Document Type : Research Paper


1 Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

2 Department of Mathematics, Imam Ali Military University, Tehran, Iran


In this note by considering a complete lattice L, we define the
notion of an L-Fuzzy hyperrelation on a given non-empty set X. Then we
define the concepts of (POM)L-Fuzzy graph, hypergraph and subhypergroup
and obtain some related results. In particular we construct the categories of
the above mentioned notions, and give a (full and faithful) functor form the
category of (POM)L-Fuzzy subhypergroups ((POM)L-Fuzzy graphs) into the
category of (POM)L-Fuzzy hypergraphs. Also we show that for each finite
objects in the category of (POM)L-Fuzzy graphs, the coproduct exists, and
under a suitable condition the product also exists.


[1] C. Berge, Graphs and Hypergraphs, North Holland, 1979.
[2] G. Birkhoff, Lattice Theory, American Math. Soc., Providence, Rhode Island, USA, Third
Edition, 1973.
[3] S. C. Cheng, J. N. Mordeson and Y. Yandong, Elements of L-algebras, Lecture Notes in
Fuzzy Mathematics and Computer Sciences, Creighton University, USA, 1994.
[4] J. A. Goguen, Categories of V-sets, Bull. Am. Math. Soc., (1975) 622-624.
[5] U. Hohle and E. P. Klement (Eds), Nonclassical Logics and their Applications to Fuzzy
Subsets, Kluwer, 1995
[6] S. R. Lopez-Permouth and D. S. Malik, On Catgegories of Fuzzy Modules, Information Sciences,
52(1990) 211-220.
[7] F. Marty, Sur une generalization de la notion de groupe, 8iem congress Math. Scandinaves,
Stockholm, (1934) 45-49.
[8] M. Mashinchi and M. Mukaidono, Generalized fuzzy quotient subgroups, Fuzzy Sets and
Systems, 74(1995) 245-257.
[9] A. Rosenfeld, Fuzzy graphs In: L.A. Zadeh, K.S. Fu and M. Shimura, Eds, Fuzzy Sets and
Their Applications, Academic press, New York, (1975) 77-95.
[10] H. Roy and Jr. Goetschel, Introduction to fuzzy hypergraphs and Hebbian Structures, Fuzzy
Sets and Systems, 76(1995) 113-130.
[11] M. M. Zahedi and M. R. Khorashadi-Zadeh, Some Categoric Connections Between Fuzzy
Hypergraphs, Subhypergroups, Graphs, Subgroups and Subsets, Journal of Discrete Mathematical
Sciences and Cryptography, Vol. 4, No. 1(2001) 17-32.