Similarity confidence level for fuzzy rulebases

A fuzzy rulebase is a model of a system, expressed as a collection of fuzzy if/then rules, whose predicates are words in nature language, given mathematical meaning by associating each word with a fuzzy set fuzzy rulebases have been proven to be powerful and intuitive tools for modeling a wide range of phenomena. The problem of how to construct fuzzy rulebases has been extensively explored. However, the problem of how to defined operations on fuzzy rulebases is still an open question. This paper addressed the second question. The purpose of this research project was to develop an algorithm for detecting and quantifying structure similarity between two fuzzy rulebases, which in turn give an approximate measure of the similarity between two systems. The proposed algorithm is based on linguistic gradient, which is a linguistic analogue of the gradient operator from calculus. For each of the two fuzzy rulebases, the gradient vector can be computed at each point in the linguistic space. Each n-dimension gradient vector is converted to a 2ndimension 3-level vector by thresholding its magnitude on each axis. Vectors lie on each axis are added to compute projection. The projection vectors of the two fuzzy rulebases are regranulated to the same granularity using weighted sum. The regranulated vectors are then compared using Euclidean distance formula. The Euclidean distance is normalized so that results of different pair of rulebases are directly comparable. Programs have been developed for C++ and Matlab to implement this algorithm.