JSM 2005 Online Program

Abstract #302339

This is the preliminary program for the 2005 Joint Statistical Meetings in Minneapolis, Minnesota. Currently included in this program is the "technical" program, schedule of invited, topic contributed, regular contributed and poster sessions; Continuing Education courses (August 7-10, 2005); and Committee and Business Meetings. This on-line program will be updated frequently to reflect the most current revisions.

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Activity Number:	3
Type:	Invited
Date/Time:	Sunday, August 7, 2005 : 2:00 PM to 3:50 PM
Sponsor:	JASA, Reviews
Abstract - #302339
Title:	Membership Functions and Probability Measures of Fuzzy Sets
Author(s):	Nozer D. Singpurwalla*+
Companies:	George Washington University
Address:	Department of Statistics, Washington, DC, 20052, United States
Keywords:	Subjective Probability ; Bayes' Law ; Likelihood ; Expert Testimony
Abstract:	The notion of fuzzy sets has proven useful in control theory, pattern recognition, medical diagnosis, and computer science. However, it also has spawned the view that probability theory is unable to deal with uncertainties in natural language processing and machine learning so that alternatives to probability are needed. One such alternative is possibility theory. Once any alternative to probability is adopted, the usual tools of the trade used by probabilists and statisticians (Bayesians and frequentists alike) lose their purpose. The aim of this talk is to propose a line of argument that demonstrates that probability and fuzzy set theory can be made to work in concert, so that probability measures can be endowed on fuzzy sets. The philosophical underpinnings that make this happen are a subjectivistic interpretation of probability, Bayes law, the mathematics of encoding expert testimonies, and Laplace's famous argument on the nature of uncertainty.

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