Construction of Rough Graph through Rough Membership Function

Abstract

Rough membership function defines the degree of relationship between conditional and decision attributes of an information system. It is defined by <img src=image/13429145_01.gif> where <img src=image/13429145_07.gif> is the subset of <img src=image/13429145_08.gif> under the relation <img src=image/13429145_09.gif> where <img src=image/13429145_08.gif> is the universe of discourse. It can be expressed in different forms like cardinality form, probabilistic form etc. In cardinality form, it is expressed as <img src=image/13429145_02.gif> where as in probabilistic form it can be denoted as <img src=image/13429145_03.gif> where <img src=image/13429145_04.gif> is the equivalence class of <img src=image/13429145_10.gif> with respect to <img src=image/13429145_09.gif>. This membership function is used to measure the value of uncertainty. In this paper we have introduced the concept of graphical representation of rough sets. Rough graph was introduced by He Tong in 2006. In this paper, we propose a novel method for the construction of rough graph through rough membership function <img src=image/13429145_05.gif>. We propose that there is an edge between vertices if <img src=image/13429145_06.gif>. The rough graph is being constructed for an information system; here objects are considered as vertices. Rough path, rough cycle, rough ladder graph are introduced in this paper. We develop the operations on rough graph and also extend the properties of rough graph.