Possibilistic constrained optimization to tune fuzzy rules formalizing medical knowledge by preserving linguistic interpretability

Fuzzy Logic can be reckoned as a suitable formal approach to represent medical rules in a computable format without loosing their linguistic interpretability. However, this capacity could be overlooked in favor of prediction accuracy. Usually, to simultaneously optimize two conflicting properties such as accuracy and semantic interpretability, multi-objective evolutionary algorithms are adopted. In this paper we propose to consider interpretability-accuracy tradeoff problem as a constrained optimization problem. A Differential Evolution algorithm, suitably adapted to the aim, is used for membership function tuning by maximizing accuracy and fulfilling several constraints for linguistic distinguishability degrees - a semantic property of fuzzy sets with notable relevance for interpretability of fuzzy models - evaluated through Possibility Theory. The proposed approach has been tested on the Vertebral Column Data set, a recent medical database publicly available, with results that confirm the effectiveness of our method.