An Algorithm for Induction of Possibilistic Set-Valued Rules by Finding Prime Disjunctions

We present a new algorithm, called Optimist, which generates possibilistic setvalued rules from tables containing categorical attributes taking a finite number of values. An example of such a rule might be “IF HOUSEHOLDSIZE={Two OR Tree} AND OCCUPATION={Professional OR Clerical} THEN PAYMENT_METHOD={CashCheck (Max=249) OR DebitCard (Max=175)}. The algorithm is based on an original formal framework generalising the conventional boolean approach in two directions: (i) finitevalued variables and (ii) continuos-valued semantics. Using this formalism we approximate the multidimensional distribution induced from data by a number of possibilistic prime disjunctions (patterns) representing the widest intervals of impossible combinations of values. The Optimist algorithm described in the paper generates the most interesting prime disjunctions for one pass through the data set by means of transformation from the DNF representing data into the possibilistic CNF representing knowledge. It consists of generation, absorption and filtration parts. The set-valued rules built from the possibilistic patterns are optimal in the sense that they have the most general condition and the most specific conclusion. For the case of finite-valued attributes and two-valued semantics the algorithm is implemented in the Chelovek rule induction system for Windows 95.