A Fluctuation Theory of Systems by Fuzzy Mapping Concept and Its Applications (Special Section on Nonlinear Theory and Its Applications)

概要

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This paper proposes a methodology for fine evaluation of the uncertain behaviors of systems affected by any fluctuation of internal structures and internal parameters, by the use of a new concept on the fuzzy mapping. For a uniformly convex real Banach space X and Y, a fuzzy mapping G is introduced as the operator by which we can define a bounded closed compact fuzzy set G(x,y) for any (x,y) ⋳ X×Y. An original system is represented by a completely continuous operator f defined on X, for instance, in a form x=<hree;(f(x)) by a continuous operator <hree;:Y → X. The nondeterministic fluctuations induced into the original system are represented by a generalized form of the fuzzy mapping equation x ⋳G_β(x,f(x))=^^Δ{ξ⋳X|μ_<G(x,f(x))>(ξ)≧β}, in order to give a fine evaluation of the solutions with respect to an arbitrarily-specified β-level. By establishing a useful fixed point theorem, the existence and evaluation problems of the "β-level-likely" solutions are discussed for this fuzzy mapping equation. The theory developed here for the fluctuation problems is applied to the fine estimation of not only the uncertain behaviors of system-fluctuations but also the validity of system-models and -simulations with uncertain properties.
社団法人電子情報通信学会の論文
1994-11-25