A Broad Prospective on Fuzzy Transforms: From Gauging Accuracy of Quantity Estimates to Gauging Accuracy and Resolution of Measuring Physical Fields

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Irina Perfilieva

Publication Date

11-2009

Comments

Technical Report: UTEP-CS-09-16b

A short version was published in Abstracts of the 10th International Student Conference on Applied Mathematics and Informatics ISCAMI, Malenovice, Czech Republic, May 13-15, 2009; full paper published in Neural Network World, 2010, Vol. 20, No. 1, pp. 7-25.

Abstract

Fuzzy transform is a new type of function transforms that has been successfully used in different application. In this paper, we provide a broad prospective on fuzzy transform. Specifically, we show that fuzzy transform naturally appears when, in addition to measurement uncertainty, we also encounter another type of localization uncertainty: that the measured value may come not only from the desired location x, but also from the nearby locations.