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Row and Column Spaces of Matrices over Residuated Lattices

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Belohlavek R. , Konecny J.

tom Vol. 115, nr 4

279-295

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.

Rough Fuzzy Concept Analysis

100%

Bartl E. , Konecny J.

Fundamenta Informaticae

2017

tom Vol. 156, nr 2

141--168

We provide a new approach to fusion of Fuzzy Formal Concept Analysis and Rough Set Theory. As a starting point we take into account a couple of fuzzy relations, one of them represents the lower approximation, while the other one the upper approximation of a given data table. By defining appropriate concept-forming operators we transfer the roughness of the input data table to the roughness of corresponding formal fuzzy concepts in the sense that a formal fuzzy concept is considered as a collection of objects accompanied with two fuzzy sets of attributes— those which are shared by all the objects and those which at least one object has. In the paper we study the properties of such formal concepts and show their relationship with concepts formed by well-known isotone and antitone operators.