scholarly journals Inverse Result of Approximation for the Max-Product Neural Network Operators of the Kantorovich Type and Their Saturation Order

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 63
Author(s):  
Marco Cantarini ◽  
Lucian Coroianu ◽  
Danilo Costarelli ◽  
Sorin G. Gal ◽  
Gianluca Vinti
Keyword(s):  
Neural Network ◽  
Rate Of Convergence ◽  
Fuzzy Theory ◽  
Linear Operators ◽  
Activation Functions ◽  
Linear Combinations ◽  
Lipschitz Continuous ◽  
Inverse Approximation ◽  
Saturation Order ◽  
Class Of Functions

In this paper, we consider the max-product neural network operators of the Kantorovich type based on certain linear combinations of sigmoidal and ReLU activation functions. In general, it is well-known that max-product type operators have applications in problems related to probability and fuzzy theory, involving both real and interval/set valued functions. In particular, here we face inverse approximation problems for the above family of sub-linear operators. We first establish their saturation order for a certain class of functions; i.e., we show that if a continuous and non-decreasing function f can be approximated by a rate of convergence higher than 1/n, as n goes to +∞, then f must be a constant. Furthermore, we prove a local inverse theorem of approximation; i.e., assuming that f can be approximated with a rate of convergence of 1/n, then f turns out to be a Lipschitz continuous function.

Research of Fault Diagnosis of Belt Conveyor Based on Fuzzy Neural Network

2014 ◽  
Vol 8 (1) ◽  
pp. 916-921
Author(s):  
Yuan Yuan ◽  
Wenjun Meng ◽  
Xiaoxia Sun
Keyword(s):  
Neural Network ◽  
Fault Diagnosis ◽  
Bp Neural Network ◽  
Fault Location ◽  
Fuzzy Neural Network ◽  
Fuzzy Theory ◽  
Belt Conveyor ◽  
Fuzzy Neural ◽  
Neural Network Algorithm ◽  
Network Fault

To address deficiencies in the process of fault diagnosis of belt conveyor, this study uses a BP neural network algorithm combined with fuzzy theory to provide an intelligent fault diagnosis method for belt conveyor and to establish a BP neural network fault diagnosis model with a predictive function. Matlab is used to simulate the fuzzy BP neural network fault diagnosis of the belt conveyor. Results show that the fuzzy neural network can filter out unnecessary information; save time and space; and improve the fault diagnosis recognition, classification, and fault location capabilities of belt conveyor. The proposed model has high practical value for engineering.

Research on visual recognition intelligent system of city brand image based on fuzzy theory and regional culture

2021 ◽  
pp. 1-9
Author(s):  
Lin Han ◽  
Lu Han
Keyword(s):  
Neural Network ◽  
Visual Recognition ◽  
Intelligent System ◽  
Brand Image ◽  
Fuzzy Theory ◽  
Recognition System ◽  
Market Competitiveness ◽  
Visual Identity ◽  
Fuzzy Neural ◽  
Intelligent Recognition

With the rapid development of China’s market economy, brand image is becoming more and more important for an enterprise to enhance its market competitiveness and occupy a favorable market share. However, the brand image of many established companies gradually loses with the development of society and the improvement of people’s aesthetic pursuit. This has forced it to change its corporate brand image and regain the favor of the market. Based on this, this article combines the related knowledge and concepts of fuzzy theory, from the perspective of visual identity design, explores the development of corporate brand image visual identity intelligent system, and aims to design a set of visual identity system that is different from competitors in order to shape the enterprise. Distinctive brand image and improve its market competitiveness. This article first collected a large amount of information through the literature investigation method, and made a systematic and comprehensive introduction to fuzzy theory, visual recognition technology and related theoretical concepts of brand image, which laid a sufficient theoretical foundation for the later discussion of the application of fuzzy theory in the design of brand image visual recognition intelligent system; then the fuzzy theory algorithm is described in detail, a fuzzy neural network is proposed and applied to the design of the brand image visual recognition intelligent system, and the design experiment of the intelligent recognition system is carried out; finally, through the use of the specific case of KFC brand logo, the designed intelligent recognition system was tested, and it was found that the visual recognition intelligent system had an overall accuracy rate of 96.08% for the KFC brand logo. Among them, the accuracy rate of color recognition was the highest, 96.62%; comparing the changes in the output value of the training sample and the test sample, the output convergence effect of the color network is the best; through the comparison test of the BP neural network, the recognition effect of the fuzzy neural network is better.

Neural Network Activation Functions with Electro-Optic Absorption Modulators

2018 ◽  
Author(s):  
Jonathan George ◽  
Armin Mehrabian ◽  
Rubab Amin ◽  
Paul R. Prucnal ◽  
Tarek El-Ghazawi ◽  
...  
Keyword(s):  
Neural Network ◽  
Activation Functions ◽  
Network Activation ◽  
Electro Optic

scholarly journals The Rate of Convergence of Lupasq-Analogue of the Bernstein Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Heping Wang ◽  
Yanbo Zhang
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Bernstein Operators ◽  
Lipschitz Continuous Functions ◽  
Lipschitz Continuous

We discuss the rate of convergence of the Lupasq-analogues of the Bernstein operatorsRn,q(f;x)which were given by Lupas in 1987. We obtain the estimates for the rate of convergence ofRn,q(f)by the modulus of continuity off, and show that the estimates are sharp in the sense of order for Lipschitz continuous functions.

The Dunkl generalization of Stancu type q-Szasz-Mirakjan-Kantorovich operators and some approximation results

2018 ◽  
Vol 34 (3) ◽  
pp. 363-370
Author(s):  
M. MURSALEEN ◽  
◽  
MOHD. AHASAN ◽  
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Exponential Function ◽  
Second Order ◽  
Lipschitz Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
Kantorovich Operators ◽  
Korovkin’S Theorem

In this paper, a Dunkl type generalization of Stancu type q-Szasz-Mirakjan-Kantorovich positive linear operators ´ of the exponential function is introduced. With the help of well-known Korovkin’s theorem, some approximation properties and also the rate of convergence for these operators in terms of the classical and second-order modulus of continuity, Peetre’s K-functional and Lipschitz functions are investigated.

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