Interval neutrosophic numbers Choquet integral operator for multi-criteria decision making

Article type: Research Article

Authors: Sun, Hong-Xia^{a; *} | Yang, Hao-Xiong^a | Wu, Jian-Zhang^b | Ouyang, Yao^c

Affiliations: [a] Business School, Beijing Technology and Business University, Beijing, China | [b] School of Business, Ningbo University, Ningbo, Zhejiang, China | [c] Faculty of Science, Huzhou University, Huzhou, Zhejiang, China

Correspondence: [*] Corresponding author. Hong-Xia Sun, Business School, Beijing Technology and Business University, No.33 Fucheng Road, Haidian District, Beijing, China. Tel.: +86 10 68985991; Fax: +86 10 68984948; E-mail: [email protected].

Abstract: In this paper, the Choquet integral and the interval neutrosophic set theory are combined to make multi-criteria decision for problems under neutrosophic fuzzy environment. Firstly, a ranking index is proposed according to its geometrical structure, and an approach for comparing two interval neutrosophic numbers is given. Then, a ≤L implied operation-invariant total order which satisfies order-preserving condition is proposed. Secondly, an interval neutrosophic number Choquet integral (INNCI) operator is established and a detailed discussion on its aggregation properties is presented. In addition, the procedure of multi-criteria decision making based on INNCI operator is given. Finally, a practical example for selecting the third party logistics providers is provided to illustrate the feasibility of the developed approach.

Keywords: Neutrosophic set (NS), order relation, fuzzy measure, Choquet integral, multi-criteria decision making (MCDM)

DOI: 10.3233/IFS-141524

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 6, pp. 2443-2455, 2015