Fuzzy hypotheses for GUHA implications

Abstract

This paper presents a fuzzy generalization of a sophisticated approach to exploratory data analysis, the general unary hypotheses automaton (GUHA). The GUHA paradigm, to automatically generate sentences of an observational calculus which are supported by given data, has been attracting attention for nearly 30 years. Most of the procedures for generating observational sentences, encountered in the existing implementations of the approach, are based on statistical hypotheses testing. However, there is an inner contradiction inherent to using common statistical tests to this end. Those tests always require a precise formulation of the tested conditions on the random variables characterizing the underlying real phenomena. On the other hand, due to its explorative purpose, GUHA is predominantly used in situations in which the user has only a rather vague knowledge of those random variables, thus being unable to precisely state the conditions to be tested. Therefore, a fuzzy generalization of the approach is proposed. It is based on a method of fuzzy hypotheses testing which was elaborated for the statistical tests used in GUHA and integrated into the context of an observational calculus. Due to space limitations, the paper concentrates on a particular kind of generated observational sentences — GUHA implications. The fuzzy counterparts of two key concepts pertaining to GUHA implications are defined, and a number of their properties are established. The proposed approach is illustrated on two commonly used GUHA implications.