Fuzzy Qualitative Trigonometry

Abstract

This paper proposes fuzzy qualitative representation of trigonometry (FQT) in order to bridge the gap between qualitative and quantitative representation of physical systems using Trigonometry. Fuzzy qualitative coordinates are defined by replacing a unit circle with a fuzzy qualitative circle; the Cartesian translation and orientation are replaced by their fuzzy membership functions. 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. We developed a MATLAB toolbox XTrig in terms of 4-tuple fuzzy numbers to demonstrate the characteristics of the FQT. This approach addresses a representation transformation interface to connect qualitative and quantitative descriptions of trigonometry-related systems (e.g., robotic systems).