Introduction and Elucidation of the Quality of Sagacity in the Extended Variable Precision Rough Sets Model

This paper introduces the quality of sagacity measure in the extended variable precision rough sets model - VPRS_l,u. The need for this measure is a direct consequence of the use of the associated l and u values. Moreover, different levels of miss-classification are allowed in the classification of objects to a decision class or its compliment. This measure attempts to take this into account, by acknowledging the classification of an object to the compliment of a decision class, as an appropriate (if not optimum) classification of that object. A consequence of the analysis is a discussion of the notion of open and closed worlds in VPRS_l,u.