Fuzzy Set-Based Approximate Reasoning and Mathematical Fuzzy Logic

Zadeh proposed and developed the theory of approximate reasoning in a long series of papers in the 1970’s (see e.g. [28–32, 34, 35]), at the same time when he introduced possibility theory [33] as a new approach to uncertainty modeling. His original approach is based on a fuzzy set-based representation of the contents of factual statements (expressing elastic restrictions on the possible values of some parameters) and of if-then rules relating such fuzzy statements.