Simplification of fuzzy-neural systems using similarity analysis

Abstract

This paper presents a fuzzy neural network system (FNNS) for implementing fuzzy inference systems. In the FNNS, a fuzzy similarity measure for fuzzy rules is proposed to eliminate redundant fuzzy logical rules, so that the number of rules in the resulting fuzzy inference system will be reduced. Moreover, a fuzzy similarity measure for fuzzy sets that indicates the degree to which two fuzzy sets are equal is applied to combine similar input linguistic term nodes. Thus we obtain a method for reducing the complexity of a fuzzy neural network. We also design a new and efficient on-line initialization method for choosing the initial parameters of the FNNS. A computer simulation is presented to illustrate the performance and applicability of the proposed FNNS. The result indicates that the FNNS still has desirable performance under fewer fuzzy logical rules and adjustable parameters.

Supervised fuzzy clustering for rule extraction

“…Following the approach in [5], [12], we substitute this orthogonal basis for in order to determine the individual contributions of the rules. By using the th column of to construct a diagonal matrix (i.e., diag ) that replaces in (6) we obtain , and the corresponding regression problem in (8) becomes , where is the OLS equivalent of the solution vector in (7). The elements of can be determined one-by-one in the orthogonal space in order to calculate the output energy contribution of the corresponding rule.…”

“…Such modeling approaches typically seek to optimize some numerical objective function, while less attention is paid to the complexity of the resulting model in terms of the number of rules [1]. Various methods have been proposed to balance the tradeoff between model accuracy and complexity, like entropy [2], genetic algorithms [3], [4], orthogonal transformation methods [5], [6], similarity measures [7], [8], and statistical information criteria [9], to mention a few.…”

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.…”

Rule Base Reduction Using Conflicting and Reinforcement Measures

“…Several approaches for reducing fuzzy rule base have been proposed using different techniques such as interpolation methods, orthogonal transformation methods, clustering techniques [3][4][5][6][7][8]. A typical tool to perform model simplification is merging similar fuzzy sets and rules using similarity measures [9][10][11][12][13][14].…”