﻿{"id":15033,"date":"2025-08-12T22:09:50","date_gmt":"2025-08-12T20:09:50","guid":{"rendered":"https:\/\/www.sigterritoires.fr\/?page_id=15033"},"modified":"2025-09-07T12:56:47","modified_gmt":"2025-09-07T10:56:47","slug":"agregation-floue","status":"publish","type":"page","link":"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/","title":{"rendered":"Agr\u00e9gation floue"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contenu <\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Mode_demploi\" >Mode d&#8217;emploi<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Fenetre_de_parametrage\" >Fen\u00eatre de param\u00e9trage<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Champs_%C2%AB_Couche_1_%C2%BB_et_%C2%AB_Couche2_%C2%BB\" >Champs \u00ab\u00a0Couche 1\u00a0\u00bb et \u00ab\u00a0Couche2\u00a0\u00bb<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Champs_%C2%AB_Champ_flou_1_%C2%BB_et_%C2%AB_Champ_flou_2_%C2%BB\" >Champs \u00ab\u00a0Champ flou 1\u00a0\u00bb et \u00ab\u00a0Champ flou 2\u00a0\u00bb<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Type_doperation_spatiale\" >Type d&rsquo;op\u00e9ration spatiale<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Nom_de_la_couche_resultat\" >Nom de la couche r\u00e9sultat<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Symbologie_de_la_couche_resultante\" >Symbologie de la couche r\u00e9sultante<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Symbologie_graduee\" >Symbologie gradu\u00e9e<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Degrade_continu_de_couleurs_de_type_AboveAndBelow\" >D\u00e9grad\u00e9 continu de couleurs de type AboveAndBelow<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Symbologie_par_defaut\" >Symbologie par d\u00e9faut<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Historique_des_transformations\" >Historique des transformations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Definir_la_fonction_dagregation\" >D\u00e9finir la fonction d&rsquo;agr\u00e9gation<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Procedure_de_determination_de_loperation_dagregation\" >Proc\u00e9dure de d\u00e9termination de l\u2019op\u00e9ration d\u2019agr\u00e9gation.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Les_trois_types_de_fonctions_implementees\" >Les trois types de fonctions impl\u00e9ment\u00e9es<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Criteres_de_meme_importance_symetriques\" >Crit\u00e8res de m\u00eame importance (sym\u00e9triques)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Methode_dajustement_pour_criteres_asymetriques\" >M\u00e9thode d\u2019ajustement pour crit\u00e8res asym\u00e9triques<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Methode_dajustement_pour_criteres_symetriques_inhabituels\" >M\u00e9thode d\u2019ajustement pour crit\u00e8res sym\u00e9triques inhabituels<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/#Couche_resultante\" >Couche r\u00e9sultante<\/a><\/li><\/ul><\/nav><\/div>\n\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Mode_demploi\"><\/span>Mode d&#8217;emploi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Fenetre_de_parametrage\"><\/span>Fen\u00eatre de param\u00e9trage<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_window.jpg?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"763\" data-attachment-id=\"15514\" data-permalink=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/fzyaggr_window-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_window.jpg?fit=1153%2C1374&amp;ssl=1\" data-orig-size=\"1153,1374\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"fzyaggr_window\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_window.jpg?fit=640%2C763&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_window.jpg?resize=640%2C763&#038;ssl=1\" alt=\"\" class=\"wp-image-15514\" srcset=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_window.jpg?resize=859%2C1024&amp;ssl=1 859w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_window.jpg?resize=252%2C300&amp;ssl=1 252w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_window.jpg?resize=768%2C915&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_window.jpg?w=1153&amp;ssl=1 1153w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Champs_%C2%AB_Couche_1_%C2%BB_et_%C2%AB_Couche2_%C2%BB\"><\/span>Champs \u00ab\u00a0Couche 1\u00a0\u00bb et \u00ab\u00a0Couche2\u00a0\u00bb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Les champs \u00ab\u00a0couches\u00a0\u00bb affiche la liste des couches charg\u00e9es, limit\u00e9es aux <strong>tables <a href=\"https:\/\/www.sigterritoires.fr\/index.php\/le-format-geopackage-et-qgis-3\/\">geopackage<\/a><\/strong>. En effet, la version actuelle ne prend en compte que des donn\u00e9es stock\u00e9es dans des fichiers geopackage (gpkg).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Champs_%C2%AB_Champ_flou_1_%C2%BB_et_%C2%AB_Champ_flou_2_%C2%BB\"><\/span>Champs \u00ab\u00a0Champ flou 1\u00a0\u00bb et \u00ab\u00a0Champ flou 2\u00a0\u00bb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Une fois s\u00e9lectionn\u00e9e les couches en entr\u00e9e, ces menus d\u00e9roulants affichent tous les <strong>champs suffix\u00e9s <em>_fuzzy<\/em><\/strong> de chacune d&rsquo;elles.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Type_doperation_spatiale\"><\/span>Type d&rsquo;op\u00e9ration spatiale<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Cette option permet de g\u00e9rer l&rsquo;\u00e9tendue spatiale de la couche r\u00e9sultante. <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_spatial_op.jpg?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"763\" data-attachment-id=\"15516\" data-permalink=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/fzyaggr_spatial_op-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_spatial_op.jpg?fit=1153%2C1374&amp;ssl=1\" data-orig-size=\"1153,1374\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"fzyaggr_spatial_op\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_spatial_op.jpg?fit=640%2C763&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_spatial_op.jpg?resize=640%2C763&#038;ssl=1\" alt=\"\" class=\"wp-image-15516\" srcset=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_spatial_op.jpg?resize=859%2C1024&amp;ssl=1 859w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_spatial_op.jpg?resize=252%2C300&amp;ssl=1 252w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_spatial_op.jpg?resize=768%2C915&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_spatial_op.jpg?w=1153&amp;ssl=1 1153w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/figure>\n\n\n\n<p><strong>L&rsquo;option intersection <\/strong>garde dans la couche r\u00e9sultat l&rsquo;\u00e9tendue correspondante \u00e0 la superposition des deux couches en entr\u00e9e.pour chaque intersection, l&rsquo;attribut r\u00e9sultat est calcul\u00e9 \u00e0 partir de la fonction d\u00e9finie plus loin. Mais ceci implique que si une couche n&rsquo;a pas de donn\u00e9es pour une zone, cette zone est ignor\u00e9e dans la couche r\u00e9sultante. Dans un processus impliquant plusieurs agr\u00e9gations d&rsquo;\u00e9tendue diff\u00e9rente, la couche r\u00e9sultante sera amput\u00e9e de mani\u00e8re importante. De plus, l\u2019absence de donn\u00e9es d&rsquo;une zone emp\u00eachera son \u00ab\u00a0rattrapage\u00a0\u00bb dans les agr\u00e9gations ult\u00e9rieures. <\/p>\n\n\n\n<p><strong>L&rsquo;option union<\/strong> garde dans la couche r\u00e9sultat l&rsquo;\u00e9tendue correspondante aux deux couches en entr\u00e9e. Pour chaque zone de superposition, l&rsquo;attribut r\u00e9sultat est calcul\u00e9 \u00e0 partir de la fonction d\u00e9finie plus loin. Pour ls zones o\u00f9 une des deux couches n&rsquo;a pas de donn\u00e9es,l&rsquo;attribut r\u00e9sultat est calcul\u00e9 \u00e0 partir de la fonction d\u00e9finie plus loin en consid\u00e9rant que la valeur de la couche absente est \u00ab\u00a0tr\u00e8s mauvais\u00a0\u00bb. Dans un processus impliquant plusieurs agr\u00e9gations d&rsquo;\u00e9tendue diff\u00e9rente, la couche r\u00e9sultante ne sera pas amput\u00e9e du tout. De plus, l\u2019absence de donn\u00e9es d&rsquo;une zone n&#8217;emp\u00eachera pas son \u00ab\u00a0rattrapage\u00a0\u00bb dans les agr\u00e9gations ult\u00e9rieures. <\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Nom_de_la_couche_resultat\"><\/span>Nom de la couche r\u00e9sultat<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Vous pouvez nommer la couche agr\u00e9g\u00e9e librement, mais elle aura comme suffixe \u00ab\u00a0_agg\u00a0\u00bb.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Symbologie_de_la_couche_resultante\"><\/span>Symbologie de la couche r\u00e9sultante<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_symbology.jpg?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"763\" data-attachment-id=\"15517\" data-permalink=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/fzyaggr_symbology\/\" data-orig-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_symbology.jpg?fit=1153%2C1374&amp;ssl=1\" data-orig-size=\"1153,1374\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"fzyaggr_symbology\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_symbology.jpg?fit=640%2C763&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_symbology.jpg?resize=640%2C763&#038;ssl=1\" alt=\"\" class=\"wp-image-15517\" srcset=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_symbology.jpg?resize=859%2C1024&amp;ssl=1 859w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_symbology.jpg?resize=252%2C300&amp;ssl=1 252w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_symbology.jpg?resize=768%2C915&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/fzyaggr_symbology.jpg?w=1153&amp;ssl=1 1153w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/figure>\n\n\n\n<p>Vous avez deux symbologies \u00e0 votre disposition pour la couche r\u00e9sultante:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Symbologie_graduee\"><\/span>Symbologie gradu\u00e9e<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>Avec 5 classes:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><a href=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/ex_echelle.jpg?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"579\" height=\"549\" data-attachment-id=\"15423\" data-permalink=\"https:\/\/www.sigterritoires.fr\/index.php\/de-lanalyse-booleenne-a-la-logique-floue-dans-un-sig-un-exemple-concret\/ex_echelle\/\" data-orig-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/ex_echelle.jpg?fit=579%2C549&amp;ssl=1\" data-orig-size=\"579,549\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"ex_echelle\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/ex_echelle.jpg?fit=579%2C549&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/ex_echelle.jpg?resize=579%2C549&#038;ssl=1\" alt=\"\" class=\"wp-image-15423\" style=\"width:840px;height:auto\" srcset=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/ex_echelle.jpg?w=579&amp;ssl=1 579w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/ex_echelle.jpg?resize=300%2C284&amp;ssl=1 300w\" sizes=\"auto, (max-width: 579px) 100vw, 579px\" \/><\/a><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Degrade_continu_de_couleurs_de_type_AboveAndBelow\"><\/span>D\u00e9grad\u00e9 continu de couleurs de type AboveAndBelow<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/aboveandbelow_ramp.jpg?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"487\" data-attachment-id=\"15518\" data-permalink=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/aboveandbelow_ramp\/\" data-orig-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/aboveandbelow_ramp.jpg?fit=2159%2C1642&amp;ssl=1\" data-orig-size=\"2159,1642\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"aboveandbelow_ramp\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/aboveandbelow_ramp.jpg?fit=640%2C487&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/aboveandbelow_ramp.jpg?resize=640%2C487&#038;ssl=1\" alt=\"\" class=\"wp-image-15518\" srcset=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/aboveandbelow_ramp.jpg?resize=1024%2C779&amp;ssl=1 1024w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/aboveandbelow_ramp.jpg?resize=300%2C228&amp;ssl=1 300w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/aboveandbelow_ramp.jpg?resize=768%2C584&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/aboveandbelow_ramp.jpg?resize=1536%2C1168&amp;ssl=1 1536w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/aboveandbelow_ramp.jpg?resize=2048%2C1558&amp;ssl=1 2048w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/aboveandbelow_ramp.jpg?w=1280&amp;ssl=1 1280w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/09\/aboveandbelow_ramp.jpg?w=1920&amp;ssl=1 1920w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/figure>\n\n\n\n<p>Les couleurs sont affect\u00e9es entre la moyenne-1\u03c3 et moyenne+1\u03c3<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Symbologie_par_defaut\"><\/span>Symbologie par d\u00e9faut<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>Si vous cochez la case correspondante, la symbologie sera stock\u00e9e comme symbologie par d\u00e9faut pour la couche, en utilisant le m\u00eame proc\u00e9d\u00e9 que QGis :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>dans la table layer_styles du geopackage<\/li>\n\n\n\n<li>dans la table public.layer_styles de <a href=\"https:\/\/www.sigterritoires.fr\/index.php\/debuter-avec-postgrespostgis\/\">postgis<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Historique_des_transformations\"><\/span>Historique des transformations<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Chaque fois qu&rsquo;une transformation ou une agr\u00e9gation est r\u00e9alis\u00e9e par le plugin, une ligne est ajout\u00e9e \u00e0 une table de gestion de l&rsquo;historique, <strong><em>metafuzzy<\/em><\/strong>, qui est cr\u00e9\u00e9e et maintenue au sein du geopackage des donn\u00e9es.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyattr_history.jpg?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"243\" data-attachment-id=\"15032\" data-permalink=\"https:\/\/www.sigterritoires.fr\/index.php\/attributs-flous\/fzyattr_history\/\" data-orig-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyattr_history.jpg?fit=2161%2C818&amp;ssl=1\" data-orig-size=\"2161,818\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"fzyattr_history\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyattr_history.jpg?fit=640%2C243&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyattr_history.jpg?resize=640%2C243&#038;ssl=1\" alt=\"\" class=\"wp-image-15032\" srcset=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyattr_history.jpg?resize=1024%2C388&amp;ssl=1 1024w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyattr_history.jpg?resize=300%2C114&amp;ssl=1 300w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyattr_history.jpg?resize=768%2C291&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyattr_history.jpg?resize=1536%2C581&amp;ssl=1 1536w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyattr_history.jpg?resize=2048%2C775&amp;ssl=1 2048w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyattr_history.jpg?w=1280&amp;ssl=1 1280w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyattr_history.jpg?w=1920&amp;ssl=1 1920w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/figure>\n\n\n\n<p>Dans le cas des agr\u00e9gations floues, les champs renseign\u00e9s sont:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><em>field<\/em><\/strong>: le nom du champ agr\u00e9g\u00e9<\/li>\n\n\n\n<li><strong><em>function<\/em><\/strong>: le type d&rsquo;op\u00e9ration spatiale et la fonction s\u00e9lectionn\u00e9e avec un code num\u00e9rique repr\u00e9sentant la r\u00e9ponse \u00e0 chacune des trois questions (1=tr\u00e8s bon, 5= tr\u00e8s mauvais)<\/li>\n\n\n\n<li><strong><em>params<\/em><\/strong>: le d\u00e9tail des param\u00e8tres num\u00e9riques utilis\u00e9s pour la g\u00e9n\u00e9ration des fonctions non r\u00e9p\u00e9rtori\u00e9es<\/li>\n\n\n\n<li><strong><em>source1<\/em><\/strong>: le nom de la couche source 1 et de son attribut<\/li>\n\n\n\n<li><strong><em>source2<\/em><\/strong>: le nom de la couche source 2 et de son attribut<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Definir_la_fonction_dagregation\"><\/span>D\u00e9finir la fonction d&rsquo;agr\u00e9gation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction.jpg?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"249\" data-attachment-id=\"15038\" data-permalink=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/fzyaggr_fonction\/\" data-orig-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction.jpg?fit=1883%2C733&amp;ssl=1\" data-orig-size=\"1883,733\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"fzyaggr_fonction\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction.jpg?fit=640%2C249&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction.jpg?resize=640%2C249&#038;ssl=1\" alt=\"\" class=\"wp-image-15038\" srcset=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction.jpg?resize=1024%2C399&amp;ssl=1 1024w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction.jpg?resize=300%2C117&amp;ssl=1 300w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction.jpg?resize=768%2C299&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction.jpg?resize=1536%2C598&amp;ssl=1 1536w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction.jpg?w=1883&amp;ssl=1 1883w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction.jpg?w=1280&amp;ssl=1 1280w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/figure>\n\n\n\n<p>Vous devez cocher une r\u00e9ponse pour chacune des trois questions.<\/p>\n\n\n\n<p>Si vous consid\u00e9rez que l&rsquo;inversion des deux crit\u00e8res modifie vos r\u00e9ponses (asym\u00e9trie des crit\u00e8res), cochez la case <em><strong>V\u00e9rifier la sym\u00e9trie<\/strong><\/em>. Une quatri\u00e8me question vosu permettra de rentrer votre r\u00e9ponse.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction_assym.jpg?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"341\" data-attachment-id=\"15039\" data-permalink=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/fzyaggr_fonction_assym\/\" data-orig-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction_assym.jpg?fit=1893%2C1007&amp;ssl=1\" data-orig-size=\"1893,1007\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"fzyaggr_fonction_assym\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction_assym.jpg?fit=640%2C341&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction_assym.jpg?resize=640%2C341&#038;ssl=1\" alt=\"\" class=\"wp-image-15039\" srcset=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction_assym.jpg?resize=1024%2C545&amp;ssl=1 1024w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction_assym.jpg?resize=300%2C160&amp;ssl=1 300w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction_assym.jpg?resize=768%2C409&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction_assym.jpg?resize=1536%2C817&amp;ssl=1 1536w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction_assym.jpg?w=1893&amp;ssl=1 1893w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/fzyaggr_fonction_assym.jpg?w=1280&amp;ssl=1 1280w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Procedure_de_determination_de_loperation_dagregation\"><\/span><strong>Proc\u00e9dure de d\u00e9termination de l\u2019op\u00e9ration d\u2019agr\u00e9gation. <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Dans le cas d\u2019agr\u00e9gation de deux objectifs il existe une proc\u00e9dure simple pour d\u00e9terminer le type d\u2019op\u00e9ration \u00e0 effectuer. Elle consiste \u00e0 proposer au d\u00e9cideur trois situations type et lui demander de les \u00e9valuer A partir des trois r\u00e9ponses donn\u00e9es on recherche dans un catalogue de fonctions celle qui correspond le mieux aux souhaits du d\u00e9cideur.<br><\/p>\n\n\n\n<p>Les trois situations type (Si, S2, S3) sont choisies en fonction des deux crit\u00e8res(C1, C2) de mani\u00e8re que:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&#8211; S1 soit incompatible (Note E ou 0) avec C1, mais totalement compatible (note A ou 1) avec C2;<\/li>\n\n\n\n<li>&#8211; S2 soit moyennement compatible (note C ou 0.5<em>) <\/em>avec les deux objectifs C1 et C2;<\/li>\n\n\n\n<li>&#8211; S3 soit moyennement compatible (note C ou 0.5<em>) <\/em>avec C1 et totalement compatible(note A ou 1) avec C2.<\/li>\n<\/ul>\n\n\n\n<p>On obtient trois r\u00e9ponses (R1, R2, R3) \u00e0 partir desquelles on cherche l\u2019op\u00e9ration d\u2019agr\u00e9gation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Les_trois_types_de_fonctions_implementees\"><\/span>Les trois types de fonctions impl\u00e9ment\u00e9es<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Deux situations sont \u00e0 \u00e9tudier:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a) deux crit\u00e8res d\u2019\u00e9gale importance; <\/li>\n\n\n\n<li>b) deux crit\u00e8res d\u2019importance in\u00e9gale<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Criteres_de_meme_importance_symetriques\"><\/span>Crit\u00e8res de m\u00eame importance (sym\u00e9triques)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Deux crit\u00e8res ont la m\u00eame importance si la fonction d\u2019agr\u00e9gation est sym\u00e9trique, c\u2019est \u00e0 dire si la r\u00e9ponse aux trois questions d\u2019\u00e9valuation est la m\u00eame si l\u2019on inverse l\u2019ordre des crit\u00e8res.<\/p>\n\n\n\n<p>Dans ce cas, \u00e0 partir des trois r\u00e9ponses (R1, R2, R3) on recherche l&rsquo;op\u00e9ration d&rsquo;agr\u00e9gation dans la table suivante:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/agreg_fonctions1-1.jpg?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"390\" height=\"1024\" data-attachment-id=\"15104\" data-permalink=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/agreg_fonctions1-2\/\" data-orig-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/agreg_fonctions1-1.jpg?fit=948%2C2489&amp;ssl=1\" data-orig-size=\"948,2489\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"agreg_fonctions1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/agreg_fonctions1-1.jpg?fit=390%2C1024&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/agreg_fonctions1-1.jpg?resize=390%2C1024&#038;ssl=1\" alt=\"\" class=\"wp-image-15104\" srcset=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/agreg_fonctions1-1.jpg?resize=390%2C1024&amp;ssl=1 390w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/agreg_fonctions1-1.jpg?resize=114%2C300&amp;ssl=1 114w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/agreg_fonctions1-1.jpg?resize=768%2C2016&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/agreg_fonctions1-1.jpg?resize=585%2C1536&amp;ssl=1 585w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/agreg_fonctions1-1.jpg?resize=780%2C2048&amp;ssl=1 780w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/agreg_fonctions1-1.jpg?w=948&amp;ssl=1 948w\" sizes=\"auto, (max-width: 390px) 100vw, 390px\" \/><\/a><\/figure>\n<\/div>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Methode_dajustement_pour_criteres_asymetriques\"><\/span>M\u00e9thode d\u2019ajustement pour crit\u00e8res asym\u00e9triques<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Lorsqu\u2019un utilisateur d\u00e9finit une fonction d\u2019agr\u00e9gation floue \u00e0 partir de r\u00e9ponses <strong>non sym\u00e9triques<\/strong> (par exemple, certains crit\u00e8res jug\u00e9s plus importants que d\u2019autres, ou des combinaisons jug\u00e9es atypiques), le plugin utilise une m\u00e9thode d\u2019approximation afin de <strong>g\u00e9n\u00e9rer automatiquement une fonction d\u2019agr\u00e9gation personnalis\u00e9e<\/strong>.<\/p>\n\n\n\n<p>La fonction <code>generate_asymmetric_function(code)<\/code> :<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Points cl\u00e9s d\u00e9finis par l\u2019utilisateur<\/strong>\n<ul class=\"wp-block-list\">\n<li>L\u2019utilisateur choisit quatre valeurs d\u2019agr\u00e9gation correspondant \u00e0 des situations de r\u00e9f\u00e9rence :\n<ul class=\"wp-block-list\">\n<li><strong>(1, 0)<\/strong> : crit\u00e8re A totalement vrai, crit\u00e8re B totalement faux-&gt;<strong><em>vA1B0<\/em><\/strong><\/li>\n\n\n\n<li><strong>(0.5, 0.5)<\/strong> : les deux crit\u00e8res moyens-&gt;<strong><em>vA05B05<\/em><\/strong><\/li>\n\n\n\n<li><strong>(0.5, 1)<\/strong> : crit\u00e8re A moyen, crit\u00e8re B totalement vrai-&gt;<strong><em>vA05B1<\/em><\/strong><\/li>\n\n\n\n<li><strong>(0, 1)<\/strong> : crit\u00e8re A totalement faux, crit\u00e8re B totalement vrai-&gt;<strong><em>vA0B1<\/em><\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Ces valeurs sont cod\u00e9es sous forme d\u2019un code \u00e0 4 chiffres (chaque chiffre de 0 \u00e0 4 correspond \u00e0 un degr\u00e9 de satisfaction entre <strong>1.0<\/strong> et <strong>0.0<\/strong>).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Construction de la fonction floue<\/strong>\n<ul class=\"wp-block-list\">\n<li>Pour les quatre points cl\u00e9s, les valeurs sont affect\u00e9es directement.<\/li>\n\n\n\n<li>Pour toutes les autres combinaisons <code>(x, y)<\/code>, la valeur est calcul\u00e9e par <strong>interpolation bilin\u00e9aire pond\u00e9r\u00e9e<\/strong>, \u00e0 l\u2019aide de la formule : <br><strong><em>vA05B05\u22c5x\u22c5y+vA05B1\u22c5x\u22c5\u2223x\u2212y\u2223+vA0B1\u22c5(1\u2212x)\u22c5y<\/em><\/strong><\/li>\n\n\n\n<li>Cette formule permet d\u2019obtenir une surface continue qui reste coh\u00e9rente avec les points cl\u00e9s d\u00e9finis.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>R\u00e9sultat<\/strong>\n<ul class=\"wp-block-list\">\n<li>La fonction retourn\u00e9e peut \u00eatre appliqu\u00e9e \u00e0 n\u2019importe quelle paire <code>(x, y)<\/code> de valeurs floues.<\/li>\n\n\n\n<li>Un dictionnaire de param\u00e8tres est \u00e9galement retourn\u00e9, documentant le type, le code, les points cl\u00e9s et la formule d\u2019approximation.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Methode_dajustement_pour_criteres_symetriques_inhabituels\"><\/span>M\u00e9thode d\u2019ajustement pour crit\u00e8res sym\u00e9triques inhabituels<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Les triplets pr\u00e9sent\u00e9s dans la table de fonction plus haut respectent les contraintes suivantes:<\/p>\n\n\n\n<p>1) R3 &gt;= max( R1,R2), l\u2019\u00e9valuation d\u2019une situation qui satisfait compl\u00e8tement le crit\u00e8re 2 et moyennement le crit\u00e8re 1 doit \u00eatre au moins \u00e9gale \u00e0 la meilleure \u00e9valuation des deux autres situations (R1 et R2) dont l\u2019une ne satisfait pas du tout le premier crit\u00e8re et l\u2019autre satisfait que moyennement les deux crit\u00e8res;<br><br>2) R3 &gt;= note C ou 0,5 , la satisfaction totale du deuxi\u00e8me crit\u00e8re ne peut faire chuter la satisfaction globale en dessous du niveau de satisfaction du premier crit\u00e8re.<\/p>\n\n\n\n<p>Mais si cette logique est utilis\u00e9e dans la plus grande partie des applications, il se peut qu&rsquo;elle ne soit pas en accord dans des situations tr\u00e8s particuli\u00e8res. Dans ce cas le plugin utilise la fonction <code>generate_fuzzy_function(code)<\/code> pour <strong>g\u00e9n\u00e9rer automatiquement<\/strong> une fonction d\u2019agr\u00e9gation adapt\u00e9e.<br>Un message d&rsquo;avertissement signale que l&rsquo;on se trouve sur une combinaison inhabituelle de r\u00e9ponses.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Points cl\u00e9s d\u00e9finis par l\u2019utilisateur<\/strong>\n<ul class=\"wp-block-list\">\n<li>L\u2019utilisateur d\u00e9finit trois situations de r\u00e9f\u00e9rence, cod\u00e9es sur trois chiffres (de 0 \u00e0 4) repr\u00e9sentant un degr\u00e9 d\u2019agr\u00e9gation compris entre <strong>1.0<\/strong> et <strong>0.0<\/strong> :\n<ul class=\"wp-block-list\">\n<li><strong>(1, 0)<\/strong> ou <strong>(0, 1)<\/strong> : un crit\u00e8re totalement vrai, l\u2019autre totalement faux -&gt;<strong><em>v1<\/em><\/strong>.<\/li>\n\n\n\n<li><strong>(0.5, 0.5)<\/strong> : les deux crit\u00e8res moyens-&gt;<strong><em>v2<\/em><\/strong>.<\/li>\n\n\n\n<li><strong>(0.5, 1)<\/strong> ou <strong>(1, 0.5)<\/strong> : un crit\u00e8re moyen, l\u2019autre totalement vrai-&gt;<strong><em>v3<\/em><\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Construction de la fonction floue sym\u00e9trique<\/strong>\n<ul class=\"wp-block-list\">\n<li>Les valeurs des trois points cl\u00e9s sont affect\u00e9es directement selon le code fourni.<\/li>\n\n\n\n<li>Pour toutes les autres paires <code>(x, y)<\/code>, la valeur est estim\u00e9e par <strong>interpolation continue<\/strong> avec la formule : <br><strong><em>v2\u22c5x\u22c5y+v3\u22c5\u2223x\u2212y\u2223<\/em><\/strong><\/li>\n\n\n\n<li>La sym\u00e9trie est respect\u00e9e car la formule et les points cl\u00e9s sont identiques si on \u00e9change <code>x<\/code> et <code>y<\/code>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>R\u00e9sultat<\/strong>\n<ul class=\"wp-block-list\">\n<li>La fonction retourn\u00e9e peut \u00eatre appliqu\u00e9e \u00e0 n\u2019importe quelle paire <code>(x, y)<\/code> de valeurs floues.<\/li>\n\n\n\n<li>Un dictionnaire de param\u00e8tres est \u00e9galement renvoy\u00e9, documentant le type, le code, les points cl\u00e9s et la formule d\u2019approximation.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Couche_resultante\"><\/span>Couche r\u00e9sultante<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>La couche r\u00e9sultante est automatiquement ajout\u00e9e au projet QGis en cours, avec une symbologie de type \u00ab\u00a0gradu\u00e9e\u00a0\u00bb sur le champ attributaire d&rsquo;agr\u00e9gation.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/resultat.jpg?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"340\" data-attachment-id=\"15351\" data-permalink=\"https:\/\/www.sigterritoires.fr\/index.php\/agregation-floue\/resultat-4\/\" data-orig-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/resultat.jpg?fit=1920%2C1020&amp;ssl=1\" data-orig-size=\"1920,1020\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"resultat\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/resultat.jpg?fit=640%2C340&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/resultat.jpg?resize=640%2C340&#038;ssl=1\" alt=\"\" class=\"wp-image-15351\" srcset=\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/resultat.jpg?resize=1024%2C544&amp;ssl=1 1024w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/resultat.jpg?resize=300%2C159&amp;ssl=1 300w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/resultat.jpg?resize=768%2C408&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/resultat.jpg?resize=1536%2C816&amp;ssl=1 1536w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/resultat.jpg?w=1920&amp;ssl=1 1920w, https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2025\/08\/resultat.jpg?w=1280&amp;ssl=1 1280w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/figure>\n<\/div>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n","protected":false},"excerpt":{"rendered":"<p>Mode d&#8217;emploi Fen\u00eatre de param\u00e9trage Champs \u00ab\u00a0Couche 1\u00a0\u00bb et \u00ab\u00a0Couche2\u00a0\u00bb Les champs \u00ab\u00a0couches\u00a0\u00bb affiche la liste des couches charg\u00e9es, limit\u00e9es aux tables geopackage. En effet, la version actuelle ne prend en compte que des donn\u00e9es stock\u00e9es&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"give_campaign_id":0,"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"sfsi_plus_gutenberg_text_before_share":"","sfsi_plus_gutenberg_show_text_before_share":"","sfsi_plus_gutenberg_icon_type":"","sfsi_plus_gutenberg_icon_alignemt":"","sfsi_plus_gutenburg_max_per_row":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"jetpack_post_was_ever_published":false,"footnotes":""},"class_list":["post-15033","page","type-page","status-publish","hentry"],"aioseo_notices":[],"campaignId":"","jetpack_shortlink":"https:\/\/wp.me\/P6XU0A-3Ut","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/pages\/15033","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/comments?post=15033"}],"version-history":[{"count":0,"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/pages\/15033\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/media?parent=15033"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}