### Journals Information

**
Mathematics and Statistics Vol. 10(6), pp. 1344 - 1353 DOI: 10.13189/ms.2022.100622 Reprint (PDF) (733Kb) **

## Construction of Rough Graph through Rough Membership Function

**R. Aruna Devi ^{1}, K. Anitha ^{2}^{,*}**

^{1}Research Scholar, Department of Mathematics, SRMIST, Ramapuram, Chennai 600089, India

^{2}Department of Mathematics, SRMIST, Ramapuram, Chennai 600089, India

**ABSTRACT**

Rough membership function defines the degree of relationship between conditional and decision attributes of an information system. It is defined by where is the subset of under the relation where 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 where as in probabilistic form it can be denoted as where is the equivalence class of with respect to . 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 . We propose that there is an edge between vertices if . 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.

**KEYWORDS**

Set Approximations, Rough Membership Function, Rough Graph

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] R. Aruna Devi , K. Anitha , "Construction of Rough Graph through Rough Membership Function," Mathematics and Statistics, Vol. 10, No. 6, pp. 1344 - 1353, 2022. DOI: 10.13189/ms.2022.100622.

(b). APA Format:

R. Aruna Devi , K. Anitha (2022). Construction of Rough Graph through Rough Membership Function. Mathematics and Statistics, 10(6), 1344 - 1353. DOI: 10.13189/ms.2022.100622.