Learning Rule Parameters of Possibilistic Rule-Based System

In this paper, we introduce a learning paradigm of the rule parameters of a possibilistic rule-based system, given training data. For a rule-based system composed of n if-then parallel possibilistic rules, we introduce an equation system denoted (Σ
n
), which is analogous to the Farreny-Prade equation system. The unknown part of the system (Σ
n
) is a vector composed of the rule parameters, whose values must be determined according to training data.We establish necessary and sufficient conditions for the system (Σ
n
) to be consistent. If this is the case, we show that the set of solutions of the system is a Cartesian product of subintervals of [0, 1] whose bounds are computed. Then, we deduce that there are a unique maximal solution and, as it is well known by Sanchez’s work on the solving of min-max fuzzy relational equations, a unique minimal one. These results are proved by relating the solutions of (Σ
n
) to those of the equation system given by the first n − 1 possibilistic rules equipped with a second member which is constructed from that of (Σ
n
).Finally, our results are illustrated by an example.