SAI Intelligent Systems Conference 2016 September21-22, 2016 | London, UK 1 | Page ©2016 IEEE Decision-Making Method Based on The Interval Valued Neutrosophic Graph Said Broumi Laboratory of Information processing, Faculty of Science Ben M’Sik, University Hassan II, B.P 7955, Sidi Othman, Casablanca, Morocco broumisaid78@gmail.com Florentin Smarandache Department of Mathematics, University of New Mexico,705 Gurley Avenue, Gallup, NM 87301, USA fsmarandache@gmail.com Mohamed Talea Laboratory of Information processing, Faculty of Science Ben M’Sik, University Hassan II, B.P 7955, Sidi Othman, Casablanca, Morocco taleamohamed@yahoo.fr Assia Bakali Ecole Royale Navale, Boulevard Sour Jdid, B.P 16303 Casablanca, Morocco. assiabakali@yahoo.fr Abstract—In this article, we extend the neutrosophic graph-based multicriteria decision making method (NGMCDM) introduced by Sahin [49] for the case of interval valued neutrosophic graph theory. We also give an algorithm to solve decision making problems by using interval valued neutrosophic graphs. Finally, an illustrative example is given and a comparison analysis is conducted between the proposed approach and other existing methods, to verify the feasibility and effectiveness of the developed approach. Keywords—interval valued neutrosophic set; interval valued neutrosophic graph; influence coefficient; decision making problem I. INTRODUCTION The Neutrosophic Set (NS), proposed by Smarandache [12, 13] as a generalization of fuzzy sets theory [30], intuitionistic fuzzy set [28, 29], interval-valued fuzzy set [19] and interval-valued intuitionistic fuzzy set [27], is a powerful mathematical tool for dealing with incomplete, indeterminate and inconsistent information in real world. The neutrosophic sets are characterized by a truth-membership function (t), an indeterminacy-membership function (i) and a falsity- membership function (f) independently, which are within the real standard or nonstandard unit interval ] − 0, 1 + [. In order to conveniently apply NS in real life applications, Wang et al. [15] introduced the concept of single-valued neutrosophic set (SVNS), a subclass of the neutrosophic sets. The same authors [16] also introduced the concept of interval valued neutrosophic set (IVNS), which is more precise and more flexible than the single valued neutrosophic set. The IVNS is a generalization of the single valued neutrosophic set, in which three membership functions are independent, and their value belong to the unit interval [0, 1]. The theory of single valued neutrosophic set and interval valued neutrosophic set have been applied in a wide diversity of fields [3, 4, 17, 35, 36, 64 ,68]. Multi-criteria decision making attempts to handle problems with imprecise goals, referring to a number of individual criteria by a set of alternatives at choice. Many scholars have begun to study the practical application of neutrosophic sets and interval valued neutrosophic sets in multi-attribute decision-making problems [1, 8, 14, 18, 20, 21, 22, 23, 24, 25, 26, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 67]. Graph theory has now become a major branch of applied mathematics and it is generally regarded as a branch of combinatorics. The graph is a widely used tool for solving combinatorial problems in different areas, such as geometry, algebra, number theory, topology, optimization and computer science. When the relations between nodes (or vertices) in problems are indeterminate, the fuzzy graphs and their extensions [5, 6, 7, 37, 51] fail. For this purpose, Smarandache [9, 10, 11] defined four main categories of neutrosophic graphs. Two of them, called I-edge neutrosophic graph and I-vertex neutrosophic graph, are based on literal indeterminacy (I); these concepts are deeply studied and gained popularity among the researchers due to applications via real world problems [2, 65, 66, 67]. The two other categories of graphs, called (t, i, f)-Edge neutrosophic graph and (t, i, f)-vertex neutrosophic graph, are based on (t, i, f) components, but they not at all developed. Later on, Broumi et al. [56, 63] introduced a third neutrosophic graph model, called single valued neutrosophic graph (SVNG), and investigated some of its properties. This model allows the attachment of truth-membership (t), indeterminacy– membership (i) and falsity-membership(f) degrees both to vertices and edges. The single valued neutrosophic graph is a generalization of fuzzy graph and intuitionistic fuzzy graph. Also, the same authors [57] introduced neighborhood degree of a vertex and closed neighborhood degree of a vertex in single