On the evaluation of Boolean operators in the extended Boolean retrieval framework

The retrieval models based on the extended boolean retrieval framework, e.g., the fuzzy set model and the extended boolean model have been proposed in the past to provide the conventional boolean retrieval system with the document ranking facility. However, due to undesirable properties of evaluation formulas for the AND and OR operations, the former generates incorrect ranked output in certain cases and the latter suffers from the complexity of computation. There have been a variety of fuzzy operators to replace the evaluation formulas. In this paper we first investigate the behavioral aspects of the fuzzy operators and address important issues to affect retrieval effectiveness. We then define an operator class called positively compensatory operators giving high retrieval effectiveness, and present a pair of positively compensatory operators providing high retrieval efficiency as well as high retrieval effectiveness. All the claims are justified through experiments.