Diptiranjan Behera¹, Snehashish Chakraverty²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.5, pp. 317-337, 2013, DOI:10.3970/cmes.2013.096.317

Abstract This paper targets to analyse the static response of structures with fuzzy parameters using fuzzy finite element method. Here the material, geometrical properties and external load applied to the structures are taken as uncertain. Uncertainties presents in the parameters are modelled through convex normalised fuzzy sets. Fuzzy finite element method converts the problem into fuzzy or fully fuzzy system of linear equations for static analysis. As such here, two new methods are proposed to solve the fuzzy and fully fuzzy system of linear equations. Numerical examples for structures with uncertain system parameters that are in term of triangular fuzzy number… More >

Zichun Yang^1,2,3, Kunfeng Li^1,4, Qi Cai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.2, pp. 143-171, 2013, DOI:10.3970/cmes.2013.095.143

Abstract The conventional probabilistic reliability model for structures is based on the “probability assumption” and “binary-state assumption”. These assumptions are often offset the reality of practical engineering and lead to a wrong conclusion. In fact, besides randomness, fuzziness which is different from randomness in nature is also a prevalent uncertainty factor and plays an important role in structural reliability assessment. In this paper, a novel structural reliability model with random variables and fuzzy variables is established by using the fuzzy set theory, possibility theory and probability measure for fuzzy events, based on the “mixed probability and possibility assumption” and “fuzzy state… 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 explicit formula. The features of… More >

Şahin Emrah Amrahov¹, Iman N. Askerzade¹

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.3&4, pp. 207-216, 2011, DOI:10.3970/cmes.2011.076.207

Abstract We consider a fuzzy linear system with crisp coefficient matrix and with an arbitrary fuzzy number in parametric form on the right-hand side. It is known that the well-known existence and uniqueness theorem of a strong fuzzy solution is equivalent to the following: The coefficient matrix is the product of a permutation matrix and a diagonal matrix. This means that this theorem can be applicable only for a special form of linear systems, namely, only when the system consists of equations, each of which has exactly one variable. We prove an existence and uniqueness theorem, which can be use on… More >

Nizami Gasilov¹, Şahin Emrah Amrahov², Afet Golayoğlu Fatullayev¹, Halil İbrahim Karakaş¹, Ömer Akın³

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 189-204, 2011, DOI:10.3970/cmes.2011.075.189

Abstract In this paper, linear systems with a crisp real coefficient matrix and with a vector of fuzzy triangular numbers on the right-hand side are studied. A new method, which is based on the geometric representations of linear transformations, is proposed to find solutions. The method uses the fact that a vector of fuzzy triangular numbers forms a rectangular prism in n-dimensional space and that the image of a parallelepiped is also a parallelepiped under a linear transformation. The suggested method clarifies why in general case different approaches do not generate solutions as fuzzy numbers. It is geometrically proved that if… More >

Şahin Emrah Amrahov¹, Iman N.Askerzade¹

CMES-Computer Modeling in Engineering & Sciences, Vol.70, No.1, pp. 1-10, 2010, DOI:10.3970/cmes.2010.070.001

Abstract In this paper we define multivariable fuzzy functions (MFF) and corresponding multivariable crisp functions (MCF). Then we give a definition for the maximum value of MFF, which in some cases coincides with the maximum value in Pareto sense. We introduce generalized maximizing and minimizing sets in order to determine the maximum values of MFF. By equating membership functions of a given fuzzy domain set and the corresponding maximizing set, we obtain a curve of equal possibilities. Then we use the method of Lagrange multipliers to solve the resulting nonlinear optimization problem when the membership functions are differentiable. We finally present… More >

S. Turrin¹, M. Hanss¹, A.P.S. Selvadurai²

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.3, pp. 237-258, 2009, DOI:10.3970/cmes.2009.052.237

Abstract Despite the continuing advances in rockfall analysis, the mathematical modeling and simulation of rockfall phenomena continues to be significantly influenced by a large amount of aleatory and epistemic uncertainty on significant number of model parameters. This paper focuses on the representation and quantification of epistemic uncertainties in rockfall modeling and simulation by fuzzy numbers. The propagation of the epistemic uncertainties considered is then calculated by the transformation method as a practical implementation of fuzzy arithmetic. Epistemic uncertainties on the material properties, on the boulder geometry and dimensions, on the kinematics of the impact and on the contact response between boulder… More >

F. Fleissner¹, T. Haag², M. Hanss², P. Eberhard¹

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.2, pp. 181-196, 2009, DOI:10.3970/cmes.2009.052.181

Abstract In alpine regions human settlements and infrastructure are at risk to be hit by landslides or other types of geological flows. This paper presents a new approach that can aid the design of protective constructions. An uncertainty analysis of the flow around a debris barrier is carried out using a chute flow laboratory model of the actual debris flow. A series of discrete element simulations thereby serves to compare and assess two different barrier designs. In this study, the transformation method of fuzzy arithmetic is used to investigate the influence of epistemically uncertain model parameters. It turns out that parameter… 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 be used in combination with… More >