{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T18:03:22Z","timestamp":1771956202806,"version":"3.50.1"},"reference-count":33,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T00:00:00Z","timestamp":1625443200000},"content-version":"vor","delay-in-days":185,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Wireless Communications and Mobile Computing"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>In this research work, an approach to determine the critical path of activity network with normalized heptagonal fuzzy data is proposed. In the proposed model, we attempt to develop a method for solving litigation problems by experts when they share the same information but differ in their opinions. The concepts for a critical path method (CPM) optimization with two kinds of data are as follows: those are to be optimistic and those considered being pessimistic. A numerical example is given for the illustration of the proposed approach and gain more insights. Based on the findings of the proposed work, we observe that the floating times with optimistic data are always smaller than or equal to the corresponding floating times for the pessimistic data.<\/jats:p>","DOI":"10.1155\/2021\/6699403","type":"journal-article","created":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T23:11:09Z","timestamp":1625526669000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["On Determining the Critical Path of Activity Network with Normalized Heptagonal Fuzzy Data"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1916-0998","authenticated-orcid":false,"given":"Hamiden Abd El-Wahed","family":"Khalifa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0623-6420","authenticated-orcid":false,"given":"Majed G.","family":"Alharbi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5340-7777","authenticated-orcid":false,"given":"Pavan","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,7,5]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.4314\/gjpas.v8i3.16018"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.4314\/gjpas.v18i3-4.11"},{"key":"e_1_2_10_3_2","first-page":"2277","article-title":"Project planning and scheduling using PERT and CPM techniques with linear programming","volume":"4","author":"Agyei W.","year":"2015","journal-title":"International Journal of Scientific & Technology Research"},{"key":"e_1_2_10_4_2","first-page":"2319","article-title":"Case study: making and monitoring of critical path in shoe production planning","volume":"4","author":"Rautela M. S.","year":"2015","journal-title":"Journal of Business Management & Social Science Research"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/547627"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.17.4.B141"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(78)90031-3"},{"key":"e_1_2_10_9_2","volume-title":"Fuzzy Sets and Systems: Theory and Applications","author":"Dubois D.","year":"1980"},{"key":"e_1_2_10_10_2","volume-title":"Fuzzy Mathematical Models in Engineering and Management Science","author":"Kaufmann A.","year":"1988"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(00)00076-2"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(99)00119-0"},{"key":"e_1_2_10_13_2","first-page":"29","article-title":"Fuzzy critical path for project network","volume":"15","author":"Liang G. S.","year":"2004","journal-title":"Information and Management Science"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2004.08.007"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2006.06.053"},{"key":"e_1_2_10_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2007.04.009"},{"key":"e_1_2_10_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00170-008-1598-y"},{"key":"e_1_2_10_18_2","first-page":"953","article-title":"An analytical method for finding critical path in a fuzzy project network","volume":"5","author":"Shankar N. R.","year":"2010","journal-title":"International Journal of Contemporary Mathematical Sciences"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2010.05.026"},{"key":"e_1_2_10_20_2","first-page":"600","article-title":"A new approach to find total float time and critical path in a fuzzy project network","volume":"2","author":"Sireesha V.","year":"2010","journal-title":"International Journal of Engineering Science and Technology"},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)CO.1943-7862.0000256"},{"key":"e_1_2_10_22_2","doi-asserted-by":"publisher","DOI":"10.5267\/j.msl.2011.22.003"},{"key":"e_1_2_10_23_2","doi-asserted-by":"publisher","DOI":"10.12732\/ijpam.v85i2.4"},{"key":"e_1_2_10_24_2","first-page":"806","article-title":"Solving the fuzzy project scheduling problem based on a ranking function","volume":"7","author":"Khalaf W. S.","year":"2013","journal-title":"Australian Journal of Basic and Applied Sciences"},{"key":"e_1_2_10_25_2","first-page":"161","article-title":"Application of fuzzy theory to project scheduling with critical path method","volume":"17","author":"Oladeinde M. H.","year":"2013","journal-title":"Journal of Applied Sciences and Environmental Management"},{"key":"e_1_2_10_26_2","doi-asserted-by":"publisher","DOI":"10.14445\/22315373\/IJMTT-V54P542"},{"key":"e_1_2_10_27_2","doi-asserted-by":"publisher","DOI":"10.1109\/3468.823483"},{"key":"e_1_2_10_28_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2013.860639"},{"key":"e_1_2_10_29_2","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/8893976"},{"key":"e_1_2_10_30_2","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/6697060"},{"key":"e_1_2_10_31_2","first-page":"405","article-title":"Fuzzy assignment problems using normalized heptagonal fuzzy numbers","volume":"117","author":"Selvam P.","year":"2017","journal-title":"International Journal of Pure and Applied Mathematics"},{"key":"e_1_2_10_32_2","first-page":"2395","article-title":"Single transmit fuzzy queuing model with two-classes: execution proportions by ranking technique","volume":"15","author":"Usha P. K.","year":"2020","journal-title":"Journal of Engineering Science and Technology"},{"key":"e_1_2_10_33_2","doi-asserted-by":"publisher","DOI":"10.26524\/krj.2020.29"}],"container-title":["Wireless Communications and Mobile Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/wcmc\/2021\/6699403.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/wcmc\/2021\/6699403.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/6699403","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T11:45:26Z","timestamp":1723031126000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/6699403"}},"subtitle":[],"editor":[{"given":"Giovanni","family":"Pau","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/6699403"],"URL":"https:\/\/doi.org\/10.1155\/2021\/6699403","archive":["Portico"],"relation":{},"ISSN":["1530-8669","1530-8677"],"issn-type":[{"value":"1530-8669","type":"print"},{"value":"1530-8677","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2020-12-05","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-06-18","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-07-05","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"6699403"}}