An Approach to Modelling and Simulation of Uncertain Dynamical Systems

Hüllermeier, Eyke

doi:10.1142/s0218488597000117

Cited by 306 publications

(190 citation statements)

References 0 publications

Supporting

Mentioning

166

Contrasting

Unclassified

Order By: Relevance

“…Adopting the latter view could lead to fruitful developments of fuzzy sets methods in a direction not yet much considered in the engineering sciences, beyond rehashing good old fuzzy rule-based systems further. For instance, the study of fuzzy differential inclusions in the style initiated by Huellermeier [44] goes in this direction (see [6]). …”

Section: Resultsmentioning

confidence: 99%

Statistical reasoning with set-valued information: Ontic vs. epistemic views

Couso

Dubois

2014

International Journal of Approximate Reasoning

160

107

View full text Add to dashboard Cite

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. In information processing tasks, sets may have a conjunctive or a disjunctive reading. In the conjunctive reading, a set represents an object of interest and its elements are subparts of the object, forming a composite description. In the disjunctive reading, a set contains mutually exclusive elements and refers to the representation of incomplete knowledge. It does not model an actual object or quantity, but partial information about an underlying object or a precise quantity. This distinction between what we call ontic vs. epistemic sets remains valid for fuzzy sets, whose membership functions, in the disjunctive reading are possibility distributions, over deterministic or random values. This paper examines the impact of this distinction in statistics. We show its importance because there is a risk of misusing basic notions and tools, such as conditioning, distance between sets, variance, regression, etc. when data are set-valued. We discuss several examples where the ontic and epistemic points of view yield different approaches to these concepts.

show abstract

Section: Resultsmentioning

confidence: 99%

Statistical reasoning with set-valued information: Ontic vs. epistemic views

Couso

Dubois

2014

International Journal of Approximate Reasoning

160

107

View full text Add to dashboard Cite

show abstract

“…After the introduction and major innovations in the theory of fuzzy differential equations [4,6,14], the term fuzzy differential equation (FDE) is instantaneously growing as a new area in fuzzy calculus. These equations are acquired interchangeably by incorporating differential equations with fuzzy initial values, fuzzy boundary values or with fuzzy functions as well.…”

Section: Introductionmentioning

confidence: 99%

Adaptive strategies for system of fuzzy differential equation: application of arms race model

Mondal¹,

Khan²,

Razzaq³

et al. 2018

J. Math. Computer Sci.

View full text Add to dashboard Cite

The paper presents adaptive stratagems to scrutinize the system of first order fuzzy differential equations (SFDE) in two modes, fuzzy and in crisp sense. Its fuzzy solutions are carried out using two approaches, namely, Zadeh's extension principle and generalized Hukuhara derivative (gH-derivative). While, different defuzzification techniques; central of area method (COA), bisector of area method (BOA), largest of maxima (LOM), smallest of maxima (SOM), mean of maxima (MOM), regular weighted point method (RWPM), graded mean integration value (GMIV), and center of approximated interval (COAI), are employed to discuss the crisp solutions. Moreover, the arms race model (ARM), which have a significant implication in international military planning, are pragmatic examples of system of first order differential equations, but not studied in fuzzy sense, hitherto. Therefore, ARM is re-established and studied here with fuzzy numbers to estimate its uncertain parameters, as a practical utilization of SFDE. Additionally, an illustrative example of ARM is undertaken to clarify the appropriateness of the proposed approaches.

show abstract

“…[20] uses Laplace transform for second-order FDE. By extending classical fuzzy set theory, [21] obtains numerical solution of an FDE. The predictorcorrector approach is applied in [22].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Fuzzy Differential Equations with Z-numbers Using Bernstein Neural Networks

Jafari¹,

Yu²,

Li³

et al. 2017

IJCIS

View full text Add to dashboard Cite

The uncertain nonlinear systems can be modeled with fuzzy equations or fuzzy differential equations (FDEs) by incorporating the fuzzy set theory. The solutions of them are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs.In this paper, the solutions of FDEs are approximated by two types of Bernstein neural networks. Here, the uncertainties are in the sense of Z-numbers. Initially the FDE is transformed into four ordinary differential equations (ODEs) with Hukuhara differentiability. Then neural models are constructed with the structure of ODEs. With modified back propagation method for Z-number variables, the neural networks are trained. The theory analysis and simulation results show that these new models, Bernstein neural networks, are effective to estimate the solutions of FDEs based on Z-numbers.

show abstract

An Approach to Modelling and Simulation of Uncertain Dynamical Systems

Cited by 306 publications

References 0 publications

Statistical reasoning with set-valued information: Ontic vs. epistemic views

Statistical reasoning with set-valued information: Ontic vs. epistemic views

Adaptive strategies for system of fuzzy differential equation: application of arms race model

Numerical Solution of Fuzzy Differential Equations with Z-numbers Using Bernstein Neural Networks

Contact Info

Product

Resources

About