A study on fuzzy plane and its application on fuzzy plane fitting

Abstract: In this paper, I obtain an $S$-type fuzzy point when two fuzzy numbers for two independent variables and a corresponding fuzzy number for the dependent variable are given. A comprehensive study on a conceptualization of a fuzzy plane as a collection of fuzzy numbers, or fuzzy points is proposed. A perpendicular fuzzy distance from a fuzzy point to a fuzzy plane is also revisited. An application of the proposed fuzzy plane is made to fit a fuzzy plane to the available data sets of imprecise locations in $\mathbb{R}^3$. Moreover, a degree of fuzzily fitted fuzzy plane to the given data sets of fuzzy points is defined. All the fuzzy geometric construction and characteristics of fuzzy planes are explored with the help of same and inverse points ideas. All the study is supported by numerical examples and illustrated by fuzzy geometrical figures. This study provides a framework for developing a fuzzy plane-fitting model that will benefit the fields of curve detecting and fitting, image processing for industrial and scientific applications, signal processing, and problems of shape recognition.