The genetic development of ordinal sums

The aim of this study is to develop an operational model of an ordinal sum of triangular norms. The essence of this construct lies in the use of different t-norms (and/or t-conorms) defined over disjoint subintervals of the unit interval. The result of such aggregation is a highly versatile logic operator that can be easily adapted to the existing experimental evidence. We propose a genetic optimisation environment (Genetic Algorithms, GAs, in particular) to construct ordinal sums and show how the GA mechanism helps optimize subintervals and to allocate individual local t-norms. The application of the genetically designed ordinal sums is shown in case of Zimmermann-Zysno logic operator data. We also demonstrate the use of the ordinal sum to the construction of neuro-fuzzy systems; in this case we quantify the performance of ordinal sums to “standard” logic operators used in such models.