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Fuzzy relational equations: Bridging theory, methodology and practice. (English) Zbl 0965.03066
The paper discusses equations with unknown fuzzy sets and with unknown fuzzy relations [cf. E. Sanchez, Inf. Control 34, 38-48 (1976; Zbl 0326.02048)]. It is a survey of problems, methods and results in solution of fuzzy relation equations with diverse relation compositions (mainly sup-t and inf-s compositions, where t and s denote triangular norm and conorm, respectively). Solvability conditions, extremal solutions and methods of approximate solution are described. This presentation is completed by a rich list of recent literature.

MSC:
03E72 Theory of fuzzy sets, etc.
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15B48 Positive matrices and their generalizations; cones of matrices
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