The min-max function differentiation and training of fuzzy neural networks

Author

Zhang, Xinghu ; Hang, Chang-Chieh ; Tan, Shaohua ; Wang, Pei-Zhuang

Author_Institution

Dept. of Electr. Eng., Nat. Univ. of Singapore, Singapore

Volume

7

Issue

5

fYear

1996

fDate

9/1/1996 12:00:00 AM

Firstpage

1139

Lastpage

1150

Abstract

This paper discusses the Δ-rule and training of min-max neural networks by developing a differentiation theory for min-max functions, the functions containing min (∧) and/or max (V) operations. We first prove that under certain conditions all min-max functions are continuously differentiable almost everywhere in the real number field ℜ and derive the explicit formulas for the differentiation. These results are the basis for developing the Δ-rule for the training of min-max neural networks. The convergence of the new Δ-rule is proved theoretically using the stochastic theory, and is demonstrated with a simulation example

Keywords

fuzzy neural nets; learning (artificial intelligence); Δ-rule convergence; differentiation theory; fuzzy neural network training; min-max function differentiation; min-max functions; min-max neural networks; stochastic theory; Algorithm design and analysis; Convergence; Functional analysis; Fuzzy control; Fuzzy neural networks; Image processing; Neural networks; Pattern recognition; Stochastic processes;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/72.536310

Filename

536310