Propagation of Random Perturbations under Fuzzy Algebraic Operators

  • Authors:

  • Zheng Zheng;Shanjie Wu;Kai-Yuan Cai

  • Affiliations:

  • Department of Automatic Control, Beijing University of Aeronautics and Astronautics, Beijing, China 10083;Department of Automatic Control, Beijing University of Aeronautics and Astronautics, Beijing, China 10083;Department of Automatic Control, Beijing University of Aeronautics and Astronautics, Beijing, China 10083

  • Venue:
  • KSEM '09 Proceedings of the 3rd International Conference on Knowledge Science, Engineering and Management
  • Year:
  • 2009

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Abstract

Since the introduction of fuzzy sets theory, fuzzy method made successful applications in many areas, such as fuzzy control and intelligent decision systems. In these areas, there are usually random perturbations caused by the constantly changing of real situations, thus the analysis of the stability and robustness is an important issue for the applications. In the side of fuzzy methods, we have a corresponding problem: will a small random perturbation of input cause a big oscillation of output of a fuzzy method? In particular, when the distributions of random perturbations are given, what is the propagation of random perturbations in fuzzy schemes? In this paper, we start to answer the question. We estimate the expectation of the propagated perturbations under different fuzzy algebraic operators with two analysis methods. Some examples are presented to show the effectiveness and features of the analysis methods.