Three-Level and Three-Way Vagueness Similarity Measurements for Electrocardiogram (ECG) Data Analysis

Abstract

Vagueness similarity measures (VS-Measures) establish similarity criteria to represent similarity degrees between vague sets, and they underlie uncertainty measurements and data analysis. VS-Measures have been applied to various fields of intelligent processing, including electrocardiogram (ECG) data analysis; however, their relevant hierarchy and diversity are rarely concerned. In this paper, a three-level and three-way strategy is systematically proposed for VS-Measures modeling, so three-longitudinal and three-horizontal uncertainty measurements are eventually implemented for ECG data analysis. At first, three vagueness factors, i.e., the truth and false membership functions t, f and hesitance function h (where t+f+h = 1), are utilized to construct three measurement certainty/uncertainty levels, and part and complete support functions $\mu$, M and opposition functions $\nu$, N are designed. The initial certainty level involves a general pair (t, f) without h, and its certainty can be enhanced by discretely reducing h uncertainty to improve measurements; thus, two novel levels with part and complete certainty-enhancements respectively resort to ($\mu,\nu$) and (M, N), and their uncertainty degrees respectively gain a part surplus h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and no remainders. Then, three characteristic types of VS-Measures at the basic level (t, f) are chosen to be promoted to the improved levels ($\mu,\nu$) and (M, N), so nine types of VS-Measures emerge on the three-level and three-way net. Their basic properties, optimal algorithms, and systematic relationships are achieved, and are effectively verified by data examples and simulation experiments. Finally, all VS-Measures are applied to the QRS-Wave pattern recognition and systematic optimization estimation of ECG data from the MIT-BIH Arrhythmia Database, and the improved level and measure exhibit the potential superiority and better performance. The three-level and three-way similarity measurements realize criss-cross informatization for vagueness, and they facilitate further intelligent pattern recognition and automatic medical diagnosis of ECG data analysis.