Analytical fuzzy plane geometry II

This paper formulates fuzzy lines in a fuzzy geometric plane. We construct a fuzzy line passing through several fuzzy points whose cores are collinear. Consecutively four different forms for fuzzy lines: a two-point form, a point-slope form, a slope-intercept form, and an intercept form are proposed. Their properties and interrelations are also investigated. We demonstrate the construction of the membership function of all four forms and illustrate this with suitable examples. It is shown that the two-point form and intercept form are equivalent. However, the two-point form or intercept form cannot, in general, be equivalent to the point-slope form or the slope-intercept form. To define and analyze all the proposed ideas, the concepts of same and inverse points in fuzzy geometry are used. All our discussions are supported by suitable examples.