{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,21]],"date-time":"2024-02-21T06:04:52Z","timestamp":1708495492928},"reference-count":27,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2011,2]]},"abstract":"<jats:p> In particular, imprecise observations or possible perturbations mean that data in a network flows may well be better represented by intervals or fuzzy numbers than crisp quantities. In this paper we first consider the minimum cost flow problem with compact interval-valued lower and upper bounds, flows, and costs. We present a new method that shows this problem is solved using two minimum cost flow problems with crisp data. Then this result is extended to networks with fuzzy lower and upper bounds, flows, and costs. One of the best algorithms to solve the minimum cost flow problem with crisp data is the cost scaling algorithm of Goldberg and Tarjan.<jats:sup>17<\/jats:sup> In this paper, the cost scaling algorithm is modified for fuzzy lower and upper bounds, flows and costs. The running time of the modified algorithm is equal to the running time of the cost scaling algorithm with crisp data. <\/jats:p>","DOI":"10.1142\/s0218488511006897","type":"journal-article","created":{"date-parts":[[2011,1,19]],"date-time":"2011-01-19T11:36:16Z","timestamp":1295436976000},"page":"71-88","source":"Crossref","is-referenced-by-count":6,"title":["A NEW APPROACH FOR SOLVING THE MINIMUM COST FLOW PROBLEM WITH INTERVAL AND FUZZY DATA"],"prefix":"10.1142","volume":"19","author":[{"given":"MEHDI","family":"GHIYASVAND","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Bu-Ali Sina University, Hamedan, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585705"},{"key":"rf2","volume-title":"Network flows: Theory, Algorithms, and Application","author":"Ahuja R. 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