Intuitionistic Fuzzy Graph Mathematical Morphology and Some of its Properties

Abstract

This paper studies the mathematical morphology operators acting on a lattice of all intuitionistic fuzzy sub graphs of an intuitionistic fuzzy graph (IFG). pn-adjacency of vertices and edges are defined as neighbourhoods of vertices and edges. We define vertex dilation, vertex erosion, edge dilation, edge erosion and some of their properties on intuionistic fuzzy graph using pn-adjacency of vertices and edges. We propose elementary mathematical morphology operators, dilation and erosion, on intuionistic fuzzy graph using pn-adjacency of vertices and edges based on lattice theory and also prove following basic properties of the proposed intuitionistic fuzzy graph mathematical morphology operators, dilation and erosion. (1) Dilation and erosion on IFG are increasing (2) Dilation is extensive. (3) Erosion is anti-extensive. (4) Dilation is distributive with respect to union and Erosion on IFG is distributive with respect to intersection. These properties are analogous to the properties of dilation and erosion in the classical Mathematical Morphology. So this paper is a theoretical extension of mathematical morphology on graphs to mathematical morphology on intuitionistic fuzzy graph. MSC Classification: 68U10 , 05C72