{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:06:18Z","timestamp":1760241978290,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,2]],"date-time":"2018-11-02T00:00:00Z","timestamp":1541116800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["2018J01527"],"award-info":[{"award-number":["2018J01527"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fujian Science and Technology Guiding Project","award":["2018Y0079"],"award-info":[{"award-number":["2018Y0079"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, a new \u03b1-representation of the inexact T2 fuzzy sets programming model (\u03b1-RITF2SP) is proposed for water resources planning under uncertainties. The developed model is a hybrid of inexact type-2 (T2) fuzzy sets (FSs) optimal programming based on \u03b1-cuts and \u03b1-planes (z-slices) algorithms, and both can be used in problems of water resource management without a loss of generality. Therefore, this novel method represents a complementary method to combine both of these algorithms to make inexact T2FSs methods easier and faster for users under uncertainties. This method provides not only a reduction in computations when computing fuzzy functions, but also a map of the primary variable of T2FSs in the secondary membership function. The \u03b1-RITF2SP is applied to a real case study of the operation of water resource systems in the southern Min River basin that involves three cities: Xiamen, Zhangzhou, and Quanzhou. The results of the water allocations and benefits have been analyzed. The symptoms of results indicate the higher profit with a higher wastewater treatment rate. It also represents that this model has enhanced abilities and it is relevant and practical as well as can serve as a guide for the development of this regional economy.<\/jats:p>","DOI":"10.3390\/sym10110579","type":"journal-article","created":{"date-parts":[[2018,11,5]],"date-time":"2018-11-05T04:26:39Z","timestamp":1541391999000},"page":"579","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The \u03b1-Representation Inexact T2 Fuzzy Sets Programming Model for Water Resources Management of the Southern Min River Basin under Uncertainty"],"prefix":"10.3390","volume":"10","author":[{"given":"Lei","family":"Jin","sequence":"first","affiliation":[{"name":"College of Environmental Science and Engineering, Xiamen University of Technology, Xiamen 361024, China"},{"name":"Department of Civil Engineering, McMaster University, Hamilton, ON L8S 4L8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiyan","family":"Fu","sequence":"additional","affiliation":[{"name":"College of Environmental Science and Engineering, Xiamen University of Technology, Xiamen 361024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Younggy","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, McMaster University, Hamilton, ON L8S 4L8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huiyan","family":"Cheng","sequence":"additional","affiliation":[{"name":"College of Environmental Science and Engineering, Xiamen University of Technology, Xiamen 361024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guohe","family":"Huang","sequence":"additional","affiliation":[{"name":"Environmental Systems Engineering Program, University of Regina, Regina, SK S4S 0A2, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s10666-009-9194-6","article-title":"Inexact fuzzy-stochastic programming for water resources management under multiple uncertainties","volume":"15","author":"Guo","year":"2010","journal-title":"Environ. 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