Similarity-Based Inverse Approximate Reasoning

This paper investigates the inverse problem of ap proximate reasoning [to conclude A´ from B´ and (A→ B)] from different angles. We develop a method to And a solution to the inverse problem by the use of the law of contrapositive symme try. In the process, generalized modus ponens, generalized modus tollens, and their generating functions are studied extensively. An attempt is made here to establish that the concept of similarity plays an important role in inverse approximate reasoning. We apply the concept of similarity to model inverse approximate reasoning and develop a new methodology that is named similarity-based inverse approximate reasoning for a solution to the problem. Algorithms are presented and illustrated with simple yet concrete examples. We then use Zadeh´s compositional rule of inference (CRI) as a combi nation of cylindrical extension and projection and, thereby, model generalized modus tollens in a different way. We, thus, develop a third way to find a solution to the inverse problem of approximate reasoning. A comparison between the result of application of our technique and the real static characteristic of a dc shunt motor is presented.