{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:44:34Z","timestamp":1740149074260,"version":"3.37.3"},"reference-count":34,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004055","name":"King Fahd University of Petroleum and Minerals","doi-asserted-by":"publisher","award":["IN161058"],"award-info":[{"award-number":["IN161058"]}],"id":[{"id":"10.13039\/501100004055","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2018]]},"abstract":"<jats:p>The present paper deals with the concepts of generalized fuzzy invex monotonocities and generalized weakly fuzzy invex functions. Some necessary conditions for weakly fuzzy invex monotonocities are presented. Moreover, the concept of fuzzy strong invex monotonocities and fuzzy strong invex functions are also discussed. To strengthen our definitions, we provide nontrivial examples of fuzzy invex monotonocities and weakly fuzzy invex functions.<\/jats:p>","DOI":"10.1155\/2018\/3749650","type":"journal-article","created":{"date-parts":[[2018,4,11]],"date-time":"2018-04-11T19:30:55Z","timestamp":1523475055000},"page":"1-9","source":"Crossref","is-referenced-by-count":1,"title":["Criterion for Generalized Weakly Fuzzy Invex Monotonocities"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6554-1228","authenticated-orcid":true,"given":"Meraj A.","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3482-8634","authenticated-orcid":true,"given":"Izhar","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"}]},{"given":"Abdulrahman","family":"Aljohani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia"}]}],"member":"311","reference":[{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(81)90123-2"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(01)00393-9"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023953823177"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2003.11.017"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2001.7574"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2004.08.033"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/BF00939384"},{"issue":"1","key":"1","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1023\/A:1008321026317","volume":"18","year":"2000","journal-title":"Journal of Global Optimization"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-007-9271-4"},{"issue":"5","key":"2","first-page":"881","volume":"21","year":"2016","journal-title":"Journal of Computational Analysis and Applications"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90256-4"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(96)00192-3"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(01)00157-9"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(86)90026-6"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90011-6"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/849104"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.09.015"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00210-8"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00415-1"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.01.003"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2008.08.012"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2015.02.007"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2008.11.005"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(02)00440-2"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2008.03.012"},{"year":"2002","key":"18"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-013-9156-y"},{"issue":"3","key":"32","first-page":"267","volume":"12","year":"2010","journal-title":"International Journal of Fuzzy Systems"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1080\/00207727808941724"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(83)90169-5"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(87)90030-3"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2004.08.001"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2012.02.001"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2012.10.003"}],"container-title":["Advances in Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/3749650.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/3749650.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/3749650.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,4,29]],"date-time":"2018-04-29T19:31:10Z","timestamp":1525030270000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/afs\/2018\/3749650\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"references-count":34,"alternative-id":["3749650","3749650"],"URL":"https:\/\/doi.org\/10.1155\/2018\/3749650","relation":{},"ISSN":["1687-7101","1687-711X"],"issn-type":[{"type":"print","value":"1687-7101"},{"type":"electronic","value":"1687-711X"}],"subject":[],"published":{"date-parts":[[2018]]}}}