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Information 2017, 8(3), 114; doi:10.3390/info8030114

Comparison of T-Norms and S-Norms for Interval Type-2 Fuzzy Numbers in Weight Adjustment for Neural Networks

1
Faculty of Engineering, Autonomous University of Chihuahua, 31110 Chihuahua, Mexico
2
Division of Graduate Studies and Research, Tijuana Institute of Technology, 22414 Tijuana, Mexico
3
Faculty of Engineering and Chemistry Sciences, Autonomous University of Baja California, 22390 Tijuana, Mexico
*
Author to whom correspondence should be addressed.
Received: 29 August 2017 / Revised: 12 September 2017 / Accepted: 18 September 2017 / Published: 20 September 2017
(This article belongs to the Section Artificial Intelligence)
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Abstract

A comparison of different T-norms and S-norms for interval type-2 fuzzy number weights is proposed in this work. The interval type-2 fuzzy number weights are used in a neural network with an interval backpropagation learning enhanced method for weight adjustment. Results of experiments and a comparative research between traditional neural networks and the neural network with interval type-2 fuzzy number weights with different T-norms and S-norms are presented to demonstrate the benefits of the proposed approach. In this research, the definitions of the lower and upper interval type-2 fuzzy numbers with random initial values are presented; this interval represents the footprint of uncertainty (FOU). The proposed work is based on recent works that have considered the adaptation of weights using type-2 fuzzy numbers. To confirm the efficiency of the proposed method, a case of data prediction is applied, in particular for the Mackey-Glass time series (for τ = 17). Noise of Gaussian type was applied to the testing data of the Mackey-Glass time series to demonstrate that the neural network using a interval type-2 fuzzy numbers method achieves a lower susceptibility to noise than other methods. View Full-Text
Keywords: fuzzy numbers; type-2 fuzzy weights; neural networks; backpropagation; time series prediction fuzzy numbers; type-2 fuzzy weights; neural networks; backpropagation; time series prediction
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Gaxiola, F.; Melin, P.; Valdez, F.; Castillo, O.; Castro, J.R. Comparison of T-Norms and S-Norms for Interval Type-2 Fuzzy Numbers in Weight Adjustment for Neural Networks. Information 2017, 8, 114.

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