Intuitionistic Fuzzy Sets and Join Spaces Associated with Ary Membership Functions
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Authors
Mohsen Asghari-Larimi
- Department of Mathematics, GolestanUniversity, Gorgan, Iran.
Piergiulio Corsini
- Dipartimento di Matematica e Informatica, ViadelleScienze 206, 33100 Udine, Italy.
Esmail Ranjbar-yanehsari
- Department of Mathematics,Faculty of Sciences, Gorgan Branch,Islamic Azad University,Gorgan, Iran.
Abstract
In this paper, we associate finite hyperstructures with fuzzy sets endowed with n-ary
membership functions and analyze the properties of this new hyperstructures. We prove that the
new hyperstructure is a commutative hypergroup, but generally it is not a join space. We give some
conditions such that the hypergroup has this property. In particular, we investigate some natural
equivalence relations on the set of all intuitionistic fuzzy sub-hypergroups of a hypergroup.
Share and Cite
ISRP Style
Mohsen Asghari-Larimi, Piergiulio Corsini, Esmail Ranjbar-yanehsari, Intuitionistic Fuzzy Sets and Join Spaces Associated with Ary Membership Functions , Journal of Mathematics and Computer Science, 5 (2012), no. 2, 115-125
AMA Style
Asghari-Larimi Mohsen, Corsini Piergiulio, Ranjbar-yanehsari Esmail, Intuitionistic Fuzzy Sets and Join Spaces Associated with Ary Membership Functions . J Math Comput SCI-JM. (2012); 5(2):115-125
Chicago/Turabian Style
Asghari-Larimi, Mohsen, Corsini, Piergiulio, Ranjbar-yanehsari, Esmail. "Intuitionistic Fuzzy Sets and Join Spaces Associated with Ary Membership Functions ." Journal of Mathematics and Computer Science, 5, no. 2 (2012): 115-125
Keywords
- Hyperstructure
- Join space
- Fuzzy subhypergroup
- Intuitionistic fuzzy subhypergroups.
MSC
References
-
[1]
M. Asghari-Larimi , Some properties of intuitionistic nil radicals of intuitionistic fuzzy ideals, International Mathematical Forum, 5 (2010), 1551 - 1558.
-
[2]
M. Asghari-Larimi, B. Davvaz, Hyperstructures associated to arithmetic functions, Ars Combitoria, 97 (2010), 51-63.
-
[3]
M. Asghari-Larimi, V. Leoreanu-Fotea, A connection between hypergroupoids and L-Fuzzy Sets of Type 2, Italian J. of Pure and Appl. Math., 26 (2009), 207-216.
-
[4]
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst, 20 (1986), 87-96.
-
[5]
K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets Syst., 61 (1994), 137-142.
-
[6]
R. Biswas, Intuitionistic fuzzy subgroups, Math. Forum, 10 (1989), 37-46.
-
[7]
P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, (1993)
-
[8]
P. Corsini, Join Spaces, Power Sets, Fuzzy Sets, Proceedings of the 5th A.H.A. Congress, 1993, Iasi (Romania) Hadronic Press, (1994), 45-52.
-
[9]
P. Corsini, Hyperstructures associated with ordered sets, Bull. Greek Math. Soc., 48 (2003), 7-18.
-
[10]
P. Corsini, Hyperstructures associated with fuzzy sets endowed with two membership functions, j. of combin. infor. system sci., 1-4 (2006), 247-254.
-
[11]
P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Asian Bull. Math., 27 (2003), 221-229.
-
[12]
P. Corsini, V. Leoreanu-Fotea, Applications of Hyperstructure Theory, Kluwer Academic Publications, Dordrecht, Advances in Mathematics (2003)
-
[13]
I. Cristea, Hyperstructures and fuzzy sets endowed with two membership functions, Fuzzy sets and Systems, 160 (2009), 1114-1124.
-
[14]
W. A. Dudek, B. Davvaz, Y. B. Jun, On intuitionistic fuzzy sub-quasihypergroups of quasihypergroups, Information Sciences, 170 (2005), 251-262.
-
[15]
F. Marty, Sur une generalisation de la notion de groupe, 8th course Math. Scandinaves Stockholm, (1934), 45-49.
-
[16]
W. Prenowitz, Projectives Geometries as Multigroups , Amer. J. Math., 65 (1943), 235-256.
-
[17]
W. Prenowitz, J. Jantosciak, Join geometries , Springer-Verlag, UTM (1979)
-
[18]
T. Vougiouklis , Hyperstructures and their representations, Hadronic Press, Inc, 115, PalmHarber, USA (1994)
-
[19]
L. A. Zadeh, Fuzzy Sets, Inform and Control, 8 (1965), 338-353.