{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T21:13:38Z","timestamp":1772745218431,"version":"3.50.1"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2016,8]]},"abstract":"<jats:p>This paper studies the minimum spanning tree problem on a graph with uncertain edge weights, which are formulated as uncertain variables. The concept of ideal uncertain minimum spanning tree (ideal UMST) is initiated by extending the definition of the uncertain [Formula: see text]-minimum spanning tree to reect the overall properties of the \u03b1-minimum spanning tree weights at any confidence level [Formula: see text]. On the basis of this new concept, the definition of uncertain distribution-minimum spanning tree is proposed in three ways. Particularly, by considering the tail value at risk from the perspective of risk management, the notion of uncertain [Formula: see text]-distribution-minimum spanning tree ([Formula: see text]-distribution-UMST) is suggested. It is shown that the [Formula: see text]-distribution-UMST is just the uncertain expected minimum spanning tree when [Formula: see text] = 0. For any [Formula: see text], this problem can be effectively solved via the proposed deterministic graph transformation-based approach with the aid of the [Formula: see text]-distribution-path optimality condition. Furthermore, the proposed definitions and solutions are illustrated by some numerical examples.<\/jats:p>","DOI":"10.1142\/s0218488516500264","type":"journal-article","created":{"date-parts":[[2016,8,4]],"date-time":"2016-08-04T03:42:17Z","timestamp":1470282137000},"page":"537-560","source":"Crossref","is-referenced-by-count":11,"title":["Uncertain Distribution-Minimum Spanning Tree Problem"],"prefix":"10.1142","volume":"24","author":[{"given":"Jian","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Management, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiajie","family":"Yi","sequence":"additional","affiliation":[{"name":"School of Management, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ke","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Management, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Management, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,8,3]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1109\/MAHC.1985.10011"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2006.06.020"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpsycho.2014.04.001"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.2307\/2346439"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1016\/S0262-8856(96)01105-5"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1956-0078686-7"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1957.tb01515.x"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(81)90004-4"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1007\/s11227-010-0484-1"},{"key":"p_10","first-page":"321","author":"Dhamdhere K.","year":"2005","journal-title":"Heidelberg"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1007\/11944836_3"},{"key":"p_12","doi-asserted-by":"crossref","first-page":"247","DOI":"10.15807\/jorsj.39.247","volume":"39","author":"Itoh T.","year":"1996","journal-title":"J. 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