A Neuro-Fuzzy System Based on Logical Interpretation of If-Then Rules
Jacek M. Łęski, Norbert Henzel · 2024
Initially, an axiomatic approach to the definition of fuzzy implication has been recalled in this chapter. Based on this definition several important fuzzy implications and their properties have been described. Then, the idea of approximate reasoning using generalized modus ponens and fuzzy implication is considered. The elimination of the non-informative part of a final fuzzy set before defuzzification plays the key role in this chapter. After reviewing well-known fuzzy systems, a new artificial neural network based on logical interpretation of if-then rules (ANBLIR) is introduced. Another novelty incorporated in the system is the moving fuzzy consequent in if-then rules. The location of this fuzzy set is determined by a linear combination of system inputs. Moreover, this system automatically generates rules from numerical data. The proposed system operates with Gaussian membership functions in thepremise part and triangular in the consequence part. Parameter estimation has been made by combination of both gradient and least squares methods. For initialization of unknown parameter values of premises, a preliminary fuzzy c-means clustering method has been employed. The applications of ANBLIR to pattern recognition on numerical examples using benchmark databases (FORENSIC GLASS, IRIS, WINE and MONKS) are shown.