A new parallel fuzzy data envelopment analysis model for parallel systems with two components based on Stackelberg game theory

This paper investigates the problem of efficiency measurement for parallel systems with two components based on Stackelberg game theory, while some inputs/outputs are fuzzy numbers. Conventional DEA models treat DMUs as “Black Boxes”. While in this paper, we propose a new parallel fuzzy DEA model to calculate the efficiency scores for each DMU’s whole system and its sub-systems. Through the Stackelberg (leader–follower) game theory, the whole system’s efficiency score of each DMU is decomposed into a set of efficiency scores for its sub-systems. This approach is independent of the α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \alpha $$\end{document}-cut which reduces the computational efforts. In order to show our method, we use the data from Beasley (J Oper Res Soc 46(4):441–452, 1995) to measure the fuzzy efficiency of the teaching and research efficiencies of chemistry departments in UK universities.