NSF-CGP Science Fellowship Program: Statistical Decision Analysis with Fuzzy Information

WPC(2 B V V Z Z Courier 10cpi Able)？X，高x 6X@8；X@HP LaserJet III HP_LJ_3.PRS x@，\，X@CCCddCYdYdYCdd88d8 ddJN8dd ddYYdY C dd dddCCCC DDDD ddd8 Y~YC8C8C8C8 d Y d DSD Y d~Y~Y d dC8C8C8C8 d d d J JkNkNkNkNkN~8~8 d JkN~8 d Y d~8 d JkN~8 d C dd CC/N d ddCYQQdd DDD dFdddd F CC HHD 44 ddzz d w oo DCH d F“d h d”DCC z XC d DOD DCD Yds z UWD Y Y CZ~o zo Y~N Y d YC8 Y o O Y d Y zsdzd~Y Y z o zzNd88YYzYz z ZZ CCddd dd zzzzzzzzzzzzzzzzzzzNNNNNNNdddddddddddddddddddd888888888888YYYYYYYYYYYYYYYYYYYzzzzzzzzzzzzzzzzzzzzC S~C ZC d DYC x t III HP_LJ_3.PRS X w P 7，\，X P 2 Z N Courier#|x x 6 X@`7 X@HP LaserJet 4 HPLAS4.PRS x@\X@2 P T#|x 2&amp；9303202 Ralescu该奖项将支持美国国家科学基金会/CGP(全球伙伴关系中心)科学奖学金计划下为俄亥俄州辛辛那提大学数学系教授Dan A.Ralescu提供的为期两年的资助。Ralescu教授将与日本东京工业大学系统科学系的Michio Sugeno博士进行为期12个月的合作研究项目。研究的重点是模糊信息的统计决策分析。直到最近，有关模糊技术的研究都是在模糊模型的假设下进行的，而不是在模糊随机模型中包含更现实的混合。研究人员将把统计推断的方法应用于包含概率信息和模糊信息的情况。他们将研究五种模型：(A)数据是模糊集，但模型是随机的，即基于经典概率的情况；(B)数据是数字的，但模型是模糊的(即，基于模糊概率的)双重情况；(C)具有模糊先验信息的贝叶斯分析框架；(D)带有模糊参数的概率分布；以及(E)可用模糊集表示的经典统计学的方面(如假设检验)。用于研究这些模型的技术包括经典概率和统计推理、随机集理论及其与贝叶斯稳健性的关系、涉及模糊度量和其他非加性度量、模糊随机变量和模糊值概率度量的技术。这项研究的结果可能包括可能用于商业产品，如自动反光相机、无人直升机和机器人。日本在模糊系统和技术的研究方面处于领先地位，杉野博士是非加法测量和模糊控制研究的先驱之一。Sugeno博士的实验室目前参与了关于模糊控制的有意义的实用研究，例如驾驶无人驾驶直升机。人们相信，合作者之间的这项研究将是富有成效的，并可能在未来几年内以非正式的方式继续进行。

WPC( 2 B V V Z Z Courier 10cpi able) ? x x x , h x 6 X @ 8 ; X @ HP LaserJet III HP_LJ_3.PRS x @ , \ , X @ CCCddCYdYdYCdd88d8 ddddJN8dd ddYYdY C dd dddCCCC dddddd ddd8 Y Y Y Y Y Y~Y~Y~Y~YC8C8C8C8 d d d d d d d d d d Y d d d d dsd Y Y Y Y Y Y Y d~Y~Y~Y~Y d d d d d d d dC8C8C8C8 oN d~8~8~8~8~8 d v d d d d J J JkNkNkNkN~8~8~8 d d d d d d d Y Y Y d~8 d JkN~8 d d d d d C dd C CC/ N d ddCYQQdd ddd dFdddd F CC hhd 44 ddzz d d d w oo dCh d F" d h dÕ dCC z xC d dod dCd Yds z Uw d Y Y C C C C z~o zo Y~N Y d YC8 Y o o Y d Y zsdzd d~Y Y z o zzzzNd88YYYzYz z zz CCddddd dd zzzzzzzzzzzzzzzzzzzNNNNNNNdddddddddddddddddddd888888888888YYYYYYYYYYYYYYYYYYYzzzzzzzzzzzzzzzzzzzzC s ~ C zC d dYC x t III HP_LJ_3.PRS X w P 7 , \ , X P 2 Z N Courier #| x x 6 X @ `7 X @ HP LaserJet 4 HPLAS4.PRS x @ \ X @ 2 P T #| x 2 & 9303202 Ralescu This award will support a two year grant under the NSF/CGP (Center for Global Partnership) Science Fellowship Program for Professor Dan A. Ralescu, Department of Mathematics, Univer sity of Cincinnati in Ohio. Professor Ralescu will undertake a twelve month cooperative research project with Dr. Michio Sugeno, Department of Systems Science, Tokyo Institute of Technology in Japan. The research will focus on statistical decision analysis with fuzzy information. Until recently, the research concerning fuzzy technologies was carried out under the assumption of a fuzzy model, rather that the more realistic mixture involved in a fuzzy random model. The researchers will apply methods of statistical inference to situations which contain a mixture of probabilistic and fuzzy information. They will study five models: (a) situations when the data are fuzzy sets, but the model is random, i.e. based on classical probabilities; (b) the dual situation where the data are numerical, but the model is fuzzy (i.e. based on fuzzy probabilities; (c) the framework of Bayesian analysis with fuzzy prior information; (d) distributions of probability with fuzzy parameters; and (e) aspects of classical statistics (such as hypothesis testing) which can be stated in terms of fuzzy sets. The techniques used to investigate these models include classical probability and statistical inference, random set theory, and their relationships with Bayesian robustness, techniques involving fuzzy measures and other nonadditive measures, fuzzy random variables, and fuzzy valued probability measures. Results of the research will likely include possible use in commercial products such as autoreflex cameras, unmanned helicopters, and robotics. Japan is in the forefront of research in fuzzy systems and technology and Dr. Sugeno is one of the pioneers in research on nonadditive measures and fuzzy control. Dr. Sugeno's Laboratory is currently involved in meaningful practical research on fuzzy control such as the piloting of an unmanned helicopter. It is believed that this research between the collaborators will be productive and will likely continue on an informal basis over the coming years.