Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data

The paper deals with implementation of a general scheme for fuzzy logic inference with the aid of fuzzy relational equations. It is shown that antecedents and consequents are related in terms of a fuzzy relation. Various implementation methods of generalized modus ponens and modus tollens are put into extensive study. It is pointed out that fuzzy relational equations form an effective and plausible tool for implementations of reasoning methods with fuzzy premises. Two examples of fuzzy controllers being a direct application of schemes of approximate reasoning are also discussed.