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0.9715662650602411
0.9911164465786314
1.0
0.9841048789857857</code></pre><p><strong>References</strong></p><p>İşletmeciler, Mühendisler ve Yöneticiler için Operasyonel, Yönetsel ve Stratejik Problemlerin Çözümünde Çok Kriterli Karar verme Yöntemleri, Editörler: Bahadır Fatih Yıldırım ve Emrah Önder, Dora, 2. Basım, 2015, ISBN: 978-605-9929-44-8</p><div class="admonition is-warning"><header class="admonition-header">Dependencies</header><div class="admonition-body"><p>This method is enabled when the JuMP and Ipopt packages are installed and loaded.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jbytecode/JMcDM/blob/2319d29c8785b41e2e6a1de85aa2b8a9e54d5e3e/src/dataenvelop.jl#L19-L82">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../game/">« Game Solver</a><a class="docs-footer-nextpage" href="../scdm/">SCDM »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Sunday 6 August 2023 17:08">Sunday 6 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
0.9841048789857857</code></pre><p><strong>References</strong></p><p>İşletmeciler, Mühendisler ve Yöneticiler için Operasyonel, Yönetsel ve Stratejik Problemlerin Çözümünde Çok Kriterli Karar verme Yöntemleri, Editörler: Bahadır Fatih Yıldırım ve Emrah Önder, Dora, 2. Basım, 2015, ISBN: 978-605-9929-44-8</p><div class="admonition is-warning"><header class="admonition-header">Dependencies</header><div class="admonition-body"><p>This method is enabled when the JuMP and Ipopt packages are installed and loaded.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jbytecode/JMcDM/blob/bdfcebc7914bf7b3e06f806d7e20ff30f8a720a3/src/dataenvelop.jl#L19-L82">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../game/">« Game Solver</a><a class="docs-footer-nextpage" href="../scdm/">SCDM »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Friday 1 September 2023 17:29">Friday 1 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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Probabilities:
[0.3333333333333333, 0.3333333333333333, 0.3333333333333333]
Value of game:
0.0</code></pre><p><strong>References</strong></p><p>Zhou, Hai-Jun. &quot;The rock–paper–scissors game.&quot; Contemporary Physics 57.2 (2016): 151-163.</p><div class="admonition is-warning"><header class="admonition-header">Dependencies</header><div class="admonition-body"><p>This method is enabled when the JuMP and Ipopt packages are installed and loaded.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jbytecode/JMcDM/blob/2319d29c8785b41e2e6a1de85aa2b8a9e54d5e3e/src/game.jl#L20-L69">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../normalizations/">« Normalization Methods</a><a class="docs-footer-nextpage" href="../dataenvelop/">Data Envelopment »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Sunday 6 August 2023 17:08">Sunday 6 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
0.0</code></pre><p><strong>References</strong></p><p>Zhou, Hai-Jun. &quot;The rock–paper–scissors game.&quot; Contemporary Physics 57.2 (2016): 151-163.</p><div class="admonition is-warning"><header class="admonition-header">Dependencies</header><div class="admonition-body"><p>This method is enabled when the JuMP and Ipopt packages are installed and loaded.</p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jbytecode/JMcDM/blob/bdfcebc7914bf7b3e06f806d7e20ff30f8a720a3/src/game.jl#L20-L69">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../normalizations/">« Normalization Methods</a><a class="docs-footer-nextpage" href="../dataenvelop/">Data Envelopment »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Friday 1 September 2023 17:29">Friday 1 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>JMcDM · JMcDM: Julia package for multiple-criteria decision making</title><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="mcdms/">JMcDM: Julia package for multiple-criteria decision making</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="mcdms/">MCDM</a></li><li><a class="tocitem" href="normalizations/">Normalization Methods</a></li><li><a class="tocitem" href="game/">Game Solver</a></li><li><a class="tocitem" href="dataenvelop/">Data Envelopment</a></li><li><a class="tocitem" href="scdm/">SCDM</a></li><li><a class="tocitem" href="utility/">Utility</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>JMcDM</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>JMcDM</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/jbytecode/JMcDM/blob/main/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="JMcDM"><a class="docs-heading-anchor" href="#JMcDM">JMcDM</a><a id="JMcDM-1"></a><a class="docs-heading-anchor-permalink" href="#JMcDM" title="Permalink"></a></h1><p>A package for Multiple-criteria decision-making techniques in Julia.</p><h2 id="The-problem"><a class="docs-heading-anchor" href="#The-problem">The problem</a><a id="The-problem-1"></a><a class="docs-heading-anchor-permalink" href="#The-problem" title="Permalink"></a></h2><p>Suppose a decision process has n alternatives and m criteria which are either to be maximized or minimized. Each single criterion has a weight <em>0 ≤ wᵢ ≤ 1</em> where sum of <em>wᵢ</em> is 1. <em>fᵢ</em> is either maximum or minimum. <em>gⱼ(.)</em> is the evolution function and it is choosen as <em>gⱼ(x) = x</em> in many methods. A multiple criteria decision problem can be represented using the decision table </p><p><img src="images/generalformula.png" alt/></p><p>without loss of generality. When <em>A₁, A₂, ..., Aₙ</em> are alternatives and <em>C₁, C₂, ..., Cₙ</em> are different situations of a single criterion then the decision problem is said to be single criterion decision problem. If <em>Cⱼ</em> are strategies of two game players then <em>gⱼ(Aᵢ)</em> is the gain of the row player when she selects the strategy <em>i</em> and the column player selects the strategy <em>Cⱼ</em>.</p><p>The package mainly focuses on solving these kinds of decision problems.</p><h2 id="For-whom?"><a class="docs-heading-anchor" href="#For-whom?">For whom?</a><a id="For-whom?-1"></a><a class="docs-heading-anchor-permalink" href="#For-whom?" title="Permalink"></a></h2><p>Multiple-criteria decision-making is an inter-discipline subject and there is a vast amount of research in the literature in this area. However, the existing software packages in this area are generally focused on a small subset of tools. JMcDM is a developer and researcher-friendly Julia package that combines the developed methods, utility functions for implementing new ones, and serves an environment for comparing results of multiple analyses. </p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><p>Please type </p><pre><code class="language-julia hljs">julia&gt; ]
(@v1.7) pkg&gt; add JMcDM</code></pre><p>or</p><pre><code class="language-julia hljs">julia&gt; using Pkg
julia&gt; Pkg.add(&quot;JMcDM&quot;)</code></pre><p>in Julia REPL to install package in the standard way, otherwise, you can clone the repository and type </p><pre><code class="language-julia hljs">julia&gt; ]
(@v1.7) pkg&gt; develop .</code></pre><p>to start developing new methods.</p><h2 id="Package-Dependencies"><a class="docs-heading-anchor" href="#Package-Dependencies">Package Dependencies</a><a id="Package-Dependencies-1"></a><a class="docs-heading-anchor-permalink" href="#Package-Dependencies" title="Permalink"></a></h2><p>Since the Julia package manager installs all of the dependencies automatically, a standard user doesn&#39;t need to install them manually. The package dependencies are listed below:</p><ul><li>DataFrames</li><li>GLPK</li><li>JuMP</li></ul></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Sunday 6 August 2023 17:08">Sunday 6 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
(@v1.7) pkg&gt; develop .</code></pre><p>to start developing new methods.</p><h2 id="Package-Dependencies"><a class="docs-heading-anchor" href="#Package-Dependencies">Package Dependencies</a><a id="Package-Dependencies-1"></a><a class="docs-heading-anchor-permalink" href="#Package-Dependencies" title="Permalink"></a></h2><p>Since the Julia package manager installs all of the dependencies automatically, a standard user doesn&#39;t need to install them manually. The package dependencies are listed below:</p><ul><li>DataFrames</li><li>GLPK</li><li>JuMP</li></ul></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Friday 1 September 2023 17:29">Friday 1 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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