Multi-dimensional fuzzy interpolation neural network

This paper presents a multi-dimensional fuzzy interpolation neural network (FINN) which extends fuzzy interpolation that was developed to approximate single input single output functions to multi-dimensional space. The multidimensional fuzzy interpolation piecewise approximates multiple-input-single-output functions with small hyper-surfaces defined over fuzzy regions. The vertices of these fuzzy regions are represented by weighted multivariate fuzzy sets which are defined over the input space of a function. Optimally arranging the fuzzy sets in the input space can achieve arbitrary accurate approximations. The proposed FINN is able to establish the optimisation of the fuzzy sets. It was used to approximate the energy distribution of light for light chip and optical fibre alignment.