Soft covering based rough graphs and corresponding decision making

Choonkil Park,Muhammad Irfan Ali,Nasir Shah,Abbas Ali,Noor Rehman,Muhammad Shabir

doi:10.1515/math-2019-0033

Abstract

Abstract Soft set theory and rough set theory are two new tools to discuss uncertainty. Graph theory is a nice way to depict certain information. Particularly soft graphs serve the purpose beautifully. In order to discuss uncertainty in soft graphs, some new types of graphs called soft covering based rough graphs are introduced. Several basic properties of these newly defined graphs are explored. Applications of soft covering based rough graphs in decision making can be very fruitful. In this regard an algorithm has been proposed.

Highlights

Many real world situations appearing in various spheres of life, such as physical sciences, chemistry, communications, computer sciences and several other areas, involve graphs
In the present paper we initiate the study of new types of graphs called soft covering based rough graphs
The applications of soft sets and rough sets that are available in the literature are usually based upon the individ’s properties of the members of the universe with the given attributes

Summary

Introduction

Many real world situations appearing in various spheres of life, such as physical sciences, chemistry, communications, computer sciences and several other areas, involve graphs. Molodtsov [5] introduced the notion of soft sets to overcome the problem of dealing with attributes This concept changed the role of above said theories as the sole representative of multiattributes and recti ed in some disciplines to tackle many problems of uncertainty [18–20]. In the present paper we initiate the study of new types of graphs called soft covering based rough graphs. Several properties of these graphs are explored. As an application of soft covering based rough graphs in decision making problems an algorithm is proposed. Section is devoted to present an application of soft covering based rough graphs in real life.

Soft Covering Based Rough Graphs

Applications of Soft Covering Based Rough Graphs

Let S

Conclusion