Interval-valued intuitionistic fuzzy soft graph

Abstract

One of the theories designed to deal with uncertainty is the soft set theory. These collections were used due to a lack of membership functions in the fields of decision-making, systems analysis, classification, data mining, medical diagnosis, etc. Fuzzy graphs based on soft sets were developed alongside fuzzy graphs. Studying these graphs, examining the properties and operators on it, give special flexibility in dealing with indeterminate problems. In particular, most of the issues around us are mixed and operations are conveniently used in many combinatorial applications. Therefore, the study of operations have a significant effect on solving problems based on decisionmaking, medical, etc. In this paper, we introduce the notion of interval-valued intuitionistic fuzzy soft graphs, by combine concepts of interval-valued intuitionistic fuzzy graphs and fuzzy soft graphs. We also present several different types of operations including cartesian product, strong product and composition on interval-valued intuitionistic fuzzy soft graphs and investigate some properties of them.