This paper presents an approach to similarity based approximate reasoning that elucidates the connection between similarity and existing approaches to inference in approximate reasoning methodology. A set of axioms is proposed to get a reasonable measure of similarity between two fuzzy sets. The similarity between the fact(s) and the antecedent of a rule is used to modify the relation between the antecedent and the consequent of the rule. An inference is drawn using the well-known projection operation on the domain of the consequent. Zadeh's compositional rule of inference and existing similarity based reasoning techniques are considered for a new similarity based approximate reasoning technique. The proposed mechanism is used to develop a modified fuzzy control system. A new defuzzification scheme is proposed. Simulation results are presented for the well-known inverted pendulum problem. © 2007 Elsevier B.V. All rights reserved.
Raha, S., Hossain, A., & Ghosh, S. (2008). Similarity based approximate reasoning: fuzzy control. Journal of Applied Logic, 6(1), 47–71. https://doi.org/10.1016/j.jal.2007.01.001