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

Gaxiola, Fernando; Melín, Patricia; Valdez, Fevrier; Castillo, Oscar; Castro, Juan R.

doi:10.3390/info8030114

Cited by 12 publications

(2 citation statements)

References 54 publications

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“…The T-norm operator (product)-the T-norm operator is a T function modelling the AND intersection operation of two or more fuzzy numbers, e.g., Ã and B. In this paper, only the ordinary product of real numbers is used as the T-norm operator [68] (10):…”

Section: Fuzzy Logic-preliminariesmentioning

confidence: 99%

How to Apply Fuzzy MISO PID in the Industry? An Empirical Study Case on Simulation of Crane Relocating Containers

et al. 2020

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The proportional-integral-derivative (PID) algorithm automatically adjusts the control output based on the difference between a set point and a measured process variable. The classical approach is broadly used in the majority of control systems. However, in complex problems, this approach is not efficient, especially when the exact mathematical formula is difficult to specify. Besides, it was already proven that highly nonlinear situations are also significantly limiting the usage of the PID algorithm, in contrast to the fuzzy algorithms, which often work correctly under such conditions. In the case of multidimensional objects, where many independently operating PID algorithms are currently used, it is worth considering the use of one fuzzy algorithm with many-input single-output (MISO) or many-input many-output (MIMO) structure. In this work, a MISO type chip is investigated in the study case on simulation of crane relocating container with the external distribution. It is an example of control objects that due to badly conditioned dynamic features (strong non-linearities) require the operator’s intervention in manual or semi-automatic mode. The possibility of fuzzy algorithm synthesis is analyzed with two linguistic variable inputs (distance from −100 to 500 mm and angle from −45° to 45°). The output signal is the speed which is modelled as a linguistic power variable (in the domain from −100% to 100%). Based on 36 fuzzy rules, we present the main contribution, the control system with external disturbance, to show the effectiveness of the identified fuzzy PID approach with different gain values. The fuzzy control system and PID control are implemented and compared concerning the time taken for the container to reach the set point. The results show that fuzzy MISO PID is more effective than the classical one because fuzzy set theory helps to deal with the environmental uncertainty. The container’s angle deviations are taken into consideration, as mitigating them and simultaneously maintaining the fastest speed possible is an essential factor of this challenge.

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Section: Fuzzy Logic-preliminariesmentioning

confidence: 99%

How to Apply Fuzzy MISO PID in the Industry? An Empirical Study Case on Simulation of Crane Relocating Containers

et al. 2020

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“…See Refs. [35][36][37]. Later, Agrawal and Pal et al did a lot of excellent work by using PSO algorithm and generalized type-2 fuzzy set in [38,39].…”

Section: Introductionmentioning

confidence: 99%

Convergence and gradient algorithm of a class of neural networks based on the polygonal fuzzy numbers representation

Sun

Wang

2022

Complex Intell. Syst.

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As a special case of general fuzzy numbers, the polygonal fuzzy number can describe a fuzzy object by means of an ordered representation of finite real numbers. Different from general fuzzy numbers, the polygonal fuzzy numbers overcome the shortcoming of complex operations based on Zadeh’s traditional expansion principle, and can maintain the closeness of arithmetic operation. Hence, it is feasible to use a polygonal fuzzy number to approximate a general fuzzy number. First, an extension theorem of continuous functions on a real compact set is given according to open set construction theorem. Then using Weierstrass approximation theorem and ordered representation of the polygonal fuzzy numbers, the convergence of a single hidden layer feedforward polygonal fuzzy neural network is proved. Secondly, the gradient vector of the approximation error function and the optimization parameter vector of the network are given by using the ordered representation of polygonal fuzzy numbers, and then the gradient descent algorithm is used to train the optimal parameters of the polygonal fuzzy neural network iteratively. Finally, two simulation examples are given to verify the approximation ability of the network. Simulation result shows that the proposed network and the gradient descent algorithm are effective, and the single hidden layer feedforward network have good abilities in learning and generalization.

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Chaotic Type-2 Transient-Fuzzy Deep Neuro-Oscillatory Network (CT2TFDNN) for Worldwide Financial Prediction

Lee¹

2019

Quantum Finance

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

Cited by 12 publications

References 54 publications

How to Apply Fuzzy MISO PID in the Industry? An Empirical Study Case on Simulation of Crane Relocating Containers

How to Apply Fuzzy MISO PID in the Industry? An Empirical Study Case on Simulation of Crane Relocating Containers

Convergence and gradient algorithm of a class of neural networks based on the polygonal fuzzy numbers representation

Chaotic Type-2 Transient-Fuzzy Deep Neuro-Oscillatory Network (CT2TFDNN) for Worldwide Financial Prediction

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