# Design algorithm for smoothly connecting curves by fuzzy membership function

Chih Yu Hsu, Ta Shan Tsui, Shyr Shen Yu, Yeong-Lin Lai

Research output: Contribution to journalArticle

### Abstract

In this paper, we propose a technique using a fuzzy membership function to generate a curve to approximate a desired function. The concave preserving issues are discussed and proved for the approximation functions. The desired function can be widely approximated piece by piece by combining two parabolic functions in each segment. The combined function passes through two given points in common and has the given slopes at their two respective points. The smooth and concave properties of approximation functions are proved to be preserved for those properties of the desired function. This paper aims to prove that the concavity preserving can be achieved by combining two parabolic functions using the fuzzy membership functions and fuzzy inference rules. Two numerical results are used to demonstrate that the approximation function can approximate parts of the ellipse and sine functions.

Original language English 189-195 7 Applied Mathematics and Information Sciences 9 1 https://doi.org/10.12785/amis/091L24 Published - 2015 Jan 1

### Fingerprint

Fuzzy Membership Function
Algorithm Design
Membership functions
Curve
Function Approximation
Fuzzy Inference
Inference Rules
Approximation of Functions
Concavity
Ellipse
Fuzzy Rules
Slope
Fuzzy inference
Numerical Results
Demonstrate

### All Science Journal Classification (ASJC) codes

• Analysis
• Numerical Analysis
• Computer Science Applications
• Computational Theory and Mathematics
• Applied Mathematics

### Cite this

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Design algorithm for smoothly connecting curves by fuzzy membership function. / Hsu, Chih Yu; Tsui, Ta Shan; Yu, Shyr Shen; Lai, Yeong-Lin.

In: Applied Mathematics and Information Sciences, Vol. 9, No. 1, 01.01.2015, p. 189-195.

Research output: Contribution to journalArticle

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