Adak, A. K., Bhowmik, M. and Pal, M., Some properties of generalized intuitionistic fuzzy nilpotent matrices over distributive lattices, Fuzzy Inf. Eng, 4 (2012), 371-387.
Atanassov, K., intuitionistic fuzzy sets, in V.Sgurev, ed.,Vii ITKRS Session, Sofia, Tune 1983.
Belohlavek, R., Concept lattices and order in fuzzy logic. emphAnn. Pure Appl. Logic, 128(3) (2004), 277-298.
Ciungu, L. C, Classes of residuated lattices, Annals of University of Craiova, Math. Comp, Sci. Ser., 33 (2006), 189-207.
Galatos, N., Jipsen, P., Kowalski, T. and Ono, H., Residuated lattices: An Algebraic Gelimpse at Substructural Logics, Volume 151 of studies in Logic and the Foundations of Mathematics, Elsevier, Amesterdam, 2007.
Ganter, B. and Wille, R., Formal Concepts Analysis, Mathematical Foundations. Springer, Berlin, 1990.
Hosseinyazdi, M., The optimization problem over a distributive lattice, Journal of Global Optimization, 41 (2008), 283-298.
Kim K. H. and Roush, F. W., Generalized fuzzy matrices, Fuzzy sets and systems, 4 (1980), 243-315.
Pal, M., Khan, S. K. and Shyamal, A. K., Intuitionistic fuzzy matrices. Notes on Intuitionistic fuzzy sets, 8(2) (2002), 51- 62.
Piciu, D., Algebras of Fuzzy Logic, Universitaria din Craiova, 2007.
Sriram S. and Murugadas, P., On semiring of intuitionistic fuzzy matrices, Applied Mathematical. Sciences, 4(23) ( 2010), 1099-1105.
Thomason, M. G., Convergence of powers of a fuzzy matrix, J. Math. Anal. Appl, 57 (1977), 476-486.
Wilding, D., Linear algebra over semiring, university of Manchester, 2014.
Wille. R., Restructuring lattice theory: An approach based on concepts. In I. Rival, editor, Ordered sets, volume 83 of NATO Advanced Study Institute Series, pages 445- 470, Springer, Dordrecht, 1982.
Xiao, Y., Xue, T., Xue, Z. and Cheng, H., A new kind of intuitionistic fuzzy implication, Journal of Information and Computational Sciences, 8(13) (2011), 2839-2849.
Algebraic structure of square matrices over residuated lattices
In this paper, we introduce the algebra Mnn(L) of square matrices over residuated lattice L. The operations are induced by the corresponding operations of L. It is shown that the defined algebra behaves like a residuated lattice, but there are some slight differences. The properties of this algebra with respect to special residuated lattices are investigated. The notions of filter and ideal together with their roles are specified.
Adak, A. K., Bhowmik, M. and Pal, M., Some properties of generalized intuitionistic fuzzy nilpotent matrices over distributive lattices, Fuzzy Inf. Eng, 4 (2012), 371-387.
Atanassov, K., intuitionistic fuzzy sets, in V.Sgurev, ed.,Vii ITKRS Session, Sofia, Tune 1983.
Belohlavek, R., Concept lattices and order in fuzzy logic. emphAnn. Pure Appl. Logic, 128(3) (2004), 277-298.
Ciungu, L. C, Classes of residuated lattices, Annals of University of Craiova, Math. Comp, Sci. Ser., 33 (2006), 189-207.
Galatos, N., Jipsen, P., Kowalski, T. and Ono, H., Residuated lattices: An Algebraic Gelimpse at Substructural Logics, Volume 151 of studies in Logic and the Foundations of Mathematics, Elsevier, Amesterdam, 2007.
Ganter, B. and Wille, R., Formal Concepts Analysis, Mathematical Foundations. Springer, Berlin, 1990.
Hosseinyazdi, M., The optimization problem over a distributive lattice, Journal of Global Optimization, 41 (2008), 283-298.
Kim K. H. and Roush, F. W., Generalized fuzzy matrices, Fuzzy sets and systems, 4 (1980), 243-315.
Pal, M., Khan, S. K. and Shyamal, A. K., Intuitionistic fuzzy matrices. Notes on Intuitionistic fuzzy sets, 8(2) (2002), 51- 62.
Piciu, D., Algebras of Fuzzy Logic, Universitaria din Craiova, 2007.
Sriram S. and Murugadas, P., On semiring of intuitionistic fuzzy matrices, Applied Mathematical. Sciences, 4(23) ( 2010), 1099-1105.
Thomason, M. G., Convergence of powers of a fuzzy matrix, J. Math. Anal. Appl, 57 (1977), 476-486.
Wilding, D., Linear algebra over semiring, university of Manchester, 2014.
Wille. R., Restructuring lattice theory: An approach based on concepts. In I. Rival, editor, Ordered sets, volume 83 of NATO Advanced Study Institute Series, pages 445- 470, Springer, Dordrecht, 1982.
Xiao, Y., Xue, T., Xue, Z. and Cheng, H., A new kind of intuitionistic fuzzy implication, Journal of Information and Computational Sciences, 8(13) (2011), 2839-2849.
Borumand Saeid, A., Eslami, E., & Balaei, S. (2019). Algebraic structure of square matrices over residuated lattices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 2216-2237. https://doi.org/10.31801/cfsuasmas.423277
AMA
Borumand Saeid A, Eslami E, Balaei S. Algebraic structure of square matrices over residuated lattices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):2216-2237. doi:10.31801/cfsuasmas.423277
Chicago
Borumand Saeid, Arsham, E Eslami, and S Balaei. “Algebraic Structure of Square Matrices over Residuated Lattices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 2216-37. https://doi.org/10.31801/cfsuasmas.423277.
EndNote
Borumand Saeid A, Eslami E, Balaei S (August 1, 2019) Algebraic structure of square matrices over residuated lattices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 2216–2237.
IEEE
A. Borumand Saeid, E. Eslami, and S. Balaei, “Algebraic structure of square matrices over residuated lattices”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 2216–2237, 2019, doi: 10.31801/cfsuasmas.423277.
ISNAD
Borumand Saeid, Arsham et al. “Algebraic Structure of Square Matrices over Residuated Lattices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 2216-2237. https://doi.org/10.31801/cfsuasmas.423277.
JAMA
Borumand Saeid A, Eslami E, Balaei S. Algebraic structure of square matrices over residuated lattices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:2216–2237.
MLA
Borumand Saeid, Arsham et al. “Algebraic Structure of Square Matrices over Residuated Lattices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 2216-37, doi:10.31801/cfsuasmas.423277.
Vancouver
Borumand Saeid A, Eslami E, Balaei S. Algebraic structure of square matrices over residuated lattices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):2216-37.