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首页> 外文期刊>Moscow University Physics Bulletin >Mathematical Modeling of Randomness and Fuzziness Phenomena in Scientific Studies: I. Mathematical and Empirical Foundations
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Mathematical Modeling of Randomness and Fuzziness Phenomena in Scientific Studies: I. Mathematical and Empirical Foundations

机译：科学研究中随机性和模糊现象的数学建模：I。数学与实证基础

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摘要

The possibility theory as a mathematical model of randomness and fuzziness phenomena is considered in a variant that enables the modeling of both probabilistic randomness, including that inherent in unpredictably evolving stochastic objects whose probabilistic models cannot be empirically reconstructed and nonprobabilistic randomness (fuzziness) inherent in real physical, technical, and economical objects, human-machine and expert systems, etc. Some principal distinctions between the considered variant and the known possibility theory variants, in particular, in mathematical formalism and its relationship with probability theory, substantive interpretation, and applications exemplified by solving the problems of identification and estimation optimization, empirical reconstruction of a fuzzy model for a studied object, measurement data analysis and interpretation, etc. (in the paper "Mathematical Modeling of Randomness and Fuzziness Phenomena in Scientific Studies. II. Applications") are shown.
机译：作为随机性和模糊现象的数学模型的可能性理论是在变体中考虑的，这使得能够建模概率随机性，包括不可预测的随机性随机对象中固有的，其概率模型不能经验重建，并且真实地固有的非产品无序（模糊）物理，技术和经济体，人机和专家系统等。所考虑的变体和已知的可能性理论变体之间的一些主要区别，特别是在数学形式主义和与概率理论，实质性解释和应用中的关系中通过解决识别和估计优化的问题，对研究对象，测量数据分析和解释等的模糊模型的实证重构（论文“在科学研究中随机性和模糊现象的数学建模。II。应用程序”） AR. e显示。

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