Abstract
In this paper a new mathematical model of basic planar imprecise geometric objects (fuzzy line, fuzzy triangle and fuzzy circle) are introduced. Also, basic measurement functions (distance between fuzzy point and fuzzy line, fuzzy point and fuzzy triangle, two fuzzy lines and two fuzzy triangles) as well as spatial operation (linear combination of two fuzzy points) and main spatial relations (coincidence, between and collinear)is proposed. Results obtained with our model can be used in various applications such as image analysis (imprecise feature extraction), GIS (imprecise spatial object modeling), robotics (environment models). Imprecise point objects are modeled as a union of linear combinations of fuzzy points in linear fuzzy space. However, it is proved that fuzzy line could be represented only by two and fuzzy triangle with three fuzzy points.
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Obradović, D., Konjović, Z., Pap, E., Rudas, I.J. (2013). Fuzzy Geometry in Linear Fuzzy Space. In: Pap, E. (eds) Intelligent Systems: Models and Applications. Topics in Intelligent Engineering and Informatics, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33959-2_8
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DOI: https://doi.org/10.1007/978-3-642-33959-2_8
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