Fuzzy identification problem for continuous extremal fuzzy dynamic system |
| |
Authors: | Gia Sirbiladze |
| |
Institution: | (1) University of Nebraska at Omaha, Omaha, NE, U.S.A;(2) Binghamton University, Binghamton, NY, U.S.A |
| |
Abstract: | This work deals with the problems of the Continuous Extremal Fuzzy Dynamic System (CEFDS) optimization and briefly discusses
the results developed by Sirbiladze (Int J Gen Syst 34(2):107–138, 2005a; 34(2):139–167, 2005b; 34(2):169–198, 2005c; 35(4):435–459,
2006a; 35(5):529–554, 2006b; 36(1): 19–58, 2007; New Math Nat Comput 4(1):41–60, 2008a; Mat Zametki, 83(3):439–460, 2008b).
The basic properties of extended extremal fuzzy measures and Sugeno’s type integrals are considered and several variants of
their representation are given. Values of extended extremal conditional fuzzy measures are defined as a levels of expert knowledge
reflections of CEFDS states in the fuzzy time intervals. The notions of extremal fuzzy time moments and intervals are introduced
and their monotone algebraic structures that form the most important part of the fuzzy instrument of modeling extremal fuzzy
dynamic systems are discussed. A new approach in modeling of CEFDS is developed. Applying the results of Sirbiladze (Int J
Gen Syst 34(2) 107–138, 2005a; 34(2):139–167, 2005b), fuzzy processes with possibilistic uncertainty, the source of which
are expert knowledge reflections on the states on CEFDS in extremal fuzzy time intervals, are constructed (Sirbiladze in Int
J Gen Syst 34(2):169–198, 2005c). The dynamics of CEFDS’s is described. Questions of the ergodicity of CEFDS are considered.
A fuzzy-integral representation of a continuous extremal fuzzy process is given. Based on the fuzzy-integral model, a method
and an algorithm are developed for identifying the transition operator of CEFDS. The CEFDS transition operator is restored
by means of expert data with possibilistic uncertainty, the source of which is expert knowledge reflections on the states
of CEFDS in the extremal fuzzy time intervals. The regularization condition for obtaining quasi-optimal estimator of the transition
operator is represented by the theorems. The corresponding calculating algorithm is provided. The results obtained are illustrated
by an example in the case of a finite set of CEFDS states. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|