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Abstrakty
In this paper, we use the fuzzy prime spectrum to define the reticulation (L(A),λ) of a residuated lattice A. We obtain some related results. In particular, we show that the lattices of fuzzy filters of a residuated lattice A and L(A) are isomorphic and the fuzzy prime spectrum of A and L(A) are homomorphic topological space.
Czasopismo
Rocznik
Tom
Strony
23--32
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
- Department of Mathematics, Bam Higher Education Complexes, Kerman, Iran, sh.gorbani@uk.ac.ir
Bibliografia
- [1] T.S. Blyth, M. F. Janowitz, Residuation Theory, Pergamon Press, 1972.
- [2] K. Blount, C. Tsinakies, The structure of residuated lattices, Internat. J. Algebra Comput., 13(2003), No. 4, 437-461.
- [3] Sh. Ghorbani, A. Hasankhani, Fuzzy Convex Subalgebras of Commutative Residuated Lattices, Iran. J. Fuzzy Syst., Vol. 7, No. 2(2010), 41-54.
- [4] Sh. Ghorbani, A. Hasankhani, Uniform topology on a residuated lattice induced by fuzzy filters, Int. Rev. Fuzzy Math. 4(2009), 45-62.
- [5] Sh. Ghorbani, Fuzzy spectrum of residuated lattices, Journal of Advanced Research in Pure Mathematics 3(2011), 56 - 68.
- [6] T. Kowalski, H. Ono, Residuated lattices: An algebraic glimpse at logics without contraction, monograph, March, 2001.
- [7] L. Leustean, The prime and maximal spectra and the reticulation of BL-algebras, Cent. Eur. J. Math. , No. 3 (2003), 382-397.
- [8] C. Muresan, The reticulation of a residuated lattice, Bull. Math. Soc. Sci. Math. Roumania, Tome 51(99) No. 1, (2008), 47-65.
- [9] D. Piciu, Algebras of fuzzy logic, Editura Universitaria, Craiova, 2007.
- [10] H. Simmons, Reticulated rings, J. Algebra 66(1980), 169-192.
- [11] E. Turunen, Mathematics behind fuzzy logic, Advances in Soft Computing, Physica-Verlag, Heidelberg, 1999.
- [12] M. Ward, R. P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc. 45(1939), 335-354.
- [13] L. A. Zadeh, Fuzzy sets, Inf. and Control 8(1965), 338-353.
- [14] J. L. Zhang, H. J. Zhou, Fuzzy filters on the residuated lattices, New Math. Nat. Comput. 1(2006), 11-28.
Typ dokumentu
Bibliografia
Identyfikatory
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