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【北航数学论坛】_From Data to Fuzzy Set Models for Words
ag平台网址:2014-07-04  浏览量:

题目:From Data to Fuzzy Set Models for Words




主讲人: Jerry. M. Mendel教授


Jerry. M. Mendel教授,于1963年博士毕业于美国纽约布鲁克林理工ag平台app下载,自1974年至今任教于美国南加州大学电子工程系,主要从事二型模糊逻辑系统理论及其应用方面的研究,包括智能油田技术、语言计算以及模糊集定性比较分析等。Jerry. M. Mendel教授是二型模糊逻辑系统的创始人,在智能科学与计算、控制系统等领域取得了卓越的研究成果,发表了550多篇学术论文,亲著或合著10本书籍,包括Uncertain Rule-based Fuzzy Logic Systems: Introduction and New Directions (Prentice-Hall, 2001), Perceptual Computing: Aiding People in Making Subjective Judgments (Wiley & IEEE Press, 2010), and Advances in Type-2 Fuzzy Sets and Systems (Springer 2013),在该领域获得多项殊荣,包括2002年和2014年Transactions on Fuzzy Systems杰出论文奖、IEEE百年奖章与千禧奖章以及2008年荣获IEEE计算智能协会授予的模糊系统先驱者奖章等。Jerry. M. Mendel教授现任IEEE终身会士,IEEE控制系统协会杰出会员、国际模糊系统协会会士和IEEE Transactions on Fuzzy Systems杂志副主编,1986年曾任IEEE控制系统协会主席,曾任9年IEEE计算智能协会管理委员会委员,以及计算智能协会模糊系统技术委员会Computing with word专门工作组主席。


Computing with words uses fuzzy set models for the words. Because words mean different things to different people, the fuzzy set models must be able to simultaneously capture the uncertainty each subject has about a word as well as the uncertainty a group of subjects has about that word. This can be accomplished by using an interval type-2 fuzzy set (IT2 FS) word model. In order to incorporate the two kinds of word uncertainties into an IT2 FS, data must be collected from a group of subjects, after which the data are mapped into an IT2 FS. The data collection method must not introduce methodological uncertainties, because such uncertainties can not be separated out from the word uncertainties; hence, we never ask a subject to provide us with the membership function for a fuzzy set, because most subjects have no idea what a fuzzy set and a membership function are. Instead, we ask a subject a question like: On a scale of 0–10 where would you locate the end points of an interval that you associate with this word?

Once the data have been collected it must be mapped into an IT2 FS. In this talk I will describe three methods that we have developed (since 2006) for doing this, each method extracting more information from the data. All three methods begin by assuming that a subject’s data interval is uniformly distributed in a probabilistic sense. As a result, each method can be interpreted as a nonlinear transformation of independent uniformly-distributed random variables. Randomness does not disappear just because the resulting IT2 FS model is a fuzzy set. Probability and statistics play very important roles in all three methods. All of this will be explained during this talk. Examples will be shown for IT2 FS word models obtained from data collected from groups of subjects. Hopefully, this talk will inspire you to research this very interesting and important interface between probability and fuzzy sets.

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