[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-293748-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-293748-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","clustering-algorithm-of-triple-rened-indeterminate-neutrosophic-set-for-personality-grouping","Clustering Algorithm of Triple Re􀀂ned Indeterminate Neutrosophic Set for Personality Grouping","","Triple Re􀀂ned Indeterminate Neutrosophic Set (TRINS) extends the re􀀂ned neutrosophic framework to model uncertain, imprecise, incomplete, and inconsistent real-world information with improved handling of indeterminacy. Indeterminacy is classified into three cases relative to membership: leaning toward truth, membership, and leaning toward false. The paper introduces the TRIN-MST clustering algorithm for data represented by triple re􀀂ned indeterminate neutrosophic information. Illustrative examples based on an indeterminacy-based personality test demonstrate the method’s applicability and effectiveness. The approach is positioned as more accurate than SVNS and DRINS and suitable where Likert scale data is used.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/clustering-algorithm-of-triple-rened-indeterminate-neutrosophic-set-for-personality-grouping/293748/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/clustering-algorithm-of-triple-rened-indeterminate-neutrosophic-set-for-personality-grouping/293748.png","ImageObject",300,407,{"name":42,"@type":43},"Melati","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-26","2026-09-17",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is TRINS and what problem does it address?","Question",{"text":63,"@type":64},"TRINS is a triple re􀀂ned indeterminate neutrosophic set that represents uncertain, imprecise, incomplete, and inconsistent information. It improves handling by classifying indeterminacy relative to truth and false membership.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How is indeterminacy classified in TRINS?",{"text":68,"@type":64},"Indeterminacy (I) is divided into three categories based on membership: leaning toward truth membership (IT), indeterminacy membership (I), and leaning toward false membership (IF).",{"name":70,"@type":61,"acceptedAnswer":71},"What clustering method does the paper propose?",{"text":72,"@type":64},"The paper proposes the TRIN-MST clustering algorithm, a triple re􀀂ned indeterminate neutrosophic minimum spanning tree approach. It clusters data represented in the TRINS form, illustrated using an indeterminacy-based personality test.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},293748,1789668446,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,100,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},8,30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":55,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":111,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":123,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":80,"read_time":143,"preview_page_count":4},962085570644,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Computing Conference 2017 18-20 July 2017 | London, UK  \nClustering Algorithm of Triple Re􀀂ned Indeterminate Neutrosophic Set for Personality Grouping  \nIlanthenral Kandasamy  \nSchool of Computer Engineering and Science Vellore Institute of Technology, India Email: [ilanthenral.k@vit.ac.in](ilanthenral.k@vit.ac.in)  \nFlorentin Smarandache  \nDepartment of Mathematics, University of New Mexico, USA Email: [smarandache@unm.edu](smarandache@unm.edu)  \nAbstract—Triple Re􀀂ned Indeterminate Neutrosophic Set (TRINS) which is a case of the re􀀂ned neutrosophic set was introduced in [27]. It provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world. More precision is provided in handling indeterminacy; by classifying indeterminacy (I) into three, based on membership; as indeterminacy leaning towards truth membership (IT ), indeterminacy membership (I) and indeterminacy leaning towards false membership (IF ). This kind of classi􀀂cation of indeterminacy is not feasible with the existing Single Valued Neutrosophic Set (SVNS). TRINS is better equipped at dealing indeterminate and inconsistent information, with more accuracy than SVNS and Double Re􀀂ned Indeterminate Neutrosophic Set (DRINS), which fuzzy sets and Intuitionistic Fuzzy Sets (IFS) are incapable of. TRINS can be used in any place where the Likert scale is used, which is an advantage. Personality test usually make use of the Likert scale. Using the Open Extended Jung Type Scale test and TRINS, an indeterminacy based personality test was introduced and personality classi􀀂cation was done [27]. A generalized distance measure between TRINS and related distance matrix is de􀀂ned, based on which a clustering algorithm is constructed. This article proposes a Triple Re􀀂ned Indeterminate Neutrosophic Minimum Spanning Tree (TRIN-MST) clustering algorithm, to cluster the data represented by Triple Re􀀂ned Indeterminate Neutrosophic information. Illustrative examples using the indeterminacy based personality test are given to exhibit the applications and effectiveness of the TRIN-MST clustering algorithm.  \nKeywords—Personality test; Personality grouping, Neutrosophic Set, Triple Re􀀂ned Neutrosophic Set (TRINS), TRIN-MST clustering algorithm  \nI. INTRODUCTION  \nCarl Jung in his collected work [1] had theorized the eight psychological types based on two main attitude types: extroversion and introversion, two perceiving functions: sensation and intuition and two judging functions: thinking and feeling. The psychological types were Extraverted sensation, Introverted sensation, Extraverted intuition, Introverted intuition, Extraverted thinking, Introverted thinking, Extraverted feeling and Introverted feeling. The MyersBriggs Type Indicator (MBTI) [2], is based on the typological theory proposed by Carl Jung. It sorts some of these psychological differences into four opposite pairs, or ”dichotomies”, with a resulting 16 possible psychological types. The MBTI is an introspective self-report questionnaire structured to indicate psychological preferences of people’s perception of the world and their decision making. These personality test are mostly objective  \nin nature, where the test taker is forced to select a dominant choice. Quoting Carl Jung himself ”There is no such thing as a pure extrovert or a pure introvert. Such a man would be in the lunatic asylum.”, it is clear that there are degrees of variations, no person 􀀂ts into a category 100% . Since it is not feasible for a person to put down his answer as single choice in reality, without ignoring the other degrees of variation. It necessitates a tool which can give more than one choice to represent their personality. The choice also depends highly on the situation and circumstance the individual faces at that time,  \nFuzzy set theory introduced by Zadeh [3] provides a constructive analytic tool for soft division of sets. Zad","cbCaiooCxUhgqBYq","https://ap.wps.com/l/cbCaiooCxUhgqBYq","pdf",174281,"English","# Introduction\n## Psychological types and personality testing frameworks\n## Motivation for representing uncertainty and indeterminacy\n## From fuzzy and intuitionistic fuzzy sets to neutrosophic sets","[{\"question\":\"What is TRINS and what problem does it address?\",\"answer\":\"TRINS is a triple re􀀂ned indeterminate neutrosophic set that represents uncertain, imprecise, incomplete, and inconsistent information. It improves handling by classifying indeterminacy relative to truth and false membership.\"},{\"question\":\"How is indeterminacy classified in TRINS?\",\"answer\":\"Indeterminacy (I) is divided into three categories based on membership: leaning toward truth membership (IT), indeterminacy membership (I), and leaning toward false membership (IF).\"},{\"question\":\"What clustering method does the paper propose?\",\"answer\":\"The paper proposes the TRIN-MST clustering algorithm, a triple re􀀂ned indeterminate neutrosophic minimum spanning tree approach. It clusters data represented in the TRINS form, illustrated using an indeterminacy-based personality test.\"}]","Clustering Algorithm of Triple Re􀀂ned Indeterminate Neutrosophic Set for Personality Grouping | PDF",25]