{"id":13042,"date":"2026-09-13T00:11:08","date_gmt":"2026-09-12T18:41:08","guid":{"rendered":"https:\/\/bijmrd.com\/?p=13042"},"modified":"2026-09-13T00:11:15","modified_gmt":"2026-09-12T18:41:15","slug":"revisiting-the-theory-of-tripolar-hyperfuzzy-graphs","status":"publish","type":"post","link":"https:\/\/bijmrd.com\/index.php\/volume4-issue8\/revisiting-the-theory-of-tripolar-hyperfuzzy-graphs\/","title":{"rendered":"Revisiting the Theory of Tripolar HyperFuzzy Graphs"},"content":{"rendered":"\n<p class=\"has-vivid-cyan-blue-color has-text-color\"><strong>Author: Takaaki Fujita<\/strong><\/p>\n\n\n\n<p class=\"has-luminous-vivid-orange-color has-text-color\"><strong>DOI Link:<\/strong> <a href=\"https:\/\/doi.org\/10.70798\/Bijmrd\/04080003\">https:\/\/doi.org\/10.70798\/Bijmrd\/04080003<\/a><\/p>\n\n\n\n<p><strong>Abstract:<\/strong> Graph-based models provide a fundamental mathematical framework for representing relational systems in terms of vertices and their connections. Fuzzy sets extend classical set theory by assigning each element a membership degree in the interval [0,1], thereby allowing partial membership rather than restricting membership to binary values. Through the use of HyperStructures [17], Fuzzy Sets have been generalized to HyperFuzzy Sets [18\u201320]. Furthermore, the HyperFuzzy Set framework has been extended to graph-theoretic settings, leading to the development of HyperFuzzy Graphs [39\u201341].Motivated by these developments, this paper investigates tripolar extensions of the hyperfuzzy framework. In particular, we study Tripolar HyperFuzzy Sets and Tripolar HyperFuzzy Graphs, which integrate the three-pole representation of tripolar fuzzy models with the set-valued membership structure underlying HyperFuzzy Sets and HyperFuzzy Graphs<\/p>\n\n\n\n<p><strong>Keywords:<\/strong> HyperFuzzy Set, HyperFuzzy Graph, Tripolar Fuzzy Set.<\/p>\n\n\n\n<p class=\"has-ast-global-color-1-color has-text-color\"><strong>Page No: 16-25<\/strong><\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-ast-global-color-6-background-color has-background wp-element-button\" href=\"https:\/\/bijmrd.com\/wp-content\/uploads\/2026\/09\/16-25.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">download journal<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Author: Takaaki Fujita DOI Link: https:\/\/doi.org\/10.70798\/Bijmrd\/04080003 Abstract: Graph-based models provide a fundamental mathematical framework for representing relational systems in terms of vertices and their connections. Fuzzy sets extend classical set theory by assigning each element a membership degree in the interval [0,1], thereby allowing partial membership rather than restricting membership to binary values. Through the &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/bijmrd.com\/index.php\/volume4-issue8\/revisiting-the-theory-of-tripolar-hyperfuzzy-graphs\/\"> <span class=\"screen-reader-text\">Revisiting the Theory of Tripolar HyperFuzzy Graphs<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":"","_joinchat":[]},"categories":[64],"tags":[],"rttpg_featured_image_url":null,"rttpg_author":{"display_name":false,"author_link":"https:\/\/bijmrd.com\/index.php\/author\/asraful-alibiswas\/"},"rttpg_comment":0,"rttpg_category":"<a href=\"https:\/\/bijmrd.com\/index.php\/category\/volume4-issue8\/\" rel=\"category tag\">Volume4 Issue8<\/a>","rttpg_excerpt":"Author: Takaaki Fujita DOI Link: https:\/\/doi.org\/10.70798\/Bijmrd\/04080003 Abstract: Graph-based models provide a fundamental mathematical framework for representing relational systems in terms of vertices and their connections. Fuzzy sets extend classical set theory by assigning each element a membership degree in the interval [0,1], thereby allowing partial membership rather than restricting membership to binary values. Through the&hellip;","_links":{"self":[{"href":"https:\/\/bijmrd.com\/index.php\/wp-json\/wp\/v2\/posts\/13042"}],"collection":[{"href":"https:\/\/bijmrd.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bijmrd.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bijmrd.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bijmrd.com\/index.php\/wp-json\/wp\/v2\/comments?post=13042"}],"version-history":[{"count":2,"href":"https:\/\/bijmrd.com\/index.php\/wp-json\/wp\/v2\/posts\/13042\/revisions"}],"predecessor-version":[{"id":13045,"href":"https:\/\/bijmrd.com\/index.php\/wp-json\/wp\/v2\/posts\/13042\/revisions\/13045"}],"wp:attachment":[{"href":"https:\/\/bijmrd.com\/index.php\/wp-json\/wp\/v2\/media?parent=13042"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bijmrd.com\/index.php\/wp-json\/wp\/v2\/categories?post=13042"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bijmrd.com\/index.php\/wp-json\/wp\/v2\/tags?post=13042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}