A New View on Fuzzy Hypermodules
Acta Mathematica Sinica, English Series
Acta Mathematica Sinica,
Chinese Series
Adv Search »  
Acta Mathematica Sinica, English Series  2007, Vol. 23 Issue (8): 1345-1356    DOI: 10.1007/s10114-007-0951-7
articles Current Issue | Next Issue | Archive | Adv Search  |   
A New View on Fuzzy Hypermodules
Jian Ming ZHAN1, Bijan DAVVAZ2, K. P. SHUM3
1. Department of Mathematics, Hubei Institute for Nationalities, Enshi, 445000, P. R. China;
2. Department of Mathematics, Yazd University, Yazd, Iran;
3. Faculty of Science, The Chinese University of Hong Kong, Shatin, Hong Kong (SAR), P. R. China
 Download: PDF (191 KB)   HTML (0 KB)   Export: BibTeX | EndNote (RIS)      Supporting Info
Abstract We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in (Fuzzy Sets Syst., 117: 477- 484, 2001) and Bhakat and Das in (Fuzzy Sets Syst., 80: 359-368, 1996). The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued (α, β)-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued (α, β)-fuzzy sub-hypermodule is a generalization of the usual fuzzy sub-hypermodule. We shall study such fuzzy sub-hypermodules and consider the implication-based interval-valued fuzzy sub-hypermodules of a hypermodule.
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
Articles by authors
Jian Ming ZHAN
Key wordshypermodule   interval-valued (α, β)-fuzzy sub-hypermodule   interval-valued (∈,∈ ∨q)-fuzzy sub-hypermodule   fuzzy logic   implication operator     
Received: 2006-05-25;
Fund: The research of the first author is partially supported by the National Natural Science Foundation of China (60474022) and the Key Science Foundation of Education Commission of Hubei Province, China (D200729003; D200529001) and the research of the third author is partially supported by an RGC grant (CUHK) #2060297 (05/07)
Cite this article:   
Jian Ming ZHAN,Bijan DAVVAZ,K. P. SHUM. A New View on Fuzzy Hypermodules[J]. Acta Mathematica Sinica, English Series, 2007, 23(8): 1345-1356.
http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/s10114-007-0951-7      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y2007/V23/I8/1345
[1] Marty, F.: Sur une generalization de la notation de groupe, 8th Congress Math. Scandianaves, Stockholm, 45-49, 1934
[2] Corsini, P.: Prolegomena of hypergroup theory, Aviani, editor, 1993
[3] Davvaz, B.: A brief survey of the theory of Hv -structures, Proc. 8th Int. Congress AHA, Greece Spanids Press, 39-70, 2003
[4] Vougiouklis, T.: Hyperstructures and their representations, Hadronic Press Inc., Palm Harber, USA, 1994
[5] Corsini, P., Leoreanu, V.: Applications of hyperstructure theory, Advances in Mathematics, Kluwer Academic Publishers, Dordrecht, 2003
[6] Zadeh, L. A.: Fuzzy sets. Inform. Control, 8, 338-353 (1965)
[7] Rosenfeld, A.: Fuzzy groups. J. Math. Anal. Appl., 35, (1971) 512-517
[8] Bhattacharya, P.: Fuzzy subgroups: Some charcterizations(Ⅱ). Fuzzy Sets Syst., 38, 293-297 (1986)
[9] Biswas, R.: Rosenfeld's fuzzy subgroups with interval valued membership functions. Fuzzy Sets Syst., 63, 87-90 (1994)
[10] Davvaz, B.: (∈,∈ ∨q)-fuzzy subnear-rings and ideals. Soft Computing, 10, 206-211 (2006)
[11] Mordeson, J. N., Malik, M. S.: Fuzzy Commutative Algebra, World Publishng, Singapore, 1998
[12] Zadeh, L. A.: The concept of a lingistic variable and its application to approximate reason. Inform. Control, 18, 199-249 (1975)
[13] Bhakat, S. K. Das, P.: On the definition of a fuzzy subgroup. Fuzzy Sets Syst., 51, 235-241 (1992)
[14] Bhakat, S. K. Das, P.: (∈,∈ ∨q)-fuzzy subgroups. Fuzzy Sets Syst., 80, 359-368 (1996)
[15] Bhakat, S. K. Das, P.: Fuzzy subrings and ideals redefined. Fuzzy Sets Syst., 81, 383-393 (1996)
[16] Pu, P. M., Liu, Y. M.: Fuzzy topology I: Neighourhood struture of a fuzzy point and Moore-Smith convergence. J. Math. Anal. Appl., 76, 571-599 (1980)
[17] Yuan, X. H., Zhang, C., Ren, Y. H.: Generalized fuzzy groups and many valued applications. Fuzzy Sets Syst., 138, 205-211 (2003)
[18] Ameri, R.: On categories of hypergroups and hypermodules. J. Discrete Math. Sci. Cryptography, 6, 121-132 (2003)
[19] Ameri, R., Zahedi, M. M.: T-fuzzy hyperalgebraic systems, Lecture Notes in Computer Science, Spring-Verlag, Berlin, 2275, 2002
[20] Davvaz, B.: Remarks on weak hypermodules. Bull. Korean Math. Soc., 36, 599-608 (1999)
[21] Davvaz, B.: Fuzzy Hv -subgroups. Fuzzy Sets Syst., 101, 191-195 (1999)
[22] Davvaz, B.: Interval-valued fuzzy subhypergroup. Korean J. Comput. Appl. Math., 6, 197-202 (1999)
[23] Davvaz, B.: Fuzzy Hv -submodules. Fuzzy Sets Syst., 117, 477-484 (2001)
[24] Davvaz, B.: Approximations in Hv -modules. Taiwanese J. Math., 6, 499-506 (2002)
[25] Davvaz, B.: TH and SH -interval valued fuzzy Hv -groups. Indian J. Pure Appl. Math., 35, 61-69 (2004)
[26] Davvaz, B., Dudek, W. A., Jun, Y. B.: Intuitionistic fuzzy Hv -submodules. Inform. Sci., 176, 285-300 (2006)
[27] Davvaz, B., Koushky, A.: On hyperring of polynomials. Ital. J. Pure Appl. Math., 15, 205-214 (2004)
[28] Davvaz, B., Poursalavati, N. S.: On polygroup hyperrings and representation of polygroups. J. Korean Math. Soc., 36, 1021-1031 (1999)
[29] Krasner, M.: A class of hyperring and hyperfields. Int. J. Math. Math. Sci., 2, 307-312 (1983)
[30] Massouros, C. G.: Free and cyclic hypermodules. Ann. Mat. Pura Appl., IV. Ser., 150, 153-166 (1998)
[31] Mittas, J.: Hypergroupes canoniques. Mathematica Balkanica, 2, 165-179 (1979)
[32] Rota, R.: Hyperaffine planes over hyperrings. Discrete Math., 155, 215-223 (1996)
[33] Vougiouklis, T.: Convolutions on WASS hyperstructures. Discrete Math., 174, 347-355(1997)
[34] Vougiouklis, T.: On Hv -rings and Hv -representations. Discrete Math., 208/209, 615-620 (1999)
[35] Yang, J. B., Luo, M. K.: Priestley Spaces, Quasialgebraic lattices and Smyth powerdomains. Acta Mathematica Sinica, English Series, 22(3), 951-958 (2006)
[36] Zahedi, M. M., Ameri, R.: On the prime, primary and maximal sub-hypermodules. Ita. J. Pure Appl. Math., 5, 61-80 (1999)
[37] Zhan, J. M.: On properties of fuzzy hyperideals in hypernear-rings with t-norms. J. Appl. Math. Computing, 20, 255-277 (2006)
[38] Zhan, J. M., Davvaz, B., Shum, K. P.: Isomorphism theorems of hypermodules. Acta Mathematica Sinica, Chinese Series, 50, (2007) (in press)
[39] Zhan, J. M., Dudek, W. A.: Interval valued intuitionistic (S, T)-fuzzy Hv-submodules. Acta Mathematica Sinica, English Series, 22, 963-970 (2006)
[40] Zhan, J. M., Ma, X. L.: Approximations in hypernear-rings. Soochow J. Math., 32, 421-431 (2006)
[41] Zhan, J. M., Tan, Z. S.: Approximations in hyperquasigroups. J. Appl. Math. Computing, 21, 485-494 (2006)
[42] Bhakat, S. K.: (∈,∈ ∨q)-level subsets. Fuzzy Sets Syst., 103, 529-533 (1999)
[43] Bhakat, S. K.: (∈,∈ ∨q)-fuzzy normal, quasinormal and maximal subgroups. Fuzzy Sets Syst., 112, 299-312 (2000)
No Similar of article
  Copyright 2012 © Editorial Office of Acta Mathematica Sinica