Fuzzy qualitative trigonometry

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dc.contributor.author Liu, Honghai
dc.contributor.author Coghill, George
dc.contributor.author Barnes, Dave
dc.date.accessioned 2009-10-19T13:52:01Z
dc.date.available 2009-10-19T13:52:01Z
dc.date.issued 2009-12
dc.identifier.citation Liu , H , Coghill , G & Barnes , D 2009 , ' Fuzzy qualitative trigonometry ' International Journal of Approximate Reasoning , vol 51 , no. 1 , pp. 71-88 . en
dc.identifier.issn 0888-613X
dc.identifier.other PURE: 124702
dc.identifier.other dspace: 2160/3244
dc.identifier.uri http://hdl.handle.net/2160/3244
dc.identifier.uri http://www.sciencedirect.com/science/journal/0888613X en
dc.description Honghai Liu, George M. Coghill, Dave P. Barnes, Fuzzy qualitative trigonometry, International Journal of Approximate Reasoning, Vol. 51, Issue 1, December 2009, pp. 71-88. Sponsorship: EPSRC en
dc.description.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. en
dc.format.extent 18 en
dc.language.iso eng
dc.relation.ispartof International Journal of Approximate Reasoning en
dc.subject Fuzzy qualitative reasoning en
dc.title Fuzzy qualitative trigonometry en
dc.type Text en
dc.type.publicationtype Article (Journal) en
dc.identifier.doi http://dx.doi.org/10.1016/j.ijar.2009.07.003
dc.contributor.institution Intelligent Robotics Group en
dc.contributor.institution Department of Computer Science en
dc.description.status Peer reviewed en


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