Geodesic
Modeling of subjective judgments of a researcher about the research object model
Matematičeskoe modelirovanie, Tome 25 (2013) no. 4, pp. 102-125 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : intellectual dialogue. 
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     author = {Y. P. Pyt'ev},
     title = {Modeling of subjective judgments of a researcher about the research object model},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {102--125},
     year = {2013},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2013_25_4_a8/}
}
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Y. P. Pyt'ev. Modeling of subjective judgments of a researcher about the research object model. Matematičeskoe modelirovanie, Tome 25 (2013) no. 4, pp. 102-125. http://geodesic.mathdoc.fr/item/MM_2013_25_4_a8/

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