Interpolative reasoning approach to sparse general type-2 fuzzy rules based on the reduced grid representation

Interpolative reasoning is one of the most interested problems with various approaches for type-1 fuzzy sets, interval type-2 fuzzy sets, recently. However, the related methods have not mentioned general type-2 fuzzy sets yet because of their computational complexity. The paper deals with an approach to representation theorem of general type-2 fuzzy sets using the reduced grid. A computational schema for interpolative reasoning of sparse general type-2 fuzzy rules is also introduced. This schema is not depended on the shape of membership functions. Beside, the parallelizing schema for GPU platform is proposed to speedup the algorithms. The proposed methods are implemented on both of GPU and CPU platforms with various membership functions.