一类随机模糊微分包含解集性质的研究及其应用

The theory of stochastic fuzzy differential equations (SFDE) is an effective tool to depict the uncertain dynamic systems of randomness and fuzziness, which is of broad application. A class of stochastic fuzzy differential inclusions (SFDI) is studied in this research as a generalization of SFDE to set-valued situation, based on the ideas of set-valued analysis, fuzzy analysis and stochastic analysis. The selection theorems and the fixed point theorems are empolyed to discuss the existence and the properties of the solution sets, including the existence conditions and description of the strong solutions and the weak solutions. As an application, the results of the research could be utilized to study the dynamic development models of some oilfield blocks considering randomness and fuzziness, which could provide theoretical basis for the reasonable development plans and decisions of an oilfield. The research of this project can not only develop the theory, methods and techniques of SFDI, but also offer us some effective methods to solve the uncertain optimization and control problems coming from the reality.

随机模糊微分方程是描述同时具备随机性和模糊性的不确定动态系统的有效方法，其应用非常广泛。随机模糊微分包含是随机模糊微分方程在集值形式下的推广，本项目拟结合集值分析，模糊分析和随机分析的思想，利用选择定理和不动点定理等工具，研究一类随机模糊微分包含问题解的存在性及解集的性质，给出该类随机模糊微分包含强解和弱解的存在性条件以及解集性质的刻画结果。作为应用，所得结果将被用于研究某些油田区块考虑随机性和模糊性的开发动态模型及其解集性质，为进行合理的开发规划和决策提供理论依据。本项目的研究成果不仅可以发展研究随机模糊微分包含问题的理论、方法和技巧，还可以为产生于现实世界中的一些不确定性优化和控制问题提供有效的解决办法。