{"id":17407,"date":"2022-06-13T11:04:50","date_gmt":"2022-06-13T04:04:50","guid":{"rendered":"https:\/\/metmar.net\/?p=17407"},"modified":"2022-06-13T11:16:39","modified_gmt":"2022-06-13T04:16:39","slug":"geometric-picture-fuzzy-numbers-and-three-dimensional-copulas-with-the-non-linear-programming-approach","status":"publish","type":"post","link":"https:\/\/metmar.net\/geometric-picture-fuzzy-numbers-and-three-dimensional-copulas-with-the-non-linear-programming-approach\/","title":{"rendered":"Geometric picture fuzzy numbers and three-dimensional copulas with the non-linear programming approach"},"content":{"rendered":"<p><strong><span style=\"color: #008000;\">Authors: <\/span><\/strong><span style=\"color: #3366ff;\">Nguyen Dinh Phu\u00aa, Nguyen Nhut Hung<sup>b<\/sup>, Ali Ahmadian<sup>c,<\/sup>*, Soheil Salahshour<sup>d<\/sup> and Norazak Senu<sup>e<\/sup><\/span><\/p>\n<p><span class=\"generated\"><strong><span style=\"color: #008000;\">Affiliations:<\/span><\/strong>\u00a0<\/span><a id=\"aff1\"><\/a><span style=\"color: #3366ff;\"><span class=\"generated\">[<\/span>a<span class=\"generated\">]\u00a0<\/span>Faculty of Engineering Technology, Quang Trung University, Quy Nhon City, Vietnam |\u00a0<\/span><a id=\"aff2\"><\/a><span style=\"color: #3366ff;\"><span class=\"generated\">[<\/span>b<span class=\"generated\">]\u00a0<\/span>Faculty of Engineering Technology, Quang Trung University, Vietnam |\u00a0<\/span><a id=\"aff3\"><\/a><span style=\"color: #3366ff;\"><span class=\"generated\">[<\/span>c<span class=\"generated\">]\u00a0<\/span>Institute of IR 4.0, The National University of Malaysia, UKM, Bangi, Selangor, Malaysia |\u00a0<\/span><a id=\"aff4\"><\/a><span style=\"color: #3366ff;\"><span class=\"generated\">[<\/span>d<span class=\"generated\">]\u00a0<\/span>Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey |\u00a0<\/span><a id=\"aff5\"><\/a><span style=\"color: #3366ff;\"><span class=\"generated\">[<\/span>e<span class=\"generated\">]\u00a0<\/span>Institute for Mathematical Research (INSPEM), University Putra Malaysia, UPM, Selangor, Malaysia<\/span><\/p>\n<p><span class=\"generated\" style=\"color: #008000;\"><strong>Journal:<\/strong>\u00a0<\/span><span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/content.iospress.com\/journals\/journal-of-intelligent-and-fuzzy-systems\" target=\"_blank\" rel=\"noopener\">Journal of Intelligent &amp; Fuzzy Systems<\/a>, vol. 40, no. 1, pp. 1-12, 2021<\/span><\/p>\n<p><strong><span class=\"generated\" style=\"color: #008000;\">Article type:\u00a0<\/span><\/strong><span style=\"color: #3366ff;\">Research Article<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #339966;\"><strong>Abstract:<\/strong><\/span><span style=\"color: #3366ff;\"> This study presents a possible relationship between two main objects, which are three-dimensional copulas (3D-Cs) and geometric picture fuzzy numbers (GPFNs). This opens up a potential field for future studies for these two objects that three-dimensional copulas can become useful tools for handling uncertainty information in the form of a picture fuzzy set (PFS). Specifically, we define a GPFN as a base element of the PFS and a defined domain of three-dimensional copulas that contains a set of GPFNs, then we show some examples of three-dimensional copulas identified on this domain. In thi framework, we present the theorems related to these two objects. At the same time, we provide some examples for three-dimensional semi-copulas, three-dimensional quasi-copulas, and three-dimensional empirical copulas defined on D, which is a defined domain of a three-dimensional copula and contains a set of GPFNs D\u2217g. In addition, we also introduce a new approach to non-linear programming problems.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #339966;\"><strong>Keywords:<\/strong> <\/span><span style=\"color: #ff00ff;\">Three-dimensional distribution functions, three-dimensional copulas (3D-Cs), geometric picture fuzzy numbers (GPFNs), additional set of geometric picture fuzzy numbers (Ad-GPFNs), non-linear programming approach<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"Authors: Nguyen Dinh Phu\u00aa, Nguyen Nhut Hungb, Ali Ahmadianc,*, Soheil Salahshourd and Norazak Senue Affiliations:\u00a0[a]\u00a0Faculty of Engineering Technology, Quang Trung University, Quy Nhon City, Vietnam |\u00a0[b]\u00a0Faculty of Engineering Technology, Quang Trung University, Vietnam |\u00a0[c]\u00a0Institute of IR 4.0, The National University of Malaysia, UKM, Bangi, Selangor, Malaysia |\u00a0[d]\u00a0Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, [&hellip;]","protected":false},"author":12,"featured_media":17414,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"site-sidebar-layout":"default","site-content-layout":"default","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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