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Advances in Fuzzy Systems
Volume 2017 (2017), Article ID 6162753, 17 pages
https://doi.org/10.1155/2017/6162753
Research Article

A New Type-2 Soft Set: Type-2 Soft Graphs and Their Applications

1School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510000, China
2Department of Mathematics, Islamabad Model College for Girls, F-6/2, Islamabad, Pakistan
3Guangzhou Vocational College of Science and Technology, Guangzhou 510550, China

Correspondence should be addressed to Muhammad Irfan Ali and Bing-Yuan Cao

Received 7 February 2017; Accepted 15 June 2017; Published 18 October 2017

Academic Editor: Katsuhiro Honda

Copyright © 2017 Khizar Hayat et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The correspondence between a vertex and its neighbors has an essential role in the structure of a graph. Type-2 soft sets are also based on the correspondence of primary parameters and underlying parameters. In this study, we present an application of type-2 soft sets in graph theory. We introduce vertex-neighbors based type-2 soft sets over (set of all vertices of a graph) and (set of all edges of a graph). Moreover, we introduce some type-2 soft operations in graphs by presenting several examples to demonstrate these new concepts. Finally, we describe an application of type-2 soft graphs in communication networks and present procedure as an algorithm.