{"id":10711,"date":"2026-03-05T14:15:20","date_gmt":"2026-03-05T06:15:20","guid":{"rendered":"https:\/\/www.archimetric.com\/pl\/understanding-uml-multiplicity\/"},"modified":"2026-03-05T14:15:20","modified_gmt":"2026-03-05T06:15:20","slug":"understanding-uml-multiplicity","status":"publish","type":"post","link":"https:\/\/www.archimetric.com\/pl\/understanding-uml-multiplicity\/","title":{"rendered":"Zrozumienie wielokrotno\u015bci UML"},"content":{"rendered":"<p>W dziedzinie projektowania i modelowania oprogramowania Unified Modeling Language (UML) pe\u0142ni wa\u017cn\u0105 rol\u0119 jako narz\u0119dzie do wizualizacji i dokumentowania struktury i zachowania system\u00f3w. Jednym z kluczowych poj\u0119\u0107 w UML jest<a href=\"https:\/\/blog.visual-paradigm.com\/what-is-multiplicity\/\"><strong>wielokrotno\u015b\u0107<\/strong><\/a>, kt\u00f3ra okre\u015bla ograniczenia dotycz\u0105ce liczby obiekt\u00f3w, kt\u00f3re mog\u0105 uczestniczy\u0107 w zwi\u0105zku. Niniejszy artyku\u0142 omawia poj\u0119cie wielokrotno\u015bci, jej znaczenie oraz spos\u00f3b jej stosowania w diagramach UML.<\/p>\n<h4>Co to jest wielokrotno\u015b\u0107?<\/h4>\n<p><a href=\"https:\/\/blog.visual-paradigm.com\/what-is-multiplicity\/\">Wielokrotno\u015b\u0107 w UML<\/a> to ograniczenie okre\u015blaj\u0105ce liczb\u0119 obiekt\u00f3w, kt\u00f3re mog\u0105 uczestniczy\u0107 w jednym ko\u0144cu zwi\u0105zku. Odpowiada na pytania takie jak \u201eIle samochod\u00f3w mo\u017ce posiada\u0107 osoba?\u201d lub \u201eIle os\u00f3b mo\u017ce prowadzi\u0107 dany samoch\u00f3d?\u201d Definiuj\u0105c wielokrotno\u015b\u0107, ustalasz zasady, jak obiekty w ka\u017cdej klasie mog\u0105 by\u0107 ze sob\u0105 powi\u0105zane, oferuj\u0105c jasny i zwi\u0119z\u0142y spos\u00f3b wyra\u017cania tych relacji.<\/p>\n<h4>Wyra\u017canie wielokrotno\u015bci<\/h4>\n<p>Wielokrotno\u015b\u0107 zwykle wyra\u017ca si\u0119 jako zakres okre\u015blaj\u0105cy minimaln\u0105 i maksymaln\u0105 liczb\u0119 obiekt\u00f3w dozwolonych w zwi\u0105zku. Format wyra\u017cania wielokrotno\u015bci to:<\/p>\n<ul>\n<li><strong>Dok\u0142adna liczba<\/strong>: Jedna liczba wskazuj\u0105ca dok\u0142adn\u0105 liczb\u0119 obiekt\u00f3w.<\/li>\n<li><strong>Zakres<\/strong>: Para liczb oddzielonych dwoma kropkami (..), wskazuj\u0105ca liczb\u0119 minimaln\u0105 i maksymaln\u0105.<\/li>\n<li><strong>Gwiazdka (*)<\/strong>: Wskazuje na nieograniczon\u0105 liczb\u0119 obiekt\u00f3w.<\/li>\n<\/ul>\n<p>Na przyk\u0142ad:<\/p>\n<ul>\n<li><code class=\"\">1<\/code>: Dok\u0142adnie jeden obiekt.<\/li>\n<li><code class=\"\">0..1<\/code>: Zero lub jeden obiekt.<\/li>\n<li><code class=\"\">1..*<\/code>: Przynajmniej jeden obiekt, bez ograniczenia g\u00f3rnego.<\/li>\n<li><code class=\"\">*<\/code>: Dowolna liczba obiekt\u00f3w, w tym zero.<\/li>\n<\/ul>\n<p><img alt=\"What is Multiplicity\" decoding=\"async\" src=\"https:\/\/www.archimetric.com\/wp-content\/uploads\/2024\/12\/05-multiplicities-examples.png\"\/><\/p>\n<h4>Stosowanie wielokrotno\u015bci w zwi\u0105zku<\/h4>\n<p>Podczas modelowania relacji mi\u0119dzy klasami, wielokrotno\u015b\u0107 przypisuje si\u0119 do ka\u017cdego ko\u0144ca zwi\u0105zku. Na przyk\u0142ad rozwa\u017cmy relacj\u0119 mi\u0119dzy klas\u0105<code class=\"\">Osoba<\/code> a klas\u0105<code class=\"\">Samoch\u00f3d<\/code> klas\u0105:<\/p>\n<ul>\n<li><strong>Pytanie 1<\/strong>: Ile samochod\u00f3w mo\u017ce posiada\u0107 osoba?<\/li>\n<li><strong>Pytanie 2<\/strong>: Ilu ludzi mo\u017ce prowadzi\u0107 dany samoch\u00f3d?<\/li>\n<\/ul>\n<p>Odpowiedzi na te pytania umieszcza si\u0119 obok odpowiednich klas w zwi\u0105zku. Je\u015bli osoba mo\u017ce posiada\u0107 od zera do wielu samochod\u00f3w, wielokrotno\u015b\u0107 obok klasy<code class=\"\">Samoch\u00f3d<\/code> b\u0119dzie<code class=\"\">0..*<\/code>. Z kolei, je\u015bli samoch\u00f3d mo\u017ce by\u0107 prowadzony przez jednego do wielu os\u00f3b, wielokrotno\u015b\u0107 obok klasy<code class=\"\">Osoba<\/code> b\u0119dzie<code class=\"\">1..*<\/code>.<\/p>\n<h4>Przyk\u0142ad: Wysy\u0142ka i Produkt<\/h4>\n<p>Aby to ilustrowa\u0107, rozwa\u017c sytuacj\u0119, w kt\u00f3rej<code class=\"\">Wysy\u0142ka<\/code> musi zawiera\u0107 co najmniej jeden<code class=\"\">Produkt<\/code> ale mo\u017ce zawiera\u0107 tyle produkt\u00f3w, ile potrzeba. Wielokrotno\u015b\u0107 dla<code class=\"\">Produkt<\/code> ko\u0144ca zwi\u0105zku b\u0119dzie<code class=\"\">1..*<\/code>, co oznacza, \u017ce wysy\u0142ka musi zawiera\u0107 co najmniej jeden produkt, ale mo\u017ce zawiera\u0107 wiele.<\/p>\n<h4>Notacja i symbole<\/h4>\n<p>W diagramach UML wielokrotno\u015b\u0107 oznacza si\u0119 za pomoc\u0105 okre\u015blonych oznacze\u0144:<\/p>\n<ul>\n<li><strong>Gwiazdka (*)<\/strong>: Oznacza nieograniczon\u0105 liczb\u0119 obiekt\u00f3w.<\/li>\n<li><strong>Zakres (<code class=\"\">min..max<\/code>)<\/strong>: Okre\u015bla minimaln\u0105 i maksymaln\u0105 liczb\u0119 obiekt\u00f3w.<\/li>\n<li><strong>Dok\u0142adna liczba<\/strong>: Wskazuje dok\u0142adn\u0105 liczb\u0119 obiekt\u00f3w.<\/li>\n<\/ul>\n<p>Te oznaczenia pomagaj\u0105 jasno okre\u015bli\u0107 ograniczenia i zasady reguluj\u0105ce relacje mi\u0119dzy klasami.<\/p>\n<h3>Przyk\u0142ad 1: Osoba i samoch\u00f3d<\/h3>\n<p>W tym przyk\u0142adzie biblioteka <code class=\"\">Osoba<\/code> mo\u017ce posiada\u0107 od zera do wielu <code class=\"\">samochod\u00f3w<\/code>, a <code class=\"\">samoch\u00f3d<\/code> mo\u017ce by\u0107 prowadzony przez jedn\u0105 do wielu <code class=\"\">os\u00f3b<\/code>.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.archimetric.com\/wp-content\/uploads\/2024\/12\/img_67652d8a9b1e6.png\"\/><\/p>\n<h3>Przyk\u0142ad 2: Przesy\u0142ka i produkt<\/h3>\n<p>W tym przyk\u0142adzie biblioteka <code class=\"\">Przesy\u0142ka<\/code> musi zawiera\u0107 co najmniej jeden <code class=\"\">produkt<\/code> ale mo\u017ce zawiera\u0107 tyle produkt\u00f3w, ile potrzeba.<\/p>\n<p><img alt=\"SoWkIImgAStDuULApaaiBbO8piWio4tDAr6evkLIKD1EpiyhISpCAmueoayfJIufrj2qKl39B2wnWGhOyNBLydB1D4C5eNepyv9pIbDIKpppO8OYjCD4OFhXrYePwkbfAIdewi9OC3Ej561kKG1gSaZDIm6x6W00 (321\u00d7218)\" decoding=\"async\" src=\"https:\/\/www.archimetric.com\/wp-content\/uploads\/2024\/12\/img_67652d8b3ea92.png\"\/><\/p>\n<h3>Przyk\u0142ad 3: Biblioteka i ksi\u0105\u017cka<\/h3>\n<p>W tym przyk\u0142adzie biblioteka <code class=\"\">bibliotece<\/code> mo\u017ce mie\u0107 wiele <code class=\"\">ksi\u0105\u017cek<\/code>, a <code class=\"\">ksi\u0105\u017cka<\/code> mo\u017ce si\u0119 znajdowa\u0107 w jednej <code class=\"\">bibliotece<\/code>.<\/p>\n<p><img alt=\"SoWkIImgAStDuULApaaiBbRmoKmgIYogLAZcvL9GqCv8B7RApyykrj2q0ieKbzY0U7QyNBMyN30D816ewhJyqhmKppoe4H0zO2PK0yni9KCb1LrT1IK3FJqj9OW1LWh9-NabYPbvnGf0unrIyrB0RW80 (210\u00d7218)\" decoding=\"async\" src=\"https:\/\/www.archimetric.com\/wp-content\/uploads\/2024\/12\/img_67652d8be004c.png\"\/><\/p>\n<h3>Przyk\u0142ad 4: Nauczyciel i ucze\u0144<\/h3>\n<p>W tym przyk\u0142adzie <code class=\"\">nauczyciela<\/code> mo\u017ce naucza\u0107 wielu<code class=\"\">uczni\u00f3w<\/code>, a <code class=\"\">ucze\u0144<\/code> mo\u017ce by\u0107 nauczany przez jednego<code class=\"\">nauczyciela<\/code>.<\/p>\n<p><img alt=\"SoWkIImgAStDuULApaaiBbO8IKrCpaWjKgZcvL9Gq2u1yug3IqfJKlDAYZKqhHHyCejBRA02ThnSjRnSCArGGPZMnDBqZ1AdIgY18ArG9bGJp2ObGoK5NLq59GCzFIqbk25M2b2x5O2MEAJcfO3T2000 (279\u00d7218)\" decoding=\"async\" src=\"https:\/\/www.archimetric.com\/wp-content\/uploads\/2024\/12\/img_67652d8c80d65.png\"\/><\/p>\n<h3>Przyk\u0142ad 5: Zam\u00f3wienie i pozycja<\/h3>\n<p>W tym przyk\u0142adzie <code class=\"\">zam\u00f3wienie<\/code>mo\u017ce zawiera\u0107 jedn\u0105 lub wi\u0119cej<code class=\"\">pozycji<\/code>, a <code class=\"\">pozycja<\/code>mo\u017ce by\u0107 cz\u0119\u015bci\u0105 zera lub wi\u0119cej<code class=\"\">zam\u00f3wie\u0144<\/code>.<\/p>\n<p><img alt=\"SoWkIImgAStDuULApaaiBbRmBqf9BLAevkLIKD1EpiyhISpCA_OiISqjrj2qKl39B2wn0V7iUBbgURbWUa0YK2q5GDFyqy2687I0kJ0j40kK3FNqj9GKT7KLb0p0BB0PLWemAnM0oXrIyrB0BWC0 (239\u00d7218)\" decoding=\"async\" src=\"https:\/\/www.archimetric.com\/wp-content\/uploads\/2024\/12\/img_67652d8d1e04f.png\"\/><\/p>\n<h3>Przyk\u0142ad 6: Firma i pracownik<\/h3>\n<p>W tym przyk\u0142adzie <code class=\"\">firmy<\/code>mo\u017ce mie\u0107 wielu<code class=\"\">pracownik\u00f3w<\/code>, a <code class=\"\">pracownik<\/code>pracuje dla jednej<code class=\"\">firmy<\/code>.<\/p>\n<p><img alt=\"SoWkIImgAStDuULApaaiBbPmpiyjICohLAZcvL9GqCv8B7RDBSZ9hqnDBTRGj5BmoImkiO69sF5orV9omJJ2HA4wo_EBielTyekWve4qGvbGNJ2Bb0oL57Hr5PGCzFIqb12cM2caWfd52a1h75BpKi1k1000 (277\u00d7218)\" decoding=\"async\" src=\"https:\/\/www.archimetric.com\/wp-content\/uploads\/2024\/12\/img_67652d8db7999.png\"\/><\/p>\n<p>Te przyk\u0142ady ilustruj\u0105, jak wielokrotno\u015b\u0107 jest u\u017cywana do definiowania liczby obiekt\u00f3w uczestnicz\u0105cych w zwi\u0105zku, zapewniaj\u0105c jasny i zwi\u0119z\u0142y spos\u00f3b wyra\u017cania relacji mi\u0119dzy<a href=\"https:\/\/online.visual-paradigm.com\/diagrams\/tutorials\/class-diagram-tutorial\/\">klasami w UML<\/a> diagramami.<\/p>\n<h2>Wnioski<\/h2>\n<p>Wielokrotno\u015b\u0107 to podstawowy koncept w UML, kt\u00f3ry zapewnia zorganizowany spos\u00f3b definiowania liczby obiekt\u00f3w uczestnicz\u0105cych w zwi\u0105zku. Okre\u015blaj\u0105c wielokrotno\u015b\u0107, projektanci mog\u0105 zapewni\u0107, \u017ce relacje mi\u0119dzy klasami s\u0105 dobrze zdefiniowane i zrozumia\u0142e, co prowadzi do bardziej wytrzyma\u0142y i utrzymywalny projekt systemu. Niezale\u017cnie od tego, czy modelujesz proste zwi\u0105zki, czy z\u0142o\u017cone relacje, zrozumienie i stosowanie wielokrotno\u015bci jest kluczowe dla skutecznego modelowania UML.<\/p>\n<h2>Zasoby<\/h2>\n<ol>\n<li><strong>Rysowanie diagramu relacji encji w Visual Paradigm<\/strong>\n<ul>\n<li>Visual Paradigm. (n.d.).\u00a0<a href=\"https:\/\/www.visual-paradigm.com\/support\/documents\/vpuserguide\/3563\/3564\/85375_drawingentit.html\">Rysowanie diagramu relacji encji w Visual Paradigm<\/a>\u00a0<a class=\"mi-ref cursor-pointer align-super text-muted-foreground fade-in hover:underline\" data-state=\"closed\" href=\"https:\/\/www.visual-paradigm.com\/support\/documents\/vpuserguide\/3563\/3564\/85375_drawingentit.html\" rel=\"noopener\" target=\"_blank\">4<\/a>.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Diagram relacji encji \u2013 wielokrotno\u015bci<\/strong>\n<ul>\n<li>Stack Overflow. (n.d.).\u00a0<a href=\"https:\/\/stackoverflow.com\/questions\/41731377\/entity-relationship-diagram-multiplicities\">Diagram relacji encji \u2013 wielokrotno\u015bci<\/a>\u00a0<a class=\"mi-ref cursor-pointer align-super text-muted-foreground fade-in hover:underline\" data-state=\"closed\" href=\"https:\/\/stackoverflow.com\/questions\/41731377\/entity-relationship-diagram-multiplicities\" rel=\"noopener\" target=\"_blank\">5<\/a>.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Diagramy relacji encji<\/strong>\n<ul>\n<li>GitHub. (n.d.).\u00a0<a href=\"https:\/\/github.com\/weston-bailey\/entity-relationship-diagrams\">Diagramy relacji encji<\/a>\u00a0<a class=\"mi-ref cursor-pointer align-super text-muted-foreground fade-in hover:underline\" data-state=\"closed\" href=\"https:\/\/github.com\/weston-bailey\/entity-relationship-diagrams\" rel=\"noopener\" target=\"_blank\">6<\/a>.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Okre\u015bl wielokrotno\u015b\u0107 na kszta\u0142cie UML<\/strong>\n<ul>\n<li>Wsparcie Microsoft. (n.d.).\u00a0<a href=\"https:\/\/support.microsoft.com\/en-us\/office\/specify-multiplicity-on-an-uml-shape-e2dcac55-e9b6-40fa-a976-eb5f6ef2df3b\">Okre\u015bl wielokrotno\u015b\u0107 na kszta\u0142cie UML<\/a>\u00a0<a class=\"mi-ref cursor-pointer align-super text-muted-foreground fade-in hover:underline\" data-state=\"closed\" href=\"https:\/\/support.microsoft.com\/en-us\/office\/specify-multiplicity-on-an-uml-shape-e2dcac55-e9b6-40fa-a976-eb5f6ef2df3b\" rel=\"noopener\" target=\"_blank\">7<\/a>.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Co to jest diagram relacji encji (ERD)?<\/strong>\n<ul>\n<li>Visual Paradigm. (n.d.).\u00a0<a href=\"https:\/\/www.visual-paradigm.com\/guide\/data-modeling\/what-is-entity-relationship-diagram\/\">Co to jest diagram relacji encji (ERD)?<\/a>\u00a0<a class=\"mi-ref cursor-pointer align-super text-muted-foreground fade-in hover:underline\" data-state=\"closed\" href=\"https:\/\/www.visual-paradigm.com\/guide\/data-modeling\/what-is-entity-relationship-diagram\/\" rel=\"noopener\" target=\"_blank\">8<\/a>.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Visual Paradigm schemat relacji encji dodawanie tabel<\/strong>\n<ul>\n<li>Stack Overflow. (brak daty).\u00a0<a href=\"https:\/\/stackoverflow.com\/questions\/36464950\/visual-paradigm-er-diagram-adding-tables\">Visual Paradigm schemat relacji encji dodawanie tabel<\/a>\u00a0<a class=\"mi-ref cursor-pointer align-super text-muted-foreground fade-in hover:underline\" data-state=\"closed\" href=\"https:\/\/stackoverflow.com\/questions\/36464950\/visual-paradigm-er-diagram-adding-tables\" rel=\"noopener\" target=\"_blank\">9<\/a>.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Jak dodajesz wielokrotno\u015b\u0107 do diagramu klas w Visual Paradigm?<\/strong>\n<ul>\n<li>TheNewsIndependent. (2020, 29 grudnia).\u00a0<a href=\"https:\/\/www.thenewsindependent.com\/how-do-you-add-a-multiplicity-to-a-class-diagram-in-visual-paradigm\/\">Jak dodajesz wielokrotno\u015b\u0107 do diagramu klas w Visual Paradigm?<\/a>\u00a0<a class=\"mi-ref cursor-pointer align-super text-muted-foreground fade-in hover:underline\" data-state=\"closed\" href=\"https:\/\/www.thenewsindependent.com\/how-do-you-add-a-multiplicity-to-a-class-diagram-in-visual-paradigm\/\" rel=\"noopener\" target=\"_blank\">10<\/a>.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Podr\u0119cznik dla pocz\u0105tkuj\u0105cych: Diagramy relacji encji (ER)<\/strong>\n<ul>\n<li>Blog Visual Paradigm. (2023, 21 wrze\u015bnia).\u00a0<a href=\"https:\/\/blog.visual-paradigm.com\/beginners-guide-to-entity-relationship-er-diagrams\/\">Podr\u0119cznik dla pocz\u0105tkuj\u0105cych: Diagramy relacji encji (ER)<\/a>\u00a0<a class=\"mi-ref cursor-pointer align-super text-muted-foreground fade-in hover:underline\" data-state=\"closed\" href=\"https:\/\/blog.visual-paradigm.com\/beginners-guide-to-entity-relationship-er-diagrams\/\" rel=\"noopener\" target=\"_blank\">11<\/a>.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Wielokrotno\u015b\u0107 w por\u00f3wnaniu z liczno\u015bci\u0105<\/strong>\n<ul>\n<li>Stack Overflow. (brak daty).\u00a0<a href=\"https:\/\/stackoverflow.com\/questions\/17877582\/multiplicity-vs-cardinality\">Wielokrotno\u015b\u0107 w por\u00f3wnaniu z liczno\u015bci\u0105<\/a>\u00a0<a class=\"mi-ref cursor-pointer align-super text-muted-foreground fade-in hover:underline\" data-state=\"closed\" href=\"https:\/\/stackoverflow.com\/questions\/17877582\/multiplicity-vs-cardinality\" rel=\"noopener\" target=\"_blank\">12<\/a>.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h2><\/h2>\n","protected":false},"excerpt":{"rendered":"<p>W dziedzinie projektowania i modelowania oprogramowania Unified Modeling Language (UML) pe\u0142ni wa\u017cn\u0105 rol\u0119 jako narz\u0119dzie do wizualizacji i dokumentowania struktury<\/p>\n","protected":false},"author":3479,"featured_media":10712,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"","fifu_image_url":"https:\/\/blog.visual-paradigm.com\/wp-content\/uploads\/2022\/10\/05-multiplicities-examples.png","fifu_image_alt":"","footnotes":""},"categories":[127],"tags":[],"class_list":["post-10711","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-unified-modeling-language"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.0 - 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