a fuzzy
set are  introduced. By means of this new idea, the  concept of
$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-ary
hypergroup is given, where $alpha,betain{in_{gamma},
 q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  and
it is shown that, in 16 kinds of $(alpha,beta)$-fuzzy $n$-ary
subhypergroups, the significant ones are the
$(in_{gamma},in_{gamma})$-fuzzy $n$-ary subhypergroups,
$(in_{gamma},ivq)$-fuzzy $n$-ary subhypergroups and the
$(in_{gamma}wedge q_{delta},in_{gamma})$-fuzzy $n$-ary
subhypergroups.

Keywords


bibitem{Bhakat1992} S. K. Bhakat and P. Das, {it On the definition of a fuzzy
subgroup}, Fuzzy Sets and Systems, {bf 51} (1992), 235-241.

bibitem{Bhakat1996} S. K. Bhakat and P. Das, {it $(in,invee q)$-fuzzy
subgroups}, Fuzzy Sets and Systems, {bf80} (1996), 359-368.
 
bibitem{Corsini1993} P. Corsini, {it Prolegomena of hypergroup theory}, Aviani editore, Italy, 1993.
 
bibitem{Corsini2003}  P. Corsini and V. Leoreanu, {it Applications of hyperstructure theory},
Advances in Mathematics (Dordrecht), Kluwer Academic Publishers,
Dordrecht, 2003.
bibitem{500} I. Cristea, {it About the fuzzy grade of the direct product of two hypergroupoids}, Iranian Journal of Fuzzy Systems,
 {bf7(2)} (2010), 95-108.
bibitem{300} B. Davvaz, {it Fuzzy hyperideals in ternary semihyperrings}, Iranian Journal of Fuzzy Systems, {bf 6}textbf{(4)} (2009), 21-36.
bibitem{10} B. Davvaz, {it Fuzzy $H_v$-groups}, Fuzzy Sets and
Systems, {bf 101} (1999), 191-195.
bibitem{cem} B. Davvaz, A. Dehghan Nezad and A. Benvidi, {it Chain reactions as experimental examples of ternary algebraic hyperstructures}, MATCH Communications in Mathematical and in Computer Chemistry, {bf 65}textbf{(2)} (2011), 491-499.
bibitem{143} B. Davvaz and  V. Leoreanu-Fotea, {it Intuitionistic fuzzy $n$-ary
hypergroups}, Journal of Multiple-Valued Logic and Soft Computing, {bf 16}textbf{(1-2)} (2010), 87-104.
bibitem{600} B. Davvaz and P. Corsini, {it On $(alpha,beta)$-fuzzy $Hsb v$-ideals of $Hsb v$-rings}, Iranian Journal of Fuzzy Systems, {bf  5}textbf{(2)} (2008),  35-47.
 
bibitem{123} B. Davvaz, P. Corsini and V.
Leoreanu-Fotea, {it Atanassov's intuitionistic $(S,T)$-fuzzy
$n$-ary subhypergroups and their properties}, Information Sciences, {bf 179} (2009), 654-666.

bibitem{136}  B. Davvaz, O. Kazanc{i} and  S. Yamak, {it Interval-valued
fuzzy $n$-ary subhypergroups  of $n$-ary hypergroups}, Neural
Comput. & Applic., {bf18} (2009), 903-911.
bibitem{140} B. Davvaz and  W. A. Dudek, {it Fuzzy
$n$-ary groups as a generalization of Rosenfeld's fuzzy groups},
Journal of Multiple-Valued Logic and Soft Computing, {bf 15}textbf{(5-6)} (2009), 451-469.
bibitem{DP} B. Davvaz and  P. Corsini, {it Fuzzy $n$-ary hypergroups}, J.
Intell. Fuzzy. Syst., {bf 18}textbf{(4)} (2007), 377-382.
 
bibitem{DP1} B. Davvaz and  P. Corsini, {it Generalized fuzzy sub-hyperquasigroups of hyperquasigroups}, Soft Computing,
 {bf10}textbf{(11)} (2006), 1109-1114.

bibitem{DP2}  B. Davvaz and  P. Corsini, {it Generalized fuzzy hyperideals of
hypernear-rings and many valued implications}, J. Intell. Fuzzy
Syst., {bf 17}textbf{(3)} (2006), 241-251.
bibitem{book} B. Davvaz and  V. Leoreanu-Fotea, {it Hyperring theory and
applications}, International Academic Press, USA, 2007.
bibitem{DV} B. Davvaz and  T. Vougiouklis, {it $n$-ary hypergroups}, Iran. J. Sci. Technol. Trans. A Sci., {bf 30} (2006), 165-174.
 
 
bibitem{D} W. D{"o}rnte, {it Untersuchungen Auber einen verallgemeinerten
Gruppenbegri}, Math. Z., {bf 2} (1928), 1-9.
bibitem{DSI} W. A. Dudek, M.
Shabir and  M. Irfan Ali, {it $(alpha,beta)$-fuzzy ideals of hemirings},
Comput. Math. Appl., {bf 58} (2009), 310-321.
bibitem{J} Y. J. Jun, {it Generalizations of $(in,invee q)$-fuzzy subalgebras in
BCK/BCI-algebras}, Comput. Math. Appl., {bf 58} (2009), 1383-1390.
bibitem{100} O. Kazanc{i}, S. Yamak and B.  Davvaz, {it On $n$-ary hypergroups and fuzzy $n$-ary homomorphism}, Iranian Journal of Fuzzy Systems, {bf8}textbf{(1)} (2011), 65-76.
bibitem{OBS} O. Kazanc{i}, B. Davvaz and  S. Yamak, {it Fuzzy $n$-ary polygroups related to fuzzy
points}, Comput. Math. Appl., {bf 58} (2009), 1466-1474.
bibitem{OBS1} O. Kazanc{i}, B. Davvaz and  S. Yamak, {it Fuzzy $n$-ary hypergroups related to fuzzy points},
Neural Comput. Applic., {bf 19} (2010), 649-655.
bibitem{400} V. Leoreanu Fotea, {it  Fuzzy rough $n$-ary subhypergroups}, Iranian Journal of Fuzzy Systems, {bf 5}textbf{(3)} (2008),  45-56.
bibitem{LD} V. Leoreanu-Fotea and B. Davvaz, {it $n$-hypergroups and binary relations},
European J. Combin., {bf 29}textbf{(5)} (2008), 1207-1218.
bibitem{LD1} V. Leoreanu-Fotea and B.
Davvaz, {it Join $n$-spaces and lattices}, J. Mult.-Valued Logic Soft Comput., {bf 15} (2009), 421-432.

bibitem{Marty1934} F. Marty, {it Sur une generalization de la notion de groupe}, In: 8th Congress Math. Scandianaves,
                      Stockholm, (1934), 45-49.

 bibitem{V} V. Murali, {it Fuzzy points of equivalent fuzzy subsets},
Information Sciences, {bf 158} (2004), 277-288.
bibitem{PM} P. M. Pu and  Y. M. Liu, {it Fuzzy topology I: neighbourhood structure of a
fuzzy point and Moore-Smith convergence}, J. Math. Anal. Appl.,
{bf76} (1980), 571-599.
bibitem{Rosenfeld} A. Rosenfeld, {it Fuzzy groups}, J. Math. Anal. Appl., {bf 35} (1971),
512-517.

bibitem{Vougiouklis1994} T. Vougiouklis, {it Hyperstructures and their representations},
 Hadronic Press Inc., Palm Harbor, USA,
1994.
bibitem{Yin} Y. Yin and  H. Li, {it Note on ``Generalized fuzzy interior ideals in
semigroups"}, Information Sciences, {bf  177} (2007), 5798-5800.
bibitem{Yin1}  Y. Yin, X. Huang, D. Xu and  F. Li, {it The characterization of $h$-semisimple hemirings},
 Int. J. Fuzzy Syst., {bf  11} (2009), 116-122.
bibitem{Yuan} X. Yuan, H. Li and  E. S. Lee, {it On the definition of the intuitionistic
fuzzy subgroups}, Comput. Math. Appl., {bf  59} (2010), 3117-3129.
bibitem{Zadeh1965} L. A. Zadeh, {it Fuzzy sets}, Information Sciences, {bf 8} (1965),
338-358.

bibitem{Zhan} J. Zhan, B. Davvaz and  K. P. Shum, {it A new view of fuzzy hypernear-
rings}, Information Sciences, {bf 178} (2008), 425-438.
bibitem{Zhan1} J. Zhan, B. Davvaz and  K. P. Shum,
    {it Generalized  fuzzy hyperideals of hyperrings},
    Comput. Math. Appl., {bf  56} (2008), 1732-1740.
bibitem{Zhan2}J. Zhan, B. Davvaz and  K. P. Shum, {it A new view of fuzzy hyperquasigroups}, J. Intell. Fuzzy Syst.,
{bf 20} (2009), 147-157.
bibitem{Zhan3} J. Zhan, B. Davvaz and  K. P. Shum, {it On probabilitic $n$-ary hypergroups},
Information Sciences, {bf  180} (2010), 1159-1166.
bibitem{200} J. Zhan, Y. B. Jun and B. Davvaz, {it On $(in,invee q)$-fuzzy ideals of BCI-algebras}, Iranian Journal of Fuzzy Systems, {bf 6}textbf{(1)} (2009),  81-94.