Modeling of subjective judgments of a researcher about the research object model

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 $x\in X$.