tailieunhanh - Interval complex neutrosophic set: Formulation and applications in decision making

In this paper we propose a new notion, called interval complex neutrosophic set (ICNS), and examine its characteristics. Firstly, we define several set theoretic operations of ICNS, such as union, intersection and complement, and afterward the operational rules. Next, a decision-making procedure in ICNS and its applications to a green supplier selection are investigated. | Int. J. Fuzzy Syst. DOI Interval Complex Neutrosophic Set: Formulation and Applications in Decision-Making Mumtaz Ali1 • Luu Quoc Dat2 • Le Hoang Son3 • Florentin Smarandache4 Received: 8 February 2017 / Revised: 19 June 2017 / Accepted: 19 August 2017 Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany 2017 Abstract Neutrosophic set is a powerful general formal framework which generalizes the concepts of classic set, fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set, etc. Recent studies have developed systems with complex fuzzy sets, for better designing and modeling real-life applications. The single-valued complex neutrosophic set, which is an extended form of the single-valued complex fuzzy set and of the single-valued complex intuitionistic fuzzy set, presents difficulties to defining a crisp neutrosophic membership degree as in the single-valued neutrosophic set. Therefore, in this paper we propose a new notion, called interval complex neutrosophic set (ICNS), and examine its characteristics. Firstly, we define several set theoretic operations of ICNS, such as union, intersection and complement, and afterward the operational rules. Next, a decision-making procedure in ICNS and its applications to a green supplier selection are investigated. & Le Hoang Son sonlh@ Mumtaz Ali Numerical examples based on real dataset of Thuan Yen JSC, which is a small-size trading service and transportation company, illustrate the efficiency and the applicability of our approach. Keywords Green supplier selection Multi-criteria decision-making Neutrosophic set Interval complex neutrosophic set Interval neutrosophic set Abbreviations NS Neutrosophic set INS Interval neutrosophic set CFS Complex fuzzy set CIFS Complex intuitionistic fuzzy set IVCFS Interval-valued complex fuzzy set CNS Complex neutrosophic set ICNS Interval-valued complex neutrosophic set, or interval complex .

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