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

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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.