Abstract
In conventional Euclidean geometry, a straight line is obtained by extending a line segment bi-infinitely (second postulate of Euclid). Thus, a line is the locus of a point along a fixed direction. The slope of the line determines its direction and it is the inclination angle of the tangent to the positive x-axis. Any linear equation of two variables represents a straight line. But in fuzzy geometry a fuzzy line may not be expressed as a fuzzy linear equation. This chapter mainly addresses the questions: What is a fuzzy line? How to construct a fuzzy line? And what is the mathematical form of fuzzy line?
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Notes
- 1.
This supremum exists in the set considered, since \(\widetilde{L}_{2P}(\alpha )\) is a compact set. (Observation 3.2.2).
- 2.
A translation is said to be rigid if it preserves relative distances—that is to say: if \(P_1\) and \(Q_1\) are transformed to \(P_2\) and \(Q_2\), then the distance from \(P_1\) to \(Q_1\) is equal to the distance from \(P_2\) to \(Q_2\).
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Ghosh, D., Chakraborty, D. (2019). Fuzzy Line. In: An Introduction to Analytical Fuzzy Plane Geometry. Studies in Fuzziness and Soft Computing, vol 381. Springer, Cham. https://doi.org/10.1007/978-3-030-15722-7_3
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DOI: https://doi.org/10.1007/978-3-030-15722-7_3
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