I. Introduction
Data mining[14] an interdisciplinary research area spanning several disciplines such as expert system, database system, intelligent information systems, machine learning and statistic. Quantitative association rule mining [8] generates positive and negative rules. Positive rules [10] specify the presence whereas negative rules [10] specify the absence. Many more properties could be concluded based on the negative rules. While mining quantitative association rules using MOPNAR(MultiObjective Positive Negative Association Rules)[7] a large number of rules might be generated. These rules might be important or might not be important. Generation of large number of rules puts more overhead on the space and time requirements of the algorithm. Hence to overcome this we design an extension to MOPNAR i.e BMPNAR to mine the best M positive and negative quantitative association rules. M is the number of rules to be generated specified by the user. We expect the algorithm to produce M best rules with better space and time efficiency. We combine MOPNAR and TOPk Algorithm [6] to produce a new algorithm BMPNAR(Best M Positive Negative Association Rules) which mines only the Best M rules with the help of minconf value. These best M rules are then given to Firefly Algorithm[12] [13]. Firefly algorithm is a metaheuristic algorithm inspired by nature. Its working is inspired by the behavior of the Fireflies. This algorithm classifies the produced set of rules for analysis purpose.