Abstract: The definitions of fuzzy random theory and fuzzy probabilistic fracture mechanics are given.The applications of fuzzy probabilistic fracture mechanics in petroleum engineering and the fuzzy random theory in petroleum engineering management are introduced.A quantitative description method for uncertainties of stress and strength, as well as a fuzzy decision method for petroleum engineering are provided.The assessment methods for safety and reliability of petroleum engineering and equipment in service are given.The problems about fuzzy optimum design of petroleum engineering and equipment are discussed.A fuzzy optimum method for risk analysis in management engineering is given.

Key words: fuzziness, randomness, fracture mechanics, petroleum engineering, petroleum equipment, management engineering, application study

摘要： 给出了模糊随机理论及模糊概率断裂力学的定义,介绍了模糊概率断裂力学在石油工程中的应用及模糊随机理论在石油管理工程中的应用,提出了定量描述应力与强度的不确定性的方法,给出了石油工程及装备在服役期间的安全可靠性评估方法及管理工程中的模糊决策方法,讨论了石油工程与装备的模糊优化设计问题,提出了石油工程中模糊优化风险分析的管理方法.

关键词: 模糊, 随机, 理论, 断裂力学, 石油工程, 石油装备, 管理工程, 应用研究