Fuzzy Differential Equations for Modeling and Control of Fuzzy Systems

Abstract

A survey of the methodologies associated with the modeling and control of uncertain nonlinear systems has been given due importance in this paper. The basic criteria that highlights the work is relied on the various patterns of techniques incorporated for the solutions of fuzzy differential equations (FDEs) that corresponds to fuzzy controllability subject. The solutions which are generated by these equations are considered to be the controllers. Currently, numerical techniques have come out as superior techniques in order to solve these types of problems. The implementation of neural networks technique is contributed in the complex way of dealing the appropriate solutions of the fuzzy systems.

A Survey on Applications of Neuro-Fuzzy Models

“…Definition 3: The -level of the -number is stated as below (6) such that . is calculated by the Nguyen's theorem (7) such that . Hence, is defined as (8) such that , ,…”

“…Fuzzy set theory is an appropriate approach to handle vagueness and has been successfully applied for solving multi-criteria decision making issues. In the past few years, important usages of fuzzy set theory in engineering have been provided [6][7][8][9][10][11][12][13][14]. Fuzzy set theory has been viewed as a proper technique to facilitate studies in engineering fields in a case that the dynamics of the decision domain bound the exact estimation of model parameters.…”

Deep Learning for Pipeline Damage Detection: an Overview of the Concepts and a Survey of the State-of-the-Art

“…Neural networks have been utilized in modeling complicated connections among inputs and outputs or acquiring patterns for the data [19][20]. Artificial neural networks have various noteworthy properties like universal function estimation abilities, as well as match of multiple nonlinear variables concerning with unknown interactions [21][22][23][24]. Due to these properties, most of the researchers consider the application of artificial neural networks for automatically recognizing the incidence of leakages in oil pipelines, substituting the human operator that observes the online trends from the sonic sensors.…”

A Novel Technique for Solving Fully Fuzzy Nonlinear Systems Based on Neural Networks

“…Arti¯cial neural networks have many applications in di®erent¯elds. [1][2][3][4][5][6][7][8][9][10][11] Fuzzy neural network with various properties such as learning ability, generalization as well as *Corresponding author. This is an Open Access article published by World Scienti¯c Publishing Company.…”