Search for: [Abstract = "A stable non stationary linear system is considered. A quality criterion is represented by a functional in the integral form of the sum of positive polynomiaes with respect to the state variables and squared control. lt is proved that the optima\[ control is an irrational Junction of polynomial depending on the state variables. The minimum value of performance index can have two forms\: the hyperelliptic integral or polynomial depending on the initial state. In the presence of a prior information about the probability distribution that governs the random output of a statistical experiment we use the Bayes decisions methodology for verification of certain statistical hypotheses. In the case of precise statistical data or imprecise data described by a fuzzy information system the existing methodology is sufficient for testing of statistical hypotheses. In this paper we propose a new procedure that can be applied for the generał fuzzy statistical data. Concepts known from of the possibility theory, such as possibility and necessity indices, have been used in order_ to evaluate the correctness of Bayes decisions for imprecisely \(e.g. linguistically\) defined statistical data."]

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