Forward and backward fuzzy rule base interpolation using fuzzy geometry

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Das S.; Chakraborty D.; Koczy L.T.

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Journal Paper

Paper Information

Journal: Iranian Journal of Fuzzy Systems Year:2023 | Volume:20 | Issue:3 Page(s): 127-146

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Information Journal Paper

Title

Forward and backward fuzzy rule base interpolation using fuzzy geometry

Author(s)

Das S. | Chakraborty D. | Koczy L.T. | Issue Writer Certificate

Keywords

Inverse rule base interpolation

scale and move transformation

transformation of fuzzy point

translation of fuzzy number

multi-dimensional rule base interpolation

Abstract

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.

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