Fuzzy c-Regression Models for Fuzzy Numbers on a Graph

With the assumption that the vertices have numerical values. The aim of this paper is to construct regression models to estimate the values from their relationship on the graph by defining the vertex and the numerical value as an independent variable and a dependent variable, respectively. Given the condition that near vertices have close values, k-Nearest Neighbor regression models (KNN) has been proposed. However, the condition is not satisfied when some near vertices have different values. To overcome such difficulty, c-regression which classify data points into some clusters has been proposed to improve performance of regression analysis. We moreover propose new c-regression models on a graph with fuzzy numbers on vertices and show some numerical examples.