Relational-product architectures for information processing
Information Sciences: an International Journal - Special issue on expert systems
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
Factor Analysis of Incidence Data via Novel Decomposition of Matrices
ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis
Optimal triangular decompositions of matrices with entries from residuated lattices
International Journal of Approximate Reasoning
Information Sciences: an International Journal
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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.