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Problems of States Estimation (Filtration) of Extremal Fuzzy Processes

  • Gia Sirbiladze
Chapter
Part of the IFSR International Series on Systems Science and Engineering book series (IFSR, volume 28)

Abstract

A fuzzy-integral model of an extremal fuzzy process is considered. The model describes the evolution of one class of weakly structurable fuzzy dynamic systems, i.e., of the so-called extremal fuzzy dynamic systems constructed in Chap. 5. In the present chapter, problems of an optimal filtering of continuous as well as of discrete extremal fuzzy processes are solved by means of “past” evaluating information. Sufficient conditions are established for the existence of an optimal estimating fuzzy process. Using only one “past” evaluating fuzzy state of the considered system, variants of fuzzy observers (representations of an optimal estimating extremal fuzzy process) are constructed in terms of approximation of piecewise-constant and extremal measurable filtration functions for continuous and discrete extremal fuzzy dynamic systems. The results obtained are illustrated by a numerical example.

Keywords

Time Moment Optimal Estimate Fuzzy Function Compatibility Function Fuzzy State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Gia Sirbiladze
    • 1
  1. 1.Department of Computer SciencesIv. Javakhishvili Tbilisi St. UniversityTbilisiGeorgia

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