Fuzzy qualitative trigonometry

Honghai Liu, George Coghill, Dave Barnes

Research output: Contribution to journalArticlepeer-review

20 Citations (SciVal)
524 Downloads (Pure)


This paper presents a fuzzy qualitative representation of conventional trigonometry with the goal of bridging the gap between symbolic cognitive functions and numerical sensing & 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 normalized 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 analyze 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 paper to demonstrate the characteristics of fuzzy qualitative trigonometry. One of the examples focuses on robot kinematics and also explains how contributions could be made by fuzzy qualitative trigonometry to the intelligent connection of low-level sensing & control tasks to high-level cognitive tasks.
Original languageEnglish
Pages (from-to)71-88
Number of pages18
JournalInternational Journal of Approximate Reasoning
Issue number1
Early online date06 Sept 2009
Publication statusPublished - Dec 2009


  • Fuzzy qualitative reasoning


Dive into the research topics of 'Fuzzy qualitative trigonometry'. Together they form a unique fingerprint.

Cite this