Boolean retrieval systems have been most widely used in the area of information retrieval due to easy implementation and efficient retrieval. Conventional Boolean retrieval systems. however, cannot rank retrieved documents in decreasing order of query-document similarities because they cannot compute similarity coefficients between queries and documents. Extended Boolean models such as fuzzy set. Waller-Kraft, Paice, P-Norm and Infinite-One have been developed to provide the document ranking facility. In extended Boolean models, the formulas evaluating Boolean operators AND and OR are an important component to affect the quality of document ranking. In this paper we present mathematical properties of the formulas, and analyse their effect on retrieval effectiveness. Our analyses show that P-Norm is the most suitable for achieving high retrieval effectiveness