Fuzzy neural networks

Fuller, Robert C.

doi:10.1007/978-3-7908-1852-9_3

Cited by 15 publications

(19 citation statements)

References 110 publications

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“…One of the famous methods is the back-propagation learning algorithm. The mentioned learning algorithm was fully introduced in 1986 by Rumelhart and Mc-Clelland 30 . The concept of forward propagation is that the given artificial neurons are located in network layers, and then generate its signal output to forward direction.…”

Section: Basic Idea Of Annsmentioning

confidence: 99%

Using ANNs Approach for Solving Fractional Order Volterra Integro-differential Equations

Jafarian¹,

Rostami²,

Golmankhaneh³

et al. 2017

IJCIS

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Indeed, interesting properties of artificial neural networks approach made this non-parametric model a powerful tool in solving various complicated mathematical problems. The current research attempts to produce an approximate polynomial solution for special type of fractional order Volterra integrodifferential equations. The present technique combines the neural networks approach with the power series method to introduce an efficient iterative technique. To do this, a multi-layer feed-forward neural architecture is depicted for constructing a power series of arbitrary degree. Combining the initial conditions with the resulted series gives us a suitable trial solution. Substituting this solution instead of the unknown function and employing the least mean square rule, converts the origin problem to an approximated unconstrained optimization problem. Subsequently, the resulting nonlinear minimization problem is solved iteratively using the neural networks approach. For this aim, a suitable three-layer feed-forward neural architecture is formed and trained using a back-propagation supervised learning algorithm which is based on the gradient descent rule. In other words, discretizing the differential domain with a classical rule produces some training rules. By importing these to designed architecture as input signals, the indicated learning algorithm can minimize the defined criterion function to achieve the solution series coefficients. Ultimately, the analysis is accompanied by two numerical examples to illustrate the ability of the method. Also, some comparisons are made between the present iterative approach and another traditional technique. The obtained results reveal that our method is very effective, and in these examples leads to the better approximations.

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Section: Basic Idea Of Annsmentioning

confidence: 99%

Using ANNs Approach for Solving Fractional Order Volterra Integro-differential Equations

Jafarian¹,

Rostami²,

Golmankhaneh³

et al. 2017

IJCIS

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“…Research studies have shown that hybrid models perform better when solving a particular problem compared to an individual model alone [11], [12]. The integration of two techniques overcomes the constraints of individual model by hybridization of various methods.…”

Section: Adaptive Neural Fuzzy Inference Systemsmentioning

confidence: 99%

Neuro Fuzzy Modelling for Prediction of Consumer Price Index

Ambukege¹,

Justo²,

Mushi³

2017

IJAIA

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“…Definition 4. Consider a one-dimensional p-fuzzy system given by (1). Consider that * is a stationary point of (1) if…”

Section: Definitionsmentioning

confidence: 99%

“…This success is due to its simplicity and interrelation with humans way of reasoning. Fuzzy rulebased systems are conceptually simple [1]. Such systems are basically threefold: an input (fuzzifier), an inference mechanism composed of a base of fuzzy rules together with an inference method, and, finally, an output (defuzzifier) stage (see Figure 1).…”

Section: Introductionmentioning

confidence: 99%

Stationary Points—I: One-Dimensional p-Fuzzy Dynamical Systems

Silva¹,

Leite²,

Bassanezi

et al. 2013

Journal of Applied Mathematics

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p-Fuzzy dynamical systems are variational systems whose dynamic is obtained by means of a Mamdani type fuzzy rule-based system. In this paper, we will show the 1-dimensional p-fuzzy dynamical systems and will present theorems that establish conditions of existence and uniqueness of stationary points. Besides the obtained analytical results, we will present examples that illustrate and confirm the obtained mathematical results.

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Fuzzy neural networks

Cited by 15 publications

References 110 publications

Using ANNs Approach for Solving Fractional Order Volterra Integro-differential Equations

Using ANNs Approach for Solving Fractional Order Volterra Integro-differential Equations

Neuro Fuzzy Modelling for Prediction of Consumer Price Index

Stationary Points—I: One-Dimensional p-Fuzzy Dynamical Systems

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