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CATEGORY OF (POM)L-FUZZY GRAPHS AND HYPERGRAPHS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 6، دوره 2، شماره 1، تابستان 2005، صفحه 49-63 اصل مقاله (219.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2005.475 | ||
| نویسندگان | ||
M. M. Zahedi1؛ M. R. Khorashadi-Zadeh  2
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| 1Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| 2Department of Mathematics, Imam Ali Military University, Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Fuzzy graph؛ Fuzzy hypergraph؛ Fuzzy subhypergroup؛ Partially ordered monoid | ||
| مراجع | ||
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[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. | ||
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