Fuzzy Regression and Interpolation with Application to Fuzzy Reliability

本研究旨在发展一种基于模糊集理论的方法，将不确定和不精确的数据用于回归和内插，并进一步应用于可靠性分析。具体地说，将使用应用于线性和非线性回归的各种回归性能度量来研究对称和非对称隶属函数情况下的模糊回归建模。模糊插值技术将使用样条插值法和克里格法来开发。作为拟议的方法发展的结果，将为在技术领域正确使用模糊集和贝叶斯技术提供指导方针，包括危险废物设施的设计问题以及结构和地质环境系统的可靠性评估。该项目是与L.Duckstein提出的ECS-8802920提案合作的。这两个PI在模糊集研究方面都很有名气，都很有资格进行这项研究。他们各自的机构--内布拉斯加州和亚利桑那州--为这项工作提供了非常合适的环境。建议为88财年发放19865美元的赔偿金，89财年继续发放44579美元的赔偿金。

The proposed research is to develop a methodology based on fuzzy set theory for the utilization of uncertain and imprecise data in regression and interpolation, with further application to reliability analysis. Specifically, fuzzy regression modeling in the cases of both symmetric and non-symmetric membership functions will be investigated using various regression performance measures, applied to linear and nonlinear regression. Fuzzy interpolation techniques will be developed using spline interpolation and kriging. As a result of the proposed methodological developments, guidelines will be provided for the proper use of fuzzy set and Bayesian techniques in technical areas including design issues in hazardous waste facilities and the reliability assessment of structures and geo-environmental systems. This project is in cooperation with proposal ECS-8802920 by L. Duckstein. Both PIs are renowned in fuzzy set research and well qualified to conduct the research. Their respective institutions, Nebraska and Arizona provide more than suitable environments for the work. An award at the level of $19,865 is recommended for FY88 with a continuation for $44,579 for FY89.