Rule base simplification with similarity measures

Abstract

elIn fuzzy rule based models, redundancy may be present in the form of similarfuzzy sets, especially i f the models are acquired from data by using techniques like fuzzy clustering or gradient learning. The result is an unnecessarily complex and a less effective linguistic description of the system. An automated method is proposed that reduces the number of fuzzy sets in the model using a similarity measure. A comprehensive linguistic description is obtained by linguistic approximation. A numerical example demonstrates the approach.

Methodology for adapting the parameters of a fuzzy system using the extended Kalman filter

“…Let n be the number of input variables and m the number of output variables of the system to model; a discrete fuzzy model Multiple Input Multiple Output -MIMO -can be represented by the following set of rules [10,11,12,13]:…”

“…First we must raise the problem of estimation by extended Kalman filter. For this we have to build a system whose states depend directly on the parameters to be estimated, then we apply recursively from (8) to (11).…”

Complexity reduction in fuzzy modeling

“…Three approaches are considered: (1) iterative compatibility analysis [1,11], (2) similarity relations, and (3) linguistic approximation. These approaches do not require additional knowledge or data acquisition.…”

A structure identification method of submodels for hierarchical fuzzy modeling using the multiple objective genetic algorithm

“…For an appropriate division of input space, several methods have been reported. [12][13][14][15][16] These conventional methods have achieved the division by merging similar membership functions or inserting new ones. This article proposes a new method for dividing the input space unevenly based on model errors.…”