Fuzzy qualitative trigonometry

Honghai Liu, George M. Coghill, Dave P. Barnes

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

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
Volume51
Issue number1
DOIs
Publication statusPublished - Dec 2009

Fingerprint

Trigonometry
MATLAB
Fuzzy logic
Artificial intelligence
Kinematics
Robotics
Robots
Sensing
Qualitative Reasoning
Fuzzy Partition
Circular function
Fuzzy numbers
Unit circle
Cartesian
Fuzzy Logic
Euclidean space
Triangle
Artificial Intelligence
Circle
Robot

Keywords

  • fuzzy qualitative reasoning

Cite this

Fuzzy qualitative trigonometry. / Liu, Honghai; Coghill, George M.; Barnes, Dave P. .

In: International Journal of Approximate Reasoning, Vol. 51, No. 1, 12.2009, p. 71-88.

Research output: Contribution to journalArticle

Liu, Honghai ; Coghill, George M. ; Barnes, Dave P. . / Fuzzy qualitative trigonometry. In: International Journal of Approximate Reasoning. 2009 ; Vol. 51, No. 1. pp. 71-88.
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