The graph games with fuzzy characteristic functions

Article type: Research Article

Authors: Nie, Cuiping^a | Nie, Tao^{a; *} | Sun, Hongxia^b

Affiliations: [a] School of Science, Shijiazhuang College, Shijiazhuang, PR China | [b] Business School, Beijing Technology and Business University, Beijing, PR China

Correspondence: [*] Corresponding author. Tao Nie, School of Science, Shijiazhuang College, Shijiazhuang 050035, PR China. Tel.: +86 311 66617199; E-mail: 1212004@sjzc.edu.cn.

Abstract: This paper proposes the H-average tree solution based on a graph game with fuzzy characteristic function. This solution is a generalization of the classical average tree solution, and is an imputation of a graph game with fuzzy characteristic function. When the game is cycle-free the H-average tree solution is the unique solution that satisfies component efficiency and component fairness. The interval average tree solution is introduced. Furthermore, we show the relationship between the H-average tree solution and the interval average tree solution. A practical application of the proposed model in outsource production is given.

Keywords: Graph game with fuzzy characteristic function, H-average tree solution, imputation, interval average tree solution

DOI: 10.3233/JIFS-17502

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 4, pp. 3851-3856, 2019