تجزیه و تحلیل سیستم های دینامیکی که ورودی آنها فرآیندهای تصادفی فازی می باشد
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|20453||2002||8 صفحه PDF||سفارش دهید||3858 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Fuzzy Sets and Systems, Volume 129, Issue 1, 1 July 2002, Pages 111–118
This paper considers systems whose input signals are fuzzy stochastic processes of second order. The analysis is entirely restricted to discrete time linear time-invariant systems. Convergence conditions of the output are given. The equations on the mean value functions and the covariance functions are derived. The representation of fuzzy stochastic processes is also discussed.
Analysis and design of complex systems often in- volve two kinds of uncertainty: randomness and fuzzi- ness. The randomness models stochastic variability and fuzziness models measurement imprecision due to linguistic structure or incomplete information. In some 8elds of application, suchas reliability modeling, de- cision making, data analysis, software reliability and earthquake prediction [2,3,7,10,13,18,19], the uncer- tainty arises from bothrandomness and fuzziness si- multaneously, and exceeds the realm of the classical probability theory and fuzzy set theory. The concept of fuzzy random variables were introduced by Kwark- ernaak , Puri and Ralescu  to describe fuzzy random quantities. The studies of fuzzy random vari- ables ranged from expectation, limit theorem  to martingale [4,16]. For analytical treatment of systems subjected to fuzzy random excitations, Wang and Zhang [17,20] studied the general theory of fuzzy stochastic processes and fuzzy stochastic dynamical systems. However, neither the covariance de8ned in Ref.  is a fuzzy number, nor does it ful8ll some main properties of covariance. Recently, Korner , Feng et al.  de8ned a real-valued covariance of fuzzy random variables that makes well-de8ned sense. In this paper, we will consider a linear time- invariant dynamical system withone input u and one output y . Assuming that the system is characterized by its weighting function h , the input–output relation f the input signal u is a fuzzy stochastic process, the response y is also a fuzzy stochastic process (Fig. 1). The problem is then to 8nd the relationships between the fuzzy random properties of the output y and those of the input u . Because of the intrinsical nonlinear- ity of fuzzy linear algorithms, some conclusions of stochastic systems  cannot be directly extended to their fuzzy counterparts. The present paper is organized as follows. In Section 2, we state some results of fuzzy stochastic processes of second order. In Section 3, conditions for the output to be a fuzzy stochastic process of second order are speci8ed. Then the characteristic equations are derived for fuzzy stochastic systems of nonnegative weighting function, symmetric member- ship or general case. Illustrative examples are given. Section 4 is dedicated to the representation of fuzzy stochastic processes.