### Abstract

Fuzzy Rule Interpolation (FRI) provides an interpretable decision in sparse fuzzy rule based system. The objective of this work is to establish a mathematical demonstration of the pattern of existing fuzzy rule base using fuzzy geometry. Though several authors contributed on fuzzy rule base interpolation but there is a need to generate closed mathematical form of interpolating pattern. The present work is an initiative to demonstrate the same. First part of this paper presents some spatial geometrical transformation of a fuzzy point. In the second part of this paper, a new FRI scheme is suggested using fuzzy geometry with above mentioned transformation. The proposed method operates in two different steps. In the first step, all the fuzzy rules are converted into fuzzy sets or mostly fuzzy points in higher dimension by using mathematical operator on the individual of antecedent and consequent parts. All rules or fuzzy points are then joined with a class of fuzzy line segments (FLS). Second step considers the identification of mathematical pattern of the interpolated piecewise linear fuzzy polynomial which is able to compute the desired conclusion of a given observation. The presented method not only associates the FRI technique to classical interpolation technique, but also promises to provide the geometrical visualization of the behaviour of fuzzy sets during the interpolation process.

Original language | English |
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Pages (from-to) | 105-118 |

Number of pages | 14 |

Journal | International Journal of Approximate Reasoning |

Volume | 112 |

DOIs | |

Publication status | Published - Sep 1 2019 |

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### Keywords

- Expansion/contraction of fuzzy point
- Fuzzy line segment
- Fuzzy point
- Fuzzy rule base interpolation
- Same points

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Artificial Intelligence
- Applied Mathematics

### Cite this

*International Journal of Approximate Reasoning*,

*112*, 105-118. https://doi.org/10.1016/j.ijar.2019.05.004