Abstract:
We discuss the methods of mathematical modeling of incomplete and
uncertain knowledge of the model $M(x)$ of research object,
expressed in a form of subjective judgments of the researcher
about possible values of unknown parameter $x\in X$ which
determines the model. The mathematical model of “subjective
judgements” is defined as space $(X,{\mathcal
P}(X),\mathrm{P}\mathrm{l}^{\widetilde{x}},\mathrm{Be}\mathrm{l}^{\widetilde{x}})$
where indeterminate element $\widetilde{x}$ characterizes (as
undefined propositional variable) researcher's subjective
judgments about the validity of each value $x\in X$ by values of
measures of Plausibility $\mathrm{P}\mathrm{l}^{\widetilde{x}}$ of
the equality $\widetilde{x}=x$ and of Belief
$\mathrm{Be}\mathrm{l}^{\widetilde{x}}$ of the inequality
$\widetilde{x}\not=x$. If the researcher has some observational
data of the object, he/she can use it to build an empirical
estimate of the indeterminate element $\widetilde{x}$ and
empirical model $(X,{\mathcal
P}(X),\mathrm{P}\mathrm{l}^{\widetilde{x}},\mathrm{Be}\mathrm{l}^{\widetilde{x}})$
of subjective judgements about possible values of $x\in X$.
Keywords:integral, measure, measure of plausibility, measure of belief, indeterminate random element, random indeterminate element, intellectual dialogue.
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