L-fuzzy roughness of n-ary polygroups

Acta Mathematica Sinica, English Series

Volumn 27, Issue 1, 2011, Pages 97-118

  Yin, Yun Qiang ^a   Zhan, Jian Ming ^b   Corsini, P ^c  

^a EAST CHINA UNIVERSITY OF TECHNOLOGY   (China)

^b HUBEI UNIVERSITY FOR NATIONALITIES   (China)

^c Department of Biology and Agro Industrial Economy ^*  (Italy)

Author keywords

(normal) TL fuzzy n ary polygroups; (strong) homomorphism; n Ary polygroups; T upper L fuzzy rough approximation; symbol lower L fuzzy rough approximation

Indexed keywords

EID: 78650412699     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10114-011-9465-4     Document Type: Article

References (45)

1. Marty, F.: Sur une generalization de la notion de groupe. In: 8th Congress Math. Scandinaves, Stockholm, 1934, 45-49.
2. Corsini, P.: Prolegomena of Hypergroup Theory, Aviani Editore, Italy, 1993.
3. Vougiouklis, T.: Hyperstructures and Their Representations, Hadronic Press Inc., Palm Harbor, USA, 1994.
4. Corsini, P., Leoreanu, V.: Applications of Hyperstructure Theory, Advances in Mathematics (Dordrecht), Kluwer Academic Publishers, Dordrecht, 2003.
5. Zadeh, L. A.: Fuzzy sets. Inform. Control, 8, 338-358 (1965).
6. Rosenfeld, A.: Fuzzy groups. J. Math. Anal. Appl., 35, 512-517 (1971).
7. Mordeson, J. N., Malik, M. S.: Fuzzy Commutative Algebra, World Publishing, Singapore, 1998.
8. Corsini, P., Leoreanu, V.: Join spaces associated with fuzzy sets. J. Comb., Inf. Syst. Sci., 20, 293-303 (1995).
9. Corsini, P., Leoreanu, V.: Fuzzy sets and join spaces associated with rough sets. Rend. Circ. Mat. Palermo, 51, 527-536 (2002).
10. Cristea, I.: Hyperstructures and fuzzy sets endowed with two membership functions. Fuzzy Sets Syst., 160, 1114-1124 (2009).
11. Davvaz, B.: Fuzzy Hv-submodules. Fuzzy Sets Syst., 117, 477-484 (2001).
12. Kehagias, A., Serafimidis, K.: The L-fuzzy Nakano hypergroup. Inform. Sci., 169, 305-327 (2005).
13. Leoreanu, V.: Fuzzy hypermodules. Comput. Math. Appl., 57, 466-475 (2009).
14. Sen, M. K., Ameri, R., Chowdhury, G.: Fuzzy hypersemigroups. Soft Comput., 12, 891-900 (2008).
15. Stefanescu, M., Cristea, I.: On the fuzzy grade of hypergroups. Fuzzy Sets Syst., 159, 1097-1106 (2008).
16. Yin, Y., Zhan, J., Xu, D., Wang, J.: The L-fuzzy hypermodules. Comput. Math. Appl., 59, 953-963 (2010).
17. Zhan, J., Davvaz, B., Shum, K. P.: Isomorphism theorems of hypermodules. Acta Mathematica Sinica, Chinese Series, 50(4), 909-914 (2007).
18. Zhan, J., Davvaz, B., Shum, K. P.: A new view of fuzzy hypermodules. Acta Mathematica Sinica, English Series, 23(8), 1345-1356 (2007).
19. Zhan, J., Dudek, W. A.: Interval valued intuitionistic (S, T)-fuzzy Hv-submodules. Acta Mathematica Sinica, English Series, 22, 963-970 (2006).
20. Davvaz, B., Vougiouklis, T.: n-Ary hypergroups. Iran. J. Sci. Technol. Trans. A, 30, 165-174 (2006).
21. Leoreanu, V., Davvaz, B.: Roughness in n-ary hypergroups. Inform. Sci., 178, 4114-4124 (2008).
22. Leoreanu, V., Davvaz, B.: n-hypergroups and binary relations. European J. Combin., 29(5), 1207-1218 (2008).
23. Davvaz, B., Corsini, P.: Fuzzy n-ary hypergroups. J. Intell. Fuzzy Systems, 18(4), 377-382 (2007).
24. Davvaz, B., Corsini, P., Leoreanu, V.: Atanassov's intuitionistic (S, T)-fuzzy n-ary subhypergroups and their properties. Inform. Sci., 179, 654-666 (2009).
25. Ghadiri, M., Waphare, B. N.: n-ary polygroups. Iran J. Sci. Technol. Trans. A, in press.
26. Davvaz, B., Corsini, P., Leoreanu, V.: Fuzzy n-ary subpolygroups. Comput. Math. Appl., 57, 141-152 (2009).
27. Davvaz, B., Leoreanu, V.: Applications of interval valued fuzzy n-ary polygroups with respect to t-norms (t-conorms). Comput. Math. Appl., 57, 1413-1424 (2009).
28. Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci., 11, 341-356 (1982).
29. Biswas, R., Nanda, S.: Rough groups and rough subgroups. Bull. Polishe Acad. Sci. Math., 42, 251-254 (1994).
30. Davvaz, B.: Roughness in rings. Inform. Sci., 164, 147-163 (2004).
31. Davvaz, B., Mahdavipour, M.: Roughness in modules. Inform. Sci., 176, 3658-3674 (2006).
32. Jun, Y. B.: Roughness of ideals in BCK-algebras. Sci. Math. Japon., 57(1), 165-169 (2003).
33. Kuroki, N.: Rough ideals in semigroups. Inform. Sci., 100, 139-163 (1997).
34. Kuroki, N., Mordeson, J. N.: Structure of rough sets and rough groups. J. Fuzzy Math., 5(1), 183-191 (1997).
35. Kuroki, N., Wang, P. P.: The lower and upper approximations in a fuzzy group. Inform. Sci., 90, 203-220 (1996).
36. Leoreanu, V.: The lower and upper approximations in a hypergroup. Inform. Sci., 178, 3605-3615 (2008).
37. Davvaz, B.: Approximations in Hv-modules. Taiwanese J. Math., 6(4), 499-505 (2002).
38. Davvaz, B.: A new view of approximations in Hv-groups. Soft Comput., 10(11), 1043-1046 (2006).
39. Dubois, D., Prade, H.: Editorial. Fuzzy Sets Syst., 122, 1-3 (2001).
40. Jiang, J. S., Wu, C. X., Chen, D. G.: The product structure of fuzzy rough sets on a group and the rough T-fuzzy group. Inform. Sci., 175, 2-11 (2004).
41. Li, F., Yin, Y., Lu, L.: (θ{symbol}, T)-fuzzy rough approximation operators and the TL-fuzzy rough ideals on a ring. Inform. Sci., 177, 4711-4726 (2007).
42. Kazanci{dotless}, O., Davvaz, B.: On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings. Inform. Sci., 178, 1343-354 (2008).
43. Kazanci{dotless}, O., Yamak, S., Davvaz, B.: The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets. Inform. Sci., 178, 2349-2359 (2008).
44. Morsi, N. N., Yakout, M. M.: Axiomatics for fuzzy rough sets. Fuzzy Sets Syst., 100, 327-342 (1998).
45. Goguen, J. A.: L-fuzzy sets. J. Math. Anal. Appl., 18, 145-174 (1967).