On general form of fuzzy lines and its application in fuzzy line fitting

Abstract

In this paper, fuzzy geometrical construction and characteristics of fuzzy lines are investigated. A general form of fuzzy lines is proposed. It is shown that a fuzzy line passing through a set of fuzzy points whose cores are collinear is unique. Slope and intercept of a fuzzy line, vertical and perpendicular distances from a fuzzy point to a fuzzy line are also studied. Sup-min composition of fuzzy sets and concepts of same and inverse points in fuzzy geometry are applied to define all the ideas. Proposed general form of fuzzy line is applied to fit a fuzzy line for a dataset of imprecise locations or fuzzy points. It is shown that the fitted fuzzy line has the minimum sum of square vertical distances between the given fuzzy points and the fitted fuzzy line. Proposed definitions and ideas are supported by several numerical and pictorial illustrations.