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  • Open Access

    ARTICLE

    Application of Geometric Approach for Fuzzy Linear Systems to a Fuzzy Input-Output Analysis

    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 >

  • Open Access

    ARTICLE

    Strong Solutions of the Fuzzy Linear Systems

    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 >

  • Open Access

    ARTICLE

    A Geometric Approach to Solve Fuzzy Linear Systems

    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 >

  • Open Access

    ARTICLE

    Fuzzy Optimization of Multivariable Fuzzy Functions

    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 >

  • Open Access

    ARTICLE

    An Approach to Uncertainty Analysis of Rockfall Simulation

    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 >

  • Open Access

    ARTICLE

    Uncertainty Analysis for a Particle Model of Granular Chute Flow

    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 >

  • Open Access

    ARTICLE

    A New Approach to Non-Homogeneous Fuzzy Initial Value Problem

    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 >

  • Open Access

    ARTICLE

    An Efficient Response Surface Based Optimisation Method for Non-Deterministic Harmonic and Transient Dynamic Analysis

    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 >

  • Open Access

    ARTICLE

    Uncertain Knowledge Reasoning Based on the Fuzzy Multi Entity Bayesian Networks

    Dun Li1, Hong Wu1, Jinzhu Gao2, Zhuoyun Liu1, Lun Li1, Zhiyun Zheng1,*

    CMC-Computers, Materials & Continua, Vol.61, No.1, pp. 301-321, 2019, DOI:10.32604/cmc.2019.05953

    Abstract With the rapid development of the semantic web and the ever-growing size of uncertain data, representing and reasoning uncertain information has become a great challenge for the semantic web application developers. In this paper, we present a novel reasoning framework based on the representation of fuzzy PR-OWL. Firstly, the paper gives an overview of the previous research work on uncertainty knowledge representation and reasoning, incorporates Ontology into the fuzzy Multi Entity Bayesian Networks theory, and introduces fuzzy PR-OWL, an Ontology language based on OWL2. Fuzzy PR-OWL describes fuzzy semantics and uncertain relations and gives grammatical definition and semantic interpretation. Secondly,… More >

  • Open Access

    ARTICLE

    Designing and Optimization of Fuzzy Sliding Mode Controller for Nonlinear Systems

    Zhe Sun1, Yunrui Bi2, Songle Chen1, Bing Hu1, Feng Xiang3, Yawen Ling1, Zhixin Sun1, ∗

    CMC-Computers, Materials & Continua, Vol.61, No.1, pp. 119-128, 2019, DOI:10.32604/cmc.2019.05274

    Abstract For enhancing the control effectiveness, we firstly design a fuzzy logic based sliding mode controller (FSMC) for nonlinear crane systems. On basis of overhead crane dynamic characteristic, the sliding mode function with regard to trolley position and payload angle. Additionally, in order to eliminate the chattering problem of sliding mode control, the fuzzy logic theory is adopted to soften the control performance. Moreover, aiming at the FSMC parameter setting problem, a DE algorithm based optimization scheme is proposed for enhancing the control performance. Finally, by implementing the computer simulation, the DE based FSMC can effectively tackle the overhead crane sway… More >

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