Row and Column Spaces of Matrices over Residuated Lattices

• Autorzy: Belohlavek, R. , Konecny, J.
• Języki publikacji: EN

Abstrakty

EN

We present results regarding row and column spaces of matrices whose entries are elements of residuated lattices. In particular, we define the notions of a row and column space for matrices over residuated lattices, provide connections to concept lattices and other structures associated to such matrices, and show several properties of the row and column spaces, including properties that relate the row and column spaces to Schein ranks of matrices over residuated lattices. Among the properties is a characterization of matrices whose row (column) spaces are isomorphic. In addition, we present observations on the relationships between results established in Boolean matrix theory on one hand and formal concept analysis on the other hand.

Słowa kluczowe

EN

graded matrix; formal concept analysis; morphism

• Czasopismo: Fundamenta Informaticae
• Rocznik: 2012
• Tom: Vol. 115, nr 4
• Strony: 279-295
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Belohlavek, R.

autor

Konecny, J.

• Department of Computer Science Palacky University Olomouc, Czech Republic,

Bibliografia

• [1] Belohlavek R.: Fuzzy Galois connections. Math. Logic Quarterly 45(4), 1999, 497-504.
• [2] Belohlavek R.: Fuzzy closure operators. J. Math. Anal. Appl. 262, 2001, 473-489.
• [3] Belohlavek R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer, Academic/Plenum Publishers, New York, 2002.
• [4] Belohlavek R.: Concept lattices and order in fuzzy logic. Annals of Pure and Applied Logic 128(1-3)2004, 277-298.
• [5] Belohlavek R.: Optimal triangular decompositions of matrices with entries from residuated lattices, Int. J. Approximate Reasoning 50(8), 2009, 1250-1258.
• [6] Belohlavek R.: Optimal decompositions of matrices with entries from residuated lattices, J. Logic and Computation (doi: 10.1093/logcom/exr023, online: September 7, 2011).
• [7] Belohlavek R., Funioková T.: Fuzzy interior operators. Int. J. General Systems 33(4), 2004, 315-330.
• [8] Belohlavek R., Konecny J.: Operators and spaces associated to matrices with grades and their decompositions. Proc. NAFIPS 2008, 6 pp., IEEE Press.
• [9] Belohlavek R., Vychodil V.: Factor analysis of incidence data via novel decomposition of matrices. Lecture Notes in Computer Science 5548, 2009, 83-97.
• [10] Ganter B., Wille R.: Formal Concept Analysis. Mathematical Foundations. Springer, Berlin, 1999.
• [11] Georgescu G., Popescu A.: Non-dual fuzzy connections. Archive for Mathematical Logic 43(2004), 1009-1039.
• [12] Gottwald S.: A Treatise on Many-Valued Logics. Research Studies Press, Baldock, Hertfordshire, England, 2001.
• [13] Hájek P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht, 1998.
• [14] Harman H. H.: Modern Factor Analysis, 2nd Ed. The Univ. Chicago Press, Chicago, 1970.
• [15] Kim K. H.: Boolean Matrix Theory and Applications.M. Dekker, 1982.
• [16] Kohout L. J., Bandler W.: Relational-product architectures for information processing. Information Sciences 37(1-3): 25-37, 1985.
• [17] MarkowskyG.: The factorization and representation of lattices. Transactions of the AMS 203, 1975, 185-200.
• [18] Pollandt S.: Fuzzy Begriffe. Springer-Verlag, Berlin/Heidelberg, 1997.
• [19] Popescu A.: A general approach to fuzzy concepts. Mathematical Logic Quarterly 50(3), 2004, 1-17.
• [20] Ward M., R. P. Dilworth. Residuated lattices. Trans. Amer. Math. Soc. 45 (1939), 335-