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System of fuzzy relation equations with sup-* composition in semi-linear spaces: minimal solutions

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2 Author(s)
Lenka Noskova ; University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, 30.dubna 22, 701 03 Ostrava 1, Czech Republic. phone: +420 596 160 207; fax: +420 596 120 478; e-mail: ; Irina Perfilieva

The problem of solvability of a system of fuzzy relation equations with sup-* composition is considered in semilinear vector spaces. Based on the fact that a complete set of solutions is determined by minimal solutions, we focused on characterization of them. At first, sets of all minimal solutions of a single equation have been described under different assumptions on an underlying algebra. Dependently on the ordering of the support set, either necessary or sufficient conditions, or criteria of being a minimal solution have been obtained. Then minimal solutions of a system are build from minimal solutions of single equations.

Published in:

2007 IEEE International Fuzzy Systems Conference

Date of Conference:

23-26 July 2007