Normal forms in BL-algebra and their contribution to universal approximation of functions

This paper continues the investigation of approximating properties of generalized normal forms in fuzzy logic. The problem is formalized and solved algebraically. Normal forms are considered in two variants: infinite and finite. It is proved that infinite normal forms are universal representation formulas whereas finite normal forms are universal approximation formulas for any L-valued function where L is a support set of any complete BL-algebra. The estimation of the quality of approximation is suggested. Moreover, functions which can be precisely represented by the discrete normal forms are considered.