Solvability of fuzzy relational equations and manipulation of fuzzy data (Q1086220)

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.