@inbook{aa56c8e56179424aacfc6df465bfd31b,
title = "Fuzzy qualitative trigonometry",
abstract = "This Chapter presents a fuzzy qualitative representation of conventional trigonometry with the goal of bridging the gap between symbolic cognitive functions and numerical sensing and control tasks in the domain of physical systems, especially in intelligent robotics. Fuzzy qualitative coordinates are defined by replacing a unit circle with a fuzzy qualitative circle; a Cartesian translation and orientation are defined by their normalised fuzzy partitions. Conventional trigonometric functions, rules and the extensions to triangles in Euclidean space are converted into their counterparts in fuzzy qualitative coordinates using fuzzy logic and qualitative reasoning techniques. This approach provides a promising representation transformation interface to analyse general trigonometry-related physical systems from an artificial intelligence perspective. Fuzzy qualitative trigonometry has been implemented as a MATLAB toolbox named XTRIG in terms of 4-tuple fuzzy numbers. Examples are given throughout the chapter to demonstrate the characteristics of fuzzy qualitative trigonometry.",
author = "Honghai Liu and Zhaojie Ju and Xiaofei Ji and Chan, \{Chee Seng\} and Mehdi Khoury",
note = "Publisher Copyright: {\textcopyright} 2017, Springer-Verlag GmbH Germany.",
year = "2017",
doi = "10.1007/978-3-662-53692-6\_2",
language = "英语",
series = "Studies in Computational Intelligence",
publisher = "Springer Verlag",
pages = "35--50",
booktitle = "Studies in Computational Intelligence",
address = "德国",
}