Many extended Boolean models such as fuzzy set, $p$-norm, et al. have been proposed in the information retrieval literature to support ranking facility for the Boolean retrieval system. They can be explained within the same framework, and each extended Boolean model is characterized by evaluation formulas for AND and OR operations. A variety of operators have been also developed in the area of fuzzy set theory for AND and OR operations, and can be used in extended Boolean models. In this paper we analyze the behavioral aspects of various operators for AND and OR operations, and address important properties in terms of retrieval effectiveness. Our analyses show that the four properties, namely single operand dependency, negative compensation, double operand dependency and unequal importance decrease retrieval effectiveness in some circumstances. This suggests that the two properties, namely positive compensation and equal importance might help retrieval effectiveness. We also provide the experimental results that coincide with our analyses.