A Study of n-ary Subgroups with Respect to t-conorm
Abstract
In this paper, we introduce a notion of fuzzy n-ary subgroups withrespect to t-conorm(s-fuzzy n-ary subgroups) in an n-ary groups (G; f) and have studied their related properties. The main contribution of this paper are studying the properties of s-fuzzy n-ary subgroups over s-level n-ary subgroup of (G; f) , n-ary homomorphism and reta(G; f). Moreover some results of the S-product of s-fuzzy n-ary relations in an n-ary groups (G; f) are also obtained.
References
[1] M.Akram and J.Zhan. On sensiable fuzzy ideals of BCK-algebras with respect to t-conorm. Int. J. Math. Math. Sci. Volume 2006, Article ID 35930, Pages 112.
[2] B.Davvaz and W.A. Dudek. Fuzzy n-ary groups as a generalization of Rosenfeld's fuzzy groups. Journal of Multiple-Valued Logic and Soft Computing 15(5-6)(2009), 451-469.
[3] W. Dornte. Untersuchungen uber einen verallgemeinerten Gruppenbegriff. Math. Z., 29(1928), 1-19.
[4] W.A. Dudek. Remarks on n-groups. Demonstratio Math., 13 (1980), 165-181.
[5] W.A. Dudek. Autodistributive n-groups. Commentationes Math. Annales Soc. Math. Polonae Prace Matematyczne, 23(1983), 1-11.
[6] W.A. Dudek. On (i; j)-associative n-groupoids with the non-empty center. Ricerche Mat. (Napoli), 35(1986), 105-111.
[7] W.A. Dudek. Medial n-groups and skew elements, in: Proc. V Universal Algebra Symp. "Universal and Applied Algebra" (pp. 55-80). Turawa 1988, World Scientic, Singapore 1989.
[8] W.A. Dudek. On n-ary group with only one skew element. Sarajevo J. Math. (Formerly: Radovi mat., 6(2)(1990), 171-175.
[9] W.A. Dudek. Varieties of polyadic groups. Filomat, 9(3)(1995), 657-674.
[10] W.A. Dudek. Fuzzification of n-ary groupoids. Quasigroups and Related Systems, 7(2000), 45-66.
[11] W. A, Dudek. Idempotents in n-ary semigroups. Southeast Asian Bull. Math., 25(2001), 97-104.
[12] W.A. Dudek. On some old and new problems in n-ary groups. Quasigroups and Related Systems, 8(2001), 15-36.
[13] W.A. Dudek. Intuitionistic fuzzy approach to n-ary systems. Quasigroups and Related Systems, 15(2005), 213-228.
[14] W.A. Dudek. Remarks to Glazeks results on n-ary groups, Discussiones Mathematicae, General Algebra and Applications, 27(2)(2007), 199-233.
[15] W. A. Dudek and K. GAlazek. Around the Hossz'u-Gluskin Theorem for n-ary groups. Discrete Math., 308(21)(2008), 4861-4876.
[16] W.A. Dudek and J.Michalski. On a generalization of Hosszu theorem, Demonstratio Mathematica, 15(1982), 783-805.
[17] W.A. Dudek, K. Gazek and B. Gleichgewicht. A note on the axioms of n-groups, Colloquia Math. Soc. J. Bolyai 29 (Universal Algebra, Esztergom (Hungary), (1977), 195-202 (North-Holland, Amsterdam 1982).
[18] W.A. Dudek and I. Grozdzinska. On ideals in regular n-semigroups. Mat. Bilten Skopje, 3/4 (29/30) (1979-1980), 35-44.
[19] W.A. Dudek and J. Michalski. On a generalization of Hossz theorem. Demonstratio Math., 15(1982), 783-805.
[20] W.A. Dudek and J. Michalski. On retracts of polyadic groups. Demonstratio Math., 17(1984), 281-301.
[21] W.A. Dudek and J. Michalski. On a generalization of a theorem of Timm. Demonstratio Math., 18 (1985), 869-883.
[22] W.A. Dudek and Z. Stojakovic. On Rusakovs n-ary rs-groups. Czechoslovak Math. J., 51 (126) (2001), 275-283.
[23] J.W. Grzymala-Busse. Automorphisms of polyadic automata. J. Assoc. Comput. Mach., 16(1969), 208 - 219.
[24] B Jagadeesha, K.B Srinivas and K.S Prasad. Interval valued L-fuzzy ideals based on t-norms and t-conorms. J. Intell. Fuzzy Syst., 28(6) (2015), 2631 - 2641.
[25] R.Karner. Ternary algebraic structures and their applications in physics, Univ. P. and M.Curie, Paris 2000.
[26] R.Kasner. An extension of the group concepts. Bull. Amer. Math. Soc., 10(1904), 290-291.
[27] D. Nikshych and L. Vainerman. Finite quantum groupoids and their Applications. Univ. California, Los Angeles 2000.
[28] A.Rosenfeld. Fuzzy groups. J. Math. Anal. Appl., 35 (1971), 512 - 517.
[29] A.Zadeh. Fuzzy sets. Inf. Control, 8 (1965), 338 - 353.
[2] B.Davvaz and W.A. Dudek. Fuzzy n-ary groups as a generalization of Rosenfeld's fuzzy groups. Journal of Multiple-Valued Logic and Soft Computing 15(5-6)(2009), 451-469.
[3] W. Dornte. Untersuchungen uber einen verallgemeinerten Gruppenbegriff. Math. Z., 29(1928), 1-19.
[4] W.A. Dudek. Remarks on n-groups. Demonstratio Math., 13 (1980), 165-181.
[5] W.A. Dudek. Autodistributive n-groups. Commentationes Math. Annales Soc. Math. Polonae Prace Matematyczne, 23(1983), 1-11.
[6] W.A. Dudek. On (i; j)-associative n-groupoids with the non-empty center. Ricerche Mat. (Napoli), 35(1986), 105-111.
[7] W.A. Dudek. Medial n-groups and skew elements, in: Proc. V Universal Algebra Symp. "Universal and Applied Algebra" (pp. 55-80). Turawa 1988, World Scientic, Singapore 1989.
[8] W.A. Dudek. On n-ary group with only one skew element. Sarajevo J. Math. (Formerly: Radovi mat., 6(2)(1990), 171-175.
[9] W.A. Dudek. Varieties of polyadic groups. Filomat, 9(3)(1995), 657-674.
[10] W.A. Dudek. Fuzzification of n-ary groupoids. Quasigroups and Related Systems, 7(2000), 45-66.
[11] W. A, Dudek. Idempotents in n-ary semigroups. Southeast Asian Bull. Math., 25(2001), 97-104.
[12] W.A. Dudek. On some old and new problems in n-ary groups. Quasigroups and Related Systems, 8(2001), 15-36.
[13] W.A. Dudek. Intuitionistic fuzzy approach to n-ary systems. Quasigroups and Related Systems, 15(2005), 213-228.
[14] W.A. Dudek. Remarks to Glazeks results on n-ary groups, Discussiones Mathematicae, General Algebra and Applications, 27(2)(2007), 199-233.
[15] W. A. Dudek and K. GAlazek. Around the Hossz'u-Gluskin Theorem for n-ary groups. Discrete Math., 308(21)(2008), 4861-4876.
[16] W.A. Dudek and J.Michalski. On a generalization of Hosszu theorem, Demonstratio Mathematica, 15(1982), 783-805.
[17] W.A. Dudek, K. Gazek and B. Gleichgewicht. A note on the axioms of n-groups, Colloquia Math. Soc. J. Bolyai 29 (Universal Algebra, Esztergom (Hungary), (1977), 195-202 (North-Holland, Amsterdam 1982).
[18] W.A. Dudek and I. Grozdzinska. On ideals in regular n-semigroups. Mat. Bilten Skopje, 3/4 (29/30) (1979-1980), 35-44.
[19] W.A. Dudek and J. Michalski. On a generalization of Hossz theorem. Demonstratio Math., 15(1982), 783-805.
[20] W.A. Dudek and J. Michalski. On retracts of polyadic groups. Demonstratio Math., 17(1984), 281-301.
[21] W.A. Dudek and J. Michalski. On a generalization of a theorem of Timm. Demonstratio Math., 18 (1985), 869-883.
[22] W.A. Dudek and Z. Stojakovic. On Rusakovs n-ary rs-groups. Czechoslovak Math. J., 51 (126) (2001), 275-283.
[23] J.W. Grzymala-Busse. Automorphisms of polyadic automata. J. Assoc. Comput. Mach., 16(1969), 208 - 219.
[24] B Jagadeesha, K.B Srinivas and K.S Prasad. Interval valued L-fuzzy ideals based on t-norms and t-conorms. J. Intell. Fuzzy Syst., 28(6) (2015), 2631 - 2641.
[25] R.Karner. Ternary algebraic structures and their applications in physics, Univ. P. and M.Curie, Paris 2000.
[26] R.Kasner. An extension of the group concepts. Bull. Amer. Math. Soc., 10(1904), 290-291.
[27] D. Nikshych and L. Vainerman. Finite quantum groupoids and their Applications. Univ. California, Los Angeles 2000.
[28] A.Rosenfeld. Fuzzy groups. J. Math. Anal. Appl., 35 (1971), 512 - 517.
[29] A.Zadeh. Fuzzy sets. Inf. Control, 8 (1965), 338 - 353.
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2017-01-01
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