S. Das - School of Computer Science and Engineering, Nanyang Technological University, ۵۰ Nanyang Ave, ۶۳۹۷۹۸, Singapore
D. Chakraborty - Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, ۷۲۱۳۰۲, West Bengal, India
L. T. Koczy - Department of Information Technology, Szechenyi Istvan University, Gyor, Hungary

Fuzzy rule interpolation (FRI) predicts an accountable outcome of a possible course of action in sparse fuzzy rule base system (FRBS). The geometry based linear fuzzy rule interpolation (GLFRI) is extended for multi-dimensional fuzzy rule base interpolation. Expansion/contraction (EC) of triangular, trapezoidal and complex polygonal fuzzy sets has been also proposed which enables the proposed FRI method to incorporate with fuzzy rules which include triangular, trapezoidal, hexagonal or complex fuzzy sets. The study further extends to introduce the process of backward rule base interpolation.It has been shown that the scale and move transformation-based FRI method can yield a non-convex fuzzy consequent which can be avoided by using the proposed method. The proposed method performs better without any risk of obtaining non-convex fuzzy consequent. The efficiency of proposed forward and backward FRI methods is projected with several numerical examples. A detailed comparison of EC transformation with scale and move transformation is also presented here.

Inverse rule base interpolation, scale and move transformation, transformation of fuzzy point, translation of fuzzy number, multi-dimensional rule base interpolation