Conceptualizing fuzzy line as a collection of fuzzy points

Genesis and geometrical properties of fuzzy line are explored in this study. The existing studies on fuzzy geometry suggest that fuzzy lines can be characterized as a union of crisp lines with varying membership values but this characterization is not capable to identify the nature of the fuzzy point situated on the fuzzy line. Expressing fuzzy line as a collection of fuzzy points in the geometrical plane is an intended goal of this paper. In the first part, a fuzzy line has been interpreted as a fuzzification function that produces a collection of fuzzy numbers. The equivalency between the union of lines with different membership grades and collection of fuzzy numbers is also shown. In the next part, the possible nature of a fuzzy points situated on a generic fuzzy line is explored. Analogous to the concept of a line in classical geometry, this paper constructs and approximates a fuzzy line as a collec-tion of fuzzy points. All the proposals and results are illustrated numerically and geomet-rically in a fuzzy geometrical plane.(c) 2022 Elsevier Inc. All rights reserved.