fix tutorial

notebooks/electre_1.ipynb

@@ -62,7 +62,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "metadata": {
     "collapsed": false
    },
@@ -113,7 +113,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 3,
    "metadata": {
     "collapsed": false
    },
@@ -166,7 +166,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false
    },
@@ -201,15 +201,16 @@
    "source": [
     "### Part 2: Exploitation\n",
     "\n",
-    "```python\n",
-    "if C(a, b) > q and D(a, b) < q:\n",
-    "    a outranks b\n",
-    "```"
+    "We need to dertermine by row and by column if **a S b** where **S** mean **dominance** and\n",
+    "\n",
+    "$$aSb = C(a, b) \\succ p \\land D(a, b) \\prec q$$\n",
+    "\n",
+    "#### By Row"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
@@ -221,47 +222,51 @@
       "Outrank:\n",
       " [[False False False False False False]\n",
       " [False False False False False False]\n",
-      " [ True False False False False False]\n",
+      " [False False False False False False]\n",
       " [ True False False False False False]\n",
       " [ True  True  True  True False  True]\n",
-      " [ True False False  True False False]]\n",
-      "Resume:\n",
-      " [0 0 1 1 5 2]\n"
+      " [False False False False False False]]\n",
+      "Resume By Row:\n",
+      " [0 0 0 1 5 0]\n",
+      "Resume By Column:\n",
+      " [2 1 1 1 0 1]\n"
      ]
     }
    ],
    "source": [
     "print(\"Outrank:\\n\", outrank)\n",
-    "print(\"Resume:\\n\", np.sum(outrank, axis=1))"
+    "print(\"Resume By Row:\\n\", np.sum(outrank, axis=1))\n",
+    "print(\"Resume By Column:\\n\", np.sum(outrank, axis=0))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Then the kernel is the alternatives that surpass all the another"
+    "Then we need to make the **difference aSb - bSa** and the alternative with the biggest positive difference are the kernel"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
-     "data": {
-      "text/plain": [
-       "array([4])"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Difference:\n",
+      " [-2 -1 -1  0  5 -1]\n",
+      "Kernel:\n",
+      " [4]\n"
+     ]
     }
    ],
    "source": [
-    "kernel"
+    "print(\"Difference:\\n\", np.sum(outrank, axis=1) - np.sum(outrank, axis=0))\n",
+    "print(\"Kernel:\\n\", kernel)"
    ]
   },
   {
@@ -275,7 +280,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
@@ -284,8 +289,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 11 s, sys: 4.29 s, total: 15.3 s\n",
-      "Wall time: 15.2 s\n"
+      "CPU times: user 11.1 s, sys: 1.19 s, total: 12.3 s\n",
+      "Wall time: 12.3 s\n"
      ]
     }
    ],
@@ -307,15 +312,6 @@
     "- Roy, B. (1968). Classement et choix en présence de points de vue multiples. Revue française d'automatique, d'informatique et de recherche opérationnelle. Recherche opérationnelle, 2(1), 57-75.\n",
     "- Cebrián, L. I. G., & Porcar, A. M. (2009). Localización empresarial en Aragón: Una aplicación empírica de la ayuda a la decisión multicriterio tipo ELECTRE I y III. Robustez de los resultados obtenidos. Revista de Métodos Cuantitativos para la Economía y la Empresa, (7), 31-56."
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {