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Based on the criterion of Value-at-Risk (VaR) and its minimization, we introduce one centralized decision model and three decentralized decision models to obtain the respective optimal decisions of both the manufacturer and the retailer, by analyzing the fuzzy uncertainties and the relationship among the demand, retail price and shelf-space. The corresponding optimal strategies of the two participants are obtained along with one example.<\/jats:p>","DOI":"10.3233\/jifs-17508","type":"journal-article","created":{"date-parts":[[2017,12,19]],"date-time":"2017-12-19T11:43:32Z","timestamp":1513683812000},"page":"733-744","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Optimal decision for a fuzzy supply chain with shrinkage under VaR criterion"],"prefix":"10.1177","volume":"34","author":[{"given":"Qingfeng","family":"Song","sequence":"first","affiliation":[{"name":"School of Science, Tianjin Chengjian University, Tianjin, China"},{"name":"School of Computer Science and Communication Engineering, Tianjin University of Technology, Tianjin, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Computer Science and Communication Engineering, Tianjin 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