Solvability of fuzzy relational equations and manipulation of fuzzy data. (English) Zbl 0607.94015
The main idea of earlier papers of the first author [Fuzzy Sets Syst. 17, 285-296 (1985; Zbl 0607.03015); Elektron. Informationsverarb. Kybernetik 22, 67-91 (1986; Zbl 0607.03016)] is applied here to problems of the design of fuzzy controllers. Such controllers are supposed to be determined by systems of fuzzy relation equations originating from control rules. To build a controller means to (approximately) solve such a system of equations. The first author’s generalized truth value of the sentence ”the considered system of fuzzy equations has a solution” is taken as a solvability degree, and some dependencies of this degree from changes in the initial data for a fuzzy controller are discussed.
Essentially, the fuzzy data constituting a controller are changed with a threshold level: all membership degrees below this threshold are ”deleted”. Then, the solvability degree of the ”remaining” system of equations is considered as a function of this threshold. Finally, these ideas are applied for the evaluation of (the quality of) fuzzy controllers.
Essentially, the fuzzy data constituting a controller are changed with a threshold level: all membership degrees below this threshold are ”deleted”. Then, the solvability degree of the ”remaining” system of equations is considered as a function of this threshold. Finally, these ideas are applied for the evaluation of (the quality of) fuzzy controllers.
MSC:
| 94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |
| 93B15 | Realizations from input-output data |
| 03B52 | Fuzzy logic; logic of vagueness |
Keywords:
solvability index; reasoning with fuzzy data; design of fuzzy controllers; systems of fuzzy relation equations; solvability degree; threshold levelReferences:
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