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Fuzzy relation equations with words. (English) Zbl 1066.03038
Nikravesh, Masoud (ed.) et al., Fuzzy partial differential equations and relational equations. Reservoir characterization and modeling. Berlin: Springer (ISBN 3-540-20322-2/hbk). Studies in Fuzziness and Soft Computing 142, 167-185 (2004).
Linguistic expressions and the corresponding fuzzy relation equations are discussed. In the first part, a systematic theory of evaluating linguistic expressions and their semantics is developed (observe that this semantics is based on the Carnap approach to the distinction between intension and extension of linguistic expressions). In the second part, fuzzy relation equations derived from the fuzzy data given by linguistic expressions are studied, stressing the rôle of fuzzy numbers (this follows from the non-solvability of typical fuzzy relation equations with purely linguistic expressions only). Finally, it is shown when the Mamadani-Assilian formula describes the solution of fuzzy relation equations derived from the fuzzy data.
For the entire collection see [Zbl 1052.68006].

##### MSC:
 03B52 Fuzzy logic; logic of vagueness 03E72 Theory of fuzzy sets, etc. 68T37 Reasoning under uncertainty in the context of artificial intelligence
##### Keywords:
fuzzy number; fuzzy relations; linguistic expression