Training Fuzzy Number Neural Networks with Alpha-cut Refinements

James P. Dunyak; Donald C. Wunsch

doi:10.1109/ICSMC.1997.625747

Training Fuzzy Number Neural Networks with Alpha-cut Refinements

James P. Dunyak
, Donald C. Wunsch

Research output: Contribution to journal › Article › peer-review

Abstract

In a fuzzy number neural network, the inputs, weights, and outputs are general fuzzy numbers. The requirement that F¯ α(1) ⊂F¯ α(2 ) whenever α(1)>α(2) imposes an enormous number of constraints on the weight parameterizations during training. This problem can be solved through a careful choice of weight representation. This new representation is unconstrained, so that standard neural network training techniques may be applied. Unfortunately, fuzzy number neural networks still have many parameters to pick during training, since each weight is represented by a vector. Thus moderate to large fuzzy number neural networks suffer from the usual maladies of very large neural networks. In this paper, we discuss a method for effectively reducing the dimensionality of networks during training. Each fuzzy number weight is represented by the endpoints of its α-cuts for some discretization 0&les;α 1 <α 2 <...<α n &les;1. To reduce dimensionality, training is first done using only a small subset of the α i . After successful training, linear interpolation is used to estimate additional α-cut endpoints. The network is then retrained to tune these interpolated values. This refinement is repeated as needed until the network is fully trained at the desired discretization in &alpha.

Original language	American English
Pages (from-to)	189-194
Number of pages	6
Journal	Systems, Man, and Cybernetics, 1997. IEEE International Conference on Computational Cybernetics and Simulation
Volume	1
DOIs	https://doi.org/10.1109/ICSMC.1997.625747
State	Published - Jan 1 1997
Event	Proceedings of the 1997 IEEE International Conference on Systems, Man, and Cybernetics. Part 1 (of 5) - Orlando, FL, USA Duration: Oct 12 1997 → Oct 15 1997

ASJC Scopus Subject Areas

Control and Systems Engineering
Hardware and Architecture

Disciplines

Electrical and Computer Engineering

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https://doi.org/10.1109/ICSMC.1997.625747

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title = "Training Fuzzy Number Neural Networks with Alpha-cut Refinements",

abstract = " In a fuzzy number neural network, the inputs, weights, and outputs are general fuzzy numbers. The requirement that F\¯ \α(1) \⊂F\¯ \α(2 ) whenever \α(1)>\α(2) imposes an enormous number of constraints on the weight parameterizations during training. This problem can be solved through a careful choice of weight representation. This new representation is unconstrained, so that standard neural network training techniques may be applied. Unfortunately, fuzzy number neural networks still have many parameters to pick during training, since each weight is represented by a vector. Thus moderate to large fuzzy number neural networks suffer from the usual maladies of very large neural networks. In this paper, we discuss a method for effectively reducing the dimensionality of networks during training. Each fuzzy number weight is represented by the endpoints of its \α-cuts for some discretization 0\&les;\α 1 <\α 2 <...<\α n \&les;1. To reduce dimensionality, training is first done using only a small subset of the \α i . After successful training, linear interpolation is used to estimate additional \α-cut endpoints. The network is then retrained to tune these interpolated values. This refinement is repeated as needed until the network is fully trained at the desired discretization in \&alpha.",

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doi = "10.1109/ICSMC.1997.625747",

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AU - Wunsch, Donald C.

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N2 - In a fuzzy number neural network, the inputs, weights, and outputs are general fuzzy numbers. The requirement that F¯ α(1) ⊂F¯ α(2 ) whenever α(1)>α(2) imposes an enormous number of constraints on the weight parameterizations during training. This problem can be solved through a careful choice of weight representation. This new representation is unconstrained, so that standard neural network training techniques may be applied. Unfortunately, fuzzy number neural networks still have many parameters to pick during training, since each weight is represented by a vector. Thus moderate to large fuzzy number neural networks suffer from the usual maladies of very large neural networks. In this paper, we discuss a method for effectively reducing the dimensionality of networks during training. Each fuzzy number weight is represented by the endpoints of its α-cuts for some discretization 0&les;α 1 <α 2 <...<α n &les;1. To reduce dimensionality, training is first done using only a small subset of the α i . After successful training, linear interpolation is used to estimate additional α-cut endpoints. The network is then retrained to tune these interpolated values. This refinement is repeated as needed until the network is fully trained at the desired discretization in &alpha.

AB - In a fuzzy number neural network, the inputs, weights, and outputs are general fuzzy numbers. The requirement that F¯ α(1) ⊂F¯ α(2 ) whenever α(1)>α(2) imposes an enormous number of constraints on the weight parameterizations during training. This problem can be solved through a careful choice of weight representation. This new representation is unconstrained, so that standard neural network training techniques may be applied. Unfortunately, fuzzy number neural networks still have many parameters to pick during training, since each weight is represented by a vector. Thus moderate to large fuzzy number neural networks suffer from the usual maladies of very large neural networks. In this paper, we discuss a method for effectively reducing the dimensionality of networks during training. Each fuzzy number weight is represented by the endpoints of its α-cuts for some discretization 0&les;α 1 <α 2 <...<α n &les;1. To reduce dimensionality, training is first done using only a small subset of the α i . After successful training, linear interpolation is used to estimate additional α-cut endpoints. The network is then retrained to tune these interpolated values. This refinement is repeated as needed until the network is fully trained at the desired discretization in &alpha.

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ER -

Training Fuzzy Number Neural Networks with Alpha-cut Refinements

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