Learning rules from examples under uncertainty--an approach based on rough-set boundaries and entropy

This research is about learning rules from examples. One contribution of this work is a simple strategy LERS/C for learning minimal production rules from both consistent and not necessarily consistent examples. In the proposed strategy, the difference between learning rules from consistent and inconsistent examples lies only in the inputs to the strategy. By incorporating proper search strategy, LERS/C can avoid the problem of attribute redundancies in ID3 and attribute-value pair redundancies in PRISM.; In the study, the problem of learning rules from examples is formulated by using the concepts of rough sets and information systems introduced by Pawlak. The notion of non-redundant attributes is formulated by the concept of covers of attributes, and the notion of non-redundant attribute-value pairs is formulated by the concept of minimal conjuncts. The induction of minimal production rules from examples is treated as a problem of finding covers of attribute-value pairs, which is a minimal set of minimal conjuncts.; The basis of finding covers of attributes and minimal conjuncts is the checking of dependencies of attributes and attribute-value pairs, respectively. We introduce the concept of rough-set boundaries to facilitate the checking of attribute dependency, and the checking of attribute-value pair dependency is done on the basis of difference of sets.; In general, the time for finding all covers of attributes (attribute-value pairs) is exponential, and it takes only polynomial time to find one cover of attributes (attribute-value pairs). Heuristics, based on rough-set boundaries and entropy function, for finding one cover of attributes and one cover of attribute-value pairs have been discussed.