The standard interpretation of the logical operators in a Boolean retrieval system is in general too strict. A standard Boolean query rarely comes close to retrieving all and only those documents which are relevant to the user. An AND query is often too narrow and an OR query is often too broad. The choice of the AND results in retrieving on the left end of a typical average recall-precision graph, while the choice of the OR results in retrieving on the right end, implying a tradeoff between precision and recall. This study basically examines various proposed schemes, the P-norm, Classical Fuzzy-Set, MMM, Paice and TIRS, which provide means to soften the interpretation of the logical operators, and thus to attain both high precision and high recall search performance. Each of the above schemes has shown great improvement over the standard Boolean scheme in terms of retrieval effectiveness. The differences in retrieval effectiveness between P-norm, Paice and MMM are shown to be relatively small. However, related performance results obtained gives evidence of the ranking: P-norm, Paice, MMM and then TIRS.