Approximating sensor signals: a rough set approach

This paper presents an approach to approximating sensor signals. In classical rough set theory, set approximation is carried out in non-empty, finite universes of objects. In contrast, we carry out set approximation inside non-empty, uncountable sets (universes) of points. This study is motivated by an interest in classifying sample values for various types of sensors. The result of this study is the introduction of a family of discrete rough integrals based on rough set theory. The discrete rough integrals have practical implications, since these integrals serve as an aid in approximate reasoning and in pattern recognition relative to segments of continuous signals. In the context of approximate reasoning, discrete rough integrals provide a basis for determining the relevance of sensors over a particular sampling period. In the context of pattern recognition, discrete rough integrals can be useful in doing such things as classifying radar weather data, vehicular traffic patterns, and waveforms of power system faults. By way of illustration, one form of discrete integral is used to assess the accuracy of set approximation of a sensor signal.