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.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics