How to extract the most from uncertain and incomplete information? From optimal fuzzy control to optimal guaranteed data processing.

Abstract

This talk is about the distinction, relation and co-existence of two popular types of uncertainty involving in systems analysis, namely Randomness and Fuzziness. We will examine these relations from a theoretical viewpoint. While fuzzy concepts in a natural language are modeled by membership functions with their own logics, there exists a formal relation with randomness via the concept of random sets. However, these two types of uncertainty are different in their modeling capability. A very general algebraic framework, known as Chu spaces, can be used to treat these two different uncertainties in a single setting, suitable for data fusion problems in which both randomness and fuzziness are present. Mathematical foundations of fuzzy technology. 講　題：How to extract the most from uncertain and incomplete information? From optimal fuzzy control to optimal guaranteed data processing 主講人：Prof. Vladik Kreinovich (Department of Computer Sciences, University of Texas at El Paso, El Paso, TX 79968 U.S.A) 摘 要 In many real-life situations, we need to make a decision in a situation in which the available information is uncertain and incomplete. Such situations have been studied in science and engineering for centuries, from Gauss' pioneer work on statistical uncertainty to the late 20th century Artificial Intelligence research into different types of expert uncertainty. As a result, for almost every type of uncertainty and incompleteness, there exists at least one (and usually many) methods and techniques for handling uncertainty of this type. So, instead of the old question - How to process uncertainty and incompleteness? A natural next question is: Which of the methods for handling uncertainty and incompleteness is the best? or, in other words - How to extract the most from the uncertain and incomplete information? In this talk, we will mention a novel approach which has already lead to the optimal choices of non-linearity's in fuzzy control, neural networks, genetic algorithms, interval computations, etc.