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Conventional DEA models treat DMUs as \u201cBlack Boxes\u201d. While in this paper, we propose a new parallel fuzzy DEA model to calculate the efficiency scores for each DMU\u2019s whole system and its sub-systems. Through the Stackelberg (leader\u2013follower) game theory, the whole system\u2019s efficiency score of each DMU is decomposed into a set of efficiency scores for its sub-systems. This approach is independent of the <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \\alpha $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:mi>\u03b1<\/mml:mi>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula>-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\u2013452, 1995) to measure the fuzzy efficiency of the teaching and research efficiencies of chemistry departments in UK universities.<\/jats:p>","DOI":"10.1007\/s10700-020-09320-1","type":"journal-article","created":{"date-parts":[[2020,4,25]],"date-time":"2020-04-25T15:03:31Z","timestamp":1587827011000},"page":"311-332","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A new parallel fuzzy data envelopment analysis model for parallel systems with two components based on Stackelberg game theory"],"prefix":"10.1007","volume":"19","author":[{"given":"Xiao","family":"Shi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali","family":"Emrouznejad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Minyue","family":"Jin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,4,25]]},"reference":[{"issue":"4","key":"9320_CR1","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1057\/jors.1995.63","volume":"46","author":"JE Beasley","year":"1995","unstructured":"Beasley, J. 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