Towards Foundations of Processing Imprecise Data: From Traditional Statistical Techniques of Processing Crisp Data to Statistical Processing of Fuzzy Data

Authors

Hung T. Nguyen
Tonghui Wang
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

1-2003

Comments

UTEP-CS-02-31a.

Published in Yingming Liu, Guoqing Chen, Mingsheng Ying and Kai-Yuan Cai (eds.), Proceedings of the International Conference on Fuzzy Information Processing: Theories and Applications FIP'2003, Beijing, China, March 1-4, 2003, Vol. II, pp. 895-900.

Abstract

In traditional statistics, we process crisp data - usually, results of measurements and/or observations. Not all the knowledge comes from measurements and observations. In many real-life situations, in addition to the results of measurements and observations, we have expert estimates, estimates that are often formulated in terms of natural language, like "x is large". Before we analyze how to process these statements, we must be able to translate them in a language that a computer can understand. This translation of expert statements from natural language into a precise language of numbers is one of the main original objectives of fuzzy logic. It is therefore important to extend traditional statistical techniques from processing crisp data to processing fuzzy data. In this paper, we provide an overview of our related research.