[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-31892":3,"doc-seo-31892":27},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"file_id":15,"file_url":16,"file_type":17,"file_size":18,"view_count":4,"is_deleted":4,"is_public":19,"is_downloadable":19,"audit_status":19,"page_count":20,"language":21,"language_code":22,"table_of_contents":23,"faqs":24,"seo_title":13,"seo_description":14,"update_tm":25,"read_time":26},31892,962075006959,"Anda","https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297",8,"Research & Report","Analytic Network Process Alternative Approach for Steady-State Decision","Analytic network process (ANP) is an MCDA method that supports qualitative and quantitative criteria while capturing dependence and feedback among elements to obtain a best alternative from a set. Despite its advantages, ANP can be computationally difficult due to the required power-matrix procedure for reaching a stable limit matrix. Authors propose an alternative route to steady state using Markov chain process concepts and Gauss–Jordan elimination, aiming for reduced complexity and faster computation, and to stimulate further ANP optimization research.","cbCaimy21MkSFA3C","https://ap.wps.com/l/cbCaimy21MkSFA3C","pdf",455350,1,6,"English","en","# Introduction\n# The analytic network process\n## General description","[{\"question\":\"What problem does ANP address in decision making?\",\"answer\":\"ANP addresses multi-criteria decisions by considering multiple qualitative and quantitative criteria together, including dependence and feedback among criteria and alternatives to produce a synthesized best solution.\"},{\"question\":\"Why can ANP calculations be difficult?\",\"answer\":\"ANP requires constructing a power method on an N×N matrix, repeatedly raising it to a sufficiently large power until convergence, which demands substantial computational effort to obtain stable and reliable results.\"},{\"question\":\"What alternative approach do the authors propose for achieving ANP steady state?\",\"answer\":\"The paper proposes an alternative mathematical approach that uses Markov chain process concepts and the Gauss–Jordan elimination method to reach the decision steady state, aiming to be less complex and slightly quicker than the traditional power-matrix approach.\"}]",1780434041,15,{"code":4,"msg":28,"data":29},"ok",{"site_id":30,"language":22,"slug":31,"title":13,"keywords":32,"description":14,"schema_data":33,"social_meta":84,"head_meta":86,"extra_data":88,"updated_unix":25},105,"analytic-network-process-alternative-approach-for-steady-state-decision","",{"@graph":34,"@context":83},[35,52,66],{"@type":36,"itemListElement":37},"BreadcrumbList",[38,42,46,49],{"item":39,"name":40,"@type":41,"position":19},"https://docshare.wps.com","Home","ListItem",{"item":43,"name":44,"@type":41,"position":45},"https://docshare.wps.com/document/","Document",2,{"item":47,"name":12,"@type":41,"position":48},"https://docshare.wps.com/document/research-report/",3,{"item":50,"name":13,"@type":41,"position":51},"https://docshare.wps.com/document/analytic-network-process-alternative-approach-for-steady-state-decision/31892/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"description":14,"dateModified":60,"datePublished":60,"encodingFormat":59,"isAccessibleForFree":61,"interactionStatistic":62},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":39,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-06-02",true,{"@type":63,"interactionType":64,"userInteractionCount":4},"InteractionCounter",{"@type":65},"ViewAction",{"@type":67,"mainEntity":68},"FAQPage",[69,75,79],{"name":70,"@type":71,"acceptedAnswer":72},"What problem does ANP address in decision making?","Question",{"text":73,"@type":74},"ANP addresses multi-criteria decisions by considering multiple qualitative and quantitative criteria together, including dependence and feedback among criteria and alternatives to produce a synthesized best solution.","Answer",{"name":76,"@type":71,"acceptedAnswer":77},"Why can ANP calculations be difficult?",{"text":78,"@type":74},"ANP requires constructing a power method on an N×N matrix, repeatedly raising it to a sufficiently large power until convergence, which demands substantial computational effort to obtain stable and reliable results.",{"name":80,"@type":71,"acceptedAnswer":81},"What alternative approach do the authors propose for achieving ANP steady state?",{"text":82,"@type":74},"The paper proposes an alternative mathematical approach that uses Markov chain process concepts and the Gauss–Jordan elimination method to reach the decision steady state, aiming to be less complex and slightly quicker than the traditional power-matrix approach.","https://schema.org",{"og:url":50,"og:type":85,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":87,"canonical":50},"index,follow",{"doc_id":7,"site_id":30}]