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Matem. Mod., 2013, Volume 25, Number 4, Pages 102–125 (Mi mm3356)  

This article is cited in 6 scientific papers (total in 6 papers)

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

Y. P. Pyt'ev

Lomonosov Moscow State University, Faculty of Physics

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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English version:
Mathematical Models and Computer Simulations, 2013, 5:6, 538–557

Bibliographic databases:

UDC: 519.21
Received: 15.11.2012

Citation: Y. P. Pyt'ev, “Modeling of subjective judgments of a researcher about the research object model”, Matem. Mod., 25:4 (2013), 102–125; Math. Models Comput. Simul., 5:6 (2013), 538–557

Citation in format AMSBIB
\Bibitem{Pyt13}
\by Y.~P.~Pyt'ev
\paper Modeling of subjective judgments of a researcher about the research object model
\jour Matem. Mod.
\yr 2013
\vol 25
\issue 4
\pages 102--125
\mathnet{http://mi.mathnet.ru/mm3356}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3114889}
\transl
\jour Math. Models Comput. Simul.
\yr 2013
\vol 5
\issue 6
\pages 538--557
\crossref{https://doi.org/10.1134/S2070048213060094}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84929088929}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. A. Balakin, Yu. P. Pytev, “Reduktsiya izmereniya pri nalichii sub'ektivnoi informatsii”, Matem. modelirovanie, 30:12 (2018), 84–110  mathnet
    2. D. A. Balakin, “Numerical methods for computing plausibility and belief distributions of consequences of a subjective model of object of research”, Comput. Math. Math. Phys., 58:5 (2018), 790–802  mathnet  crossref  crossref  isi  elib
    3. Zubyuk V A., “A New Approach to Specificity in Possibility Theory: Decision-Making Point of View”, Fuzzy Sets Syst., 364 (2019), 76–95  crossref  isi
    4. Belov S.Yu., Belova I.N., Turbulence, Atmosphere and Climate Dynamics, IOP Conf. Ser. Earth Envir. Sci., IOP Conference Series-Earth and Environmental Science, 231, IOP Publishing Ltd, 2019  crossref  isi
    5. Mikheev N.G., Chulichkov I A., Antonyuk V.A., “The Algorithm For Reconstruction Piecewise Constant Image Distorted By a Linear Transformation”, Proceedings of Spie, 11433, eds. Osten W., Nikolaev D., Zhou J., Spie-Int Soc Optical Engineering, 2020, UNSP 114331S  crossref  isi
    6. Balakin D.A., “Reduction of Images to the Form Typical For Measuring the Distribution of Object Transparency With Subjective Information About Its Sparsity in a Given Basis”, Mosc. Univ. Phys. Bull., 75:1 (2020), 26–34  crossref  isi
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