The sum interaction indices of some particular families of monotone measures

Article type: Research Article

Authors: Wu, Jian-Zhang^{a; b} | Yu, Li-Ping^{a; b; *} | Li, Guiping^{a; b} | Jin, Jia^{a; b} | Du, Bisheng^{a; b}

Affiliations: [a] School of Business, Ningbo University, Ningbo, China | [b] Zhejiang port and shipping logistics service system collaborative innovation center, Ningbo, China

Correspondence: [*] Corresponding author. Li-Ping Yu, School of Business, Ningbo University, No. 818, Fenghua Road, Jiangbei District, Ningbo 315211, China. Tel.: +86 15058836418; Fax: +86 0574 87600383; E-mail: yswjz@163.com.

Abstract: In the literature [40], the authors proposed the sum interaction index and discussed its basic mathematical properties. And by some comparison analyses, the authors demonstrated that the sum interaction index can be taken as an alternative of the probabilistic interaction index to measure the interaction phenomenon of the multiple decision criteria. In this paper, we further investigate the properties of the sum interaction index with respect to some particular families of monotone measures, such as the λ-monotone measures, the possibility monotone measures, the k-additive monotone measures, the p-symmetric monotone measures, and the k-tolerant and k-intolerant monotone measures. Some illustrative examples are also given to show the comparison analyses between the sum interaction index and the probabilistic interaction index.

Keywords: Multicriteria decision analysis, monotone measure, shapley interaction index, sum interaction index, k-additive monotone measure

DOI: 10.3233/IFS-162211

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1447-1457, 2016