Ş. Emrah Amrahov¹, N. A. Gasilov², A. G. Fatullayev²

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.5, pp. 351-369, 2014, DOI:10.3970/cmes.2014.099.351

Abstract In this paper, we present a new approach to a time-optimal control problem with uncertainties. The dynamics of the controlled object, expressed by a linear system of differential equations, is assumed to be crisp, while the initial and final phase states are fuzzy sets. We interpret the problem as a set of crisp problems. We introduce a new notion of fuzzy optimal time and transform its calculation to two classical time-optimal control problems with initial and final sets. We examine the proposed approach on an example which is a problem of fuzzy control of mathematical More >

Nizami Gasilov¹, Sahin Emrah Amrahov² , Afet Golayoglu Fatullayev ˇ ¹, Halil Ibrahim Karaka¸s¹, Ömer Akın³

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.2, pp. 93-106, 2012, DOI:10.3970/cmes.2012.088.093

Abstract Uncertainties in some parameters of problems of Leontief input-output analysis lead naturally to fuzzy linear systems. In this work, we consider input-output model, where the technology matrix is crisp and the vector of final outputs is fuzzy. The model is expressed by a fuzzy linear system with crisp matrix and with fuzzy right-hand side vector. We apply a geometric method for solving the system. The method finds the solution in the form of a fuzzy set of vectors. The solution set is shown to be a parallelepiped in coordinate space and is expressed by an More >

N.A. Gasilov¹, I.F. Hashimoglu², S.E. Amrahov³, A.G. Fatullayev¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.4, pp. 367-378, 2012, DOI:10.3970/cmes.2012.085.367

Abstract In this paper, we consider a high-order linear differential equation with fuzzy forcing function and with fuzzy initial values. We assume the forcing function be in a special form, which we call triangular fuzzy function. We present solution as a fuzzy set of real functions such that each real function satisfies the initial value problem by some membership degree. We propose a method to find the fuzzy solution. We present an example to illustrate applicability of the proposed method. More >

M. De Munck¹, D. Moens², W. Desmet³, D.Vandepitte³

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.2, pp. 119-166, 2009, DOI:10.3970/cmes.2009.047.119

Abstract Deterministic simulation tools enable a very precise simulation of physical phenomena using numerical models. In many real life situations however, a deterministic analysis is not sufficient to assess the quality of a design. In a design stage, some physical properties of the model may not be determined yet. But even in a design ready for production, design tolerances and production inaccuracies introduce variability and uncertainty. In these cases, a non-deterministic analysis procedure is required, either using a probabilistic or a non-probabilistic approach. The authors developed an intelligent Kriging response surface based optimisation procedure that can More >