Fuzzy minimum weight edge covering problem
Minimum weight edge covering problem, known as a classic problem in graph theory, is employed in many scientific and engineering applications. In the applications, the weight may denote cost, time, or opponent’s payoff, which can be vague in practice. This paper considers the edge covering problem u...
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| Veröffentlicht in: | Applied mathematical modelling 2008-07, Vol.32 (7), p.1327-1337 |
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| creator | Ni, Yaodong |
| description | Minimum weight edge covering problem, known as a classic problem in graph theory, is employed in many scientific and engineering applications. In the applications, the weight may denote cost, time, or opponent’s payoff, which can be vague in practice. This paper considers the edge covering problem under fuzzy environment, and formulates three models which are expected minimum weight edge cover model,
α-minimum weight edge cover model, and the most minimum weight edge cover model. As an extension for the models, we respectively introduce the crisp equivalent of each model in the case that the weights are independent trapezoidal fuzzy variables. Due to the complexity of the problem, a hybrid intelligent algorithm is employed to solve the models, which can deal with the problem with any type of fuzzy weights. At last, some numerical experiments are given to show the application of the models and the robustness of the algorithm. |
| doi_str_mv | 10.1016/j.apm.2007.04.007 |
| format | Article |
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α-minimum weight edge cover model, and the most minimum weight edge cover model. As an extension for the models, we respectively introduce the crisp equivalent of each model in the case that the weights are independent trapezoidal fuzzy variables. Due to the complexity of the problem, a hybrid intelligent algorithm is employed to solve the models, which can deal with the problem with any type of fuzzy weights. At last, some numerical experiments are given to show the application of the models and the robustness of the algorithm.</description><identifier>ISSN: 0307-904X</identifier><identifier>DOI: 10.1016/j.apm.2007.04.007</identifier><identifier>CODEN: AMMODL</identifier><language>eng</language><publisher>New York, NY: Elsevier Inc</publisher><subject>Applied sciences ; Combinatorics ; Combinatorics. Ordered structures ; Computer science; control theory; systems ; Credibility measure ; Edge cover ; Exact sciences and technology ; Fuzzy programming ; Genetic algorithm ; Graph theory ; Information retrieval. Graph ; Mathematics ; Sciences and techniques of general use ; Theoretical computing</subject><ispartof>Applied mathematical modelling, 2008-07, Vol.32 (7), p.1327-1337</ispartof><rights>2007 Elsevier Inc.</rights><rights>2008 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c401t-a75b5346bedb786f1d8930424b0ab206723a5f14afaccaa8aa835f855041f9e53</citedby><cites>FETCH-LOGICAL-c401t-a75b5346bedb786f1d8930424b0ab206723a5f14afaccaa8aa835f855041f9e53</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0307904X07001084$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20233176$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Ni, Yaodong</creatorcontrib><title>Fuzzy minimum weight edge covering problem</title><title>Applied mathematical modelling</title><description>Minimum weight edge covering problem, known as a classic problem in graph theory, is employed in many scientific and engineering applications. In the applications, the weight may denote cost, time, or opponent’s payoff, which can be vague in practice. This paper considers the edge covering problem under fuzzy environment, and formulates three models which are expected minimum weight edge cover model,
α-minimum weight edge cover model, and the most minimum weight edge cover model. As an extension for the models, we respectively introduce the crisp equivalent of each model in the case that the weights are independent trapezoidal fuzzy variables. Due to the complexity of the problem, a hybrid intelligent algorithm is employed to solve the models, which can deal with the problem with any type of fuzzy weights. At last, some numerical experiments are given to show the application of the models and the robustness of the algorithm.</description><subject>Applied sciences</subject><subject>Combinatorics</subject><subject>Combinatorics. Ordered structures</subject><subject>Computer science; control theory; systems</subject><subject>Credibility measure</subject><subject>Edge cover</subject><subject>Exact sciences and technology</subject><subject>Fuzzy programming</subject><subject>Genetic algorithm</subject><subject>Graph theory</subject><subject>Information retrieval. Graph</subject><subject>Mathematics</subject><subject>Sciences and techniques of general use</subject><subject>Theoretical computing</subject><issn>0307-904X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLw0AUhWehYH38AHfZ6EJIvPNKUlxJsSoU3Ci4GyaTO3VKHnUmqbS_3iktLoULhwvfOZd7CLmmkFGg-f0q0-s2YwBFBiKLckImwKFIpyA-z8h5CCsAkHGbkLv5uNttk9Z1rh3b5Afd8mtIsF5iYvoNetctk7XvqwbbS3JqdRPw6qgX5GP-9D57SRdvz6-zx0VqBNAh1YWsJBd5hXVVlLmldTnlIJioQFcM8oJxLS0V2mpjtC7jcGlLKUFQO0XJL8jtITfe_R4xDKp1wWDT6A77MSjOSk5ZySJID6DxfQgerVp712q_VRTUvgm1UrEJtW9CgVBRoufmGK6D0Y31ujMu_BkZMM5pkUfu4cBh_HTj0KtgHHYGa-fRDKru3T9XfgE8yHSS</recordid><startdate>20080701</startdate><enddate>20080701</enddate><creator>Ni, Yaodong</creator><general>Elsevier Inc</general><general>Elsevier Science</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20080701</creationdate><title>Fuzzy minimum weight edge covering problem</title><author>Ni, Yaodong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c401t-a75b5346bedb786f1d8930424b0ab206723a5f14afaccaa8aa835f855041f9e53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Applied sciences</topic><topic>Combinatorics</topic><topic>Combinatorics. Ordered structures</topic><topic>Computer science; control theory; systems</topic><topic>Credibility measure</topic><topic>Edge cover</topic><topic>Exact sciences and technology</topic><topic>Fuzzy programming</topic><topic>Genetic algorithm</topic><topic>Graph theory</topic><topic>Information retrieval. Graph</topic><topic>Mathematics</topic><topic>Sciences and techniques of general use</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ni, Yaodong</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Applied mathematical modelling</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ni, Yaodong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fuzzy minimum weight edge covering problem</atitle><jtitle>Applied mathematical modelling</jtitle><date>2008-07-01</date><risdate>2008</risdate><volume>32</volume><issue>7</issue><spage>1327</spage><epage>1337</epage><pages>1327-1337</pages><issn>0307-904X</issn><coden>AMMODL</coden><abstract>Minimum weight edge covering problem, known as a classic problem in graph theory, is employed in many scientific and engineering applications. In the applications, the weight may denote cost, time, or opponent’s payoff, which can be vague in practice. This paper considers the edge covering problem under fuzzy environment, and formulates three models which are expected minimum weight edge cover model,
α-minimum weight edge cover model, and the most minimum weight edge cover model. As an extension for the models, we respectively introduce the crisp equivalent of each model in the case that the weights are independent trapezoidal fuzzy variables. Due to the complexity of the problem, a hybrid intelligent algorithm is employed to solve the models, which can deal with the problem with any type of fuzzy weights. At last, some numerical experiments are given to show the application of the models and the robustness of the algorithm.</abstract><cop>New York, NY</cop><pub>Elsevier Inc</pub><doi>10.1016/j.apm.2007.04.007</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Applied sciences Combinatorics Combinatorics. Ordered structures Computer science control theory systems Credibility measure Edge cover Exact sciences and technology Fuzzy programming Genetic algorithm Graph theory Information retrieval. Graph Mathematics Sciences and techniques of general use Theoretical computing |
| title | Fuzzy minimum weight edge covering problem |
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