roc.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "timely-antibody",
   "metadata": {},
   "source": [
    "# ROC\n",
    "---\n",
    "_**R**ank **O**rder **C**entroid_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "liked-monaco",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "vulnerable-music",
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "seventh-toner",
   "metadata": {},
   "source": [
    "## 1. Introduction\n",
    "---\n",
    "The **ROC** (_Rank Order Centroid_) method is a simple and intuitive technique for defining criteria weights in multi-criteria decision problems. It is very useful when the decision maker does not know the degree of weighting of each criterion, but knows their order of importance. Therefore, the weights are calculated based on this ordering and distinct in terms of contribution (none of them will have the same weight)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "magnetic-stone",
   "metadata": {},
   "source": [
    "### 1.1. Applications\n",
    "---\n",
    "The _ROC method_ can be used in a variety of situations where ease of understanding are relevant, such as:\n",
    "\n",
    "- Supplier selection\n",
    "- Assessment of job candidates\n",
    "- Choice of products\n",
    "- Feature priorization\n",
    "\n",
    "For example, let's consider a set of elements with 5 random criteria $\\{C_1, C_2, C_3, C_4, C_5\\}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "tutorial-hardware",
   "metadata": {},
   "outputs": [
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       "      <th class=\"col_heading level0 col0\" >C1</th>\n",
       "      <th class=\"col_heading level0 col1\" >C2</th>\n",
       "      <th class=\"col_heading level0 col2\" >C3</th>\n",
       "      <th class=\"col_heading level0 col3\" >C4</th>\n",
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    "np.random.seed(0)\n",
    "df = pd.DataFrame({\n",
    "    \"C1\": np.random.randint(1, 10, 10),\n",
    "    \"C2\": np.random.randint(1, 50, 10),\n",
    "    \"C3\": np.random.randint(1, 20, 10),\n",
    "    \"C4\": np.random.randint(1, 5, 10),\n",
    "    \"C5\": np.random.randint(1, 8, 10)\n",
    "})\n",
    "\n",
    "df.style.background_gradient()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "miniature-planet",
   "metadata": {},
   "source": [
    "## 2. Method steps\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "understood-investor",
   "metadata": {},
   "source": [
    "### 2.1. Order of importance\n",
    "---\n",
    "The first step is to classify the criteria in **order of importance**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "perfect-reference",
   "metadata": {},
   "outputs": [],
   "source": [
    "ORDER = {\n",
    "    # {criteria: order of importance}\n",
    "    \"C1\": 3,\n",
    "    \"C2\": 5,\n",
    "    \"C3\": 2,\n",
    "    \"C4\": 1,\n",
    "    \"C5\": 4\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "studied-israel",
   "metadata": {},
   "source": [
    "### 2.2. Criteria weights\n",
    "---\n",
    "The second step is to **calculate the weight** of each criterion using the formula:\n",
    "\n",
    "$$ \\large\n",
    "w_o = \\frac{1}{m} \\sum_{k=o}^m \\frac{1}{k}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "chief-bubble",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "C1    0.156667\n",
       "C2    0.040000\n",
       "C3    0.256667\n",
       "C4    0.456667\n",
       "C5    0.090000\n",
       "dtype: float64"
      ]
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   ],
   "source": [
    "m = len(ORDER)\n",
    "K = np.arange(m) + 1\n",
    "\n",
    "WEIGHTS = pd.Series({\n",
    "    k: 1/m*(1/K[o-1:]).sum()\n",
    "    for k, o in ORDER.items()\n",
    "})\n",
    "\n",
    "WEIGHTS"
   ]
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  {
   "cell_type": "markdown",
   "id": "social-sponsorship",
   "metadata": {},
   "source": [
    "### 2.3. Application\n",
    "---\n",
    "The _ROC method_ is supposed to be used together with other methods such as [PROMETHEE](./promethee.ipynb) ans others. As an example, we are going to calculate a kind of **score** for each data point, based on the weights applied for their criteria.\n",
    "\n",
    "$$ \\large\n",
    "S_i = \\sum_{k=1}^m w_k \\cdot \\frac{C_{ik}}{max(C_k)}\n",
    "$$\n",
    "\n",
    "Having that, we are able to define a **ranking** by ordering the score in descending way. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "hollywood-underwear",
   "metadata": {},
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       "      <th class=\"col_heading level0 col0\" >C1</th>\n",
       "      <th class=\"col_heading level0 col1\" >C2</th>\n",
       "      <th class=\"col_heading level0 col2\" >C3</th>\n",
       "      <th class=\"col_heading level0 col3\" >C4</th>\n",
       "      <th class=\"col_heading level0 col4\" >C5</th>\n",
       "      <th class=\"col_heading level0 col5\" >score</th>\n",
       "      <th class=\"col_heading level0 col6\" >ranking</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_357dd_level0_row0\" class=\"row_heading level0 row0\" >7</th>\n",
       "      <td id=\"T_357dd_row0_col0\" class=\"data row0 col0\" >3</td>\n",
       "      <td id=\"T_357dd_row0_col1\" class=\"data row0 col1\" >24</td>\n",
       "      <td id=\"T_357dd_row0_col2\" class=\"data row0 col2\" >16</td>\n",
       "      <td id=\"T_357dd_row0_col3\" class=\"data row0 col3\" >4</td>\n",
       "      <td id=\"T_357dd_row0_col4\" class=\"data row0 col4\" >4</td>\n",
       "      <td id=\"T_357dd_row0_col5\" class=\"data row0 col5\" >0.815419</td>\n",
       "      <td id=\"T_357dd_row0_col6\" class=\"data row0 col6\" >1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_357dd_level0_row1\" class=\"row_heading level0 row1\" >8</th>\n",
       "      <td id=\"T_357dd_row1_col0\" class=\"data row1 col0\" >5</td>\n",
       "      <td id=\"T_357dd_row1_col1\" class=\"data row1 col1\" >47</td>\n",
       "      <td id=\"T_357dd_row1_col2\" class=\"data row1 col2\" >16</td>\n",
       "      <td id=\"T_357dd_row1_col3\" class=\"data row1 col3\" >3</td>\n",
       "      <td id=\"T_357dd_row1_col4\" class=\"data row1 col4\" >7</td>\n",
       "      <td id=\"T_357dd_row1_col5\" class=\"data row1 col5\" >0.798565</td>\n",
       "      <td id=\"T_357dd_row1_col6\" class=\"data row1 col6\" >2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_357dd_level0_row2\" class=\"row_heading level0 row2\" >4</th>\n",
       "      <td id=\"T_357dd_row2_col0\" class=\"data row2 col0\" >8</td>\n",
       "      <td id=\"T_357dd_row2_col1\" class=\"data row2 col1\" >2</td>\n",
       "      <td id=\"T_357dd_row2_col2\" class=\"data row2 col2\" >10</td>\n",
       "      <td id=\"T_357dd_row2_col3\" class=\"data row2 col3\" >4</td>\n",
       "      <td id=\"T_357dd_row2_col4\" class=\"data row2 col4\" >1</td>\n",
       "      <td id=\"T_357dd_row2_col5\" class=\"data row2 col5\" >0.770485</td>\n",
       "      <td id=\"T_357dd_row2_col6\" class=\"data row2 col6\" >3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_357dd_level0_row3\" class=\"row_heading level0 row3\" >6</th>\n",
       "      <td id=\"T_357dd_row3_col0\" class=\"data row3 col0\" >6</td>\n",
       "      <td id=\"T_357dd_row3_col1\" class=\"data row3 col1\" >40</td>\n",
       "      <td id=\"T_357dd_row3_col2\" class=\"data row3 col2\" >6</td>\n",
       "      <td id=\"T_357dd_row3_col3\" class=\"data row3 col3\" >4</td>\n",
       "      <td id=\"T_357dd_row3_col4\" class=\"data row3 col4\" >5</td>\n",
       "      <td id=\"T_357dd_row3_col5\" class=\"data row3 col5\" >0.758050</td>\n",
       "      <td id=\"T_357dd_row3_col6\" class=\"data row3 col6\" >4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_357dd_level0_row4\" class=\"row_heading level0 row4\" >0</th>\n",
       "      <td id=\"T_357dd_row4_col0\" class=\"data row4 col0\" >6</td>\n",
       "      <td id=\"T_357dd_row4_col1\" class=\"data row4 col1\" >7</td>\n",
       "      <td id=\"T_357dd_row4_col2\" class=\"data row4 col2\" >18</td>\n",
       "      <td id=\"T_357dd_row4_col3\" class=\"data row4 col3\" >3</td>\n",
       "      <td id=\"T_357dd_row4_col4\" class=\"data row4 col4\" >1</td>\n",
       "      <td id=\"T_357dd_row4_col5\" class=\"data row4 col5\" >0.735481</td>\n",
       "      <td id=\"T_357dd_row4_col6\" class=\"data row4 col6\" >5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_357dd_level0_row5\" class=\"row_heading level0 row5\" >9</th>\n",
       "      <td id=\"T_357dd_row5_col0\" class=\"data row5 col0\" >8</td>\n",
       "      <td id=\"T_357dd_row5_col1\" class=\"data row5 col1\" >25</td>\n",
       "      <td id=\"T_357dd_row5_col2\" class=\"data row5 col2\" >1</td>\n",
       "      <td id=\"T_357dd_row5_col3\" class=\"data row5 col3\" >4</td>\n",
       "      <td id=\"T_357dd_row5_col4\" class=\"data row5 col4\" >4</td>\n",
       "      <td id=\"T_357dd_row5_col5\" class=\"data row5 col5\" >0.700298</td>\n",
       "      <td id=\"T_357dd_row5_col6\" class=\"data row5 col6\" >6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_357dd_level0_row6\" class=\"row_heading level0 row6\" >5</th>\n",
       "      <td id=\"T_357dd_row6_col0\" class=\"data row6 col0\" >4</td>\n",
       "      <td id=\"T_357dd_row6_col1\" class=\"data row6 col1\" >39</td>\n",
       "      <td id=\"T_357dd_row6_col2\" class=\"data row6 col2\" >17</td>\n",
       "      <td id=\"T_357dd_row6_col3\" class=\"data row6 col3\" >2</td>\n",
       "      <td id=\"T_357dd_row6_col4\" class=\"data row6 col4\" >3</td>\n",
       "      <td id=\"T_357dd_row6_col5\" class=\"data row6 col5\" >0.620837</td>\n",
       "      <td id=\"T_357dd_row6_col6\" class=\"data row6 col6\" >7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_357dd_level0_row7\" class=\"row_heading level0 row7\" >1</th>\n",
       "      <td id=\"T_357dd_row7_col0\" class=\"data row7 col0\" >1</td>\n",
       "      <td id=\"T_357dd_row7_col1\" class=\"data row7 col1\" >25</td>\n",
       "      <td id=\"T_357dd_row7_col2\" class=\"data row7 col2\" >6</td>\n",
       "      <td id=\"T_357dd_row7_col3\" class=\"data row7 col3\" >4</td>\n",
       "      <td id=\"T_357dd_row7_col4\" class=\"data row7 col4\" >2</td>\n",
       "      <td id=\"T_357dd_row7_col5\" class=\"data row7 col5\" >0.608796</td>\n",
       "      <td id=\"T_357dd_row7_col6\" class=\"data row7 col6\" >8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_357dd_level0_row8\" class=\"row_heading level0 row8\" >3</th>\n",
       "      <td id=\"T_357dd_row8_col0\" class=\"data row8 col0\" >4</td>\n",
       "      <td id=\"T_357dd_row8_col1\" class=\"data row8 col1\" >13</td>\n",
       "      <td id=\"T_357dd_row8_col2\" class=\"data row8 col2\" >9</td>\n",
       "      <td id=\"T_357dd_row8_col3\" class=\"data row8 col3\" >2</td>\n",
       "      <td id=\"T_357dd_row8_col4\" class=\"data row8 col4\" >2</td>\n",
       "      <td id=\"T_357dd_row8_col5\" class=\"data row8 col5\" >0.471778</td>\n",
       "      <td id=\"T_357dd_row8_col6\" class=\"data row8 col6\" >9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_357dd_level0_row9\" class=\"row_heading level0 row9\" >2</th>\n",
       "      <td id=\"T_357dd_row9_col0\" class=\"data row9 col0\" >4</td>\n",
       "      <td id=\"T_357dd_row9_col1\" class=\"data row9 col1\" >25</td>\n",
       "      <td id=\"T_357dd_row9_col2\" class=\"data row9 col2\" >14</td>\n",
       "      <td id=\"T_357dd_row9_col3\" class=\"data row9 col3\" >1</td>\n",
       "      <td id=\"T_357dd_row9_col4\" class=\"data row9 col4\" >2</td>\n",
       "      <td id=\"T_357dd_row9_col5\" class=\"data row9 col5\" >0.439121</td>\n",
       "      <td id=\"T_357dd_row9_col6\" class=\"data row9 col6\" >10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x271f4942688>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_ = df[list(ORDER)]\n",
    "df_ = df_/df_.max()\n",
    "\n",
    "df[\"score\"] = np.sum(WEIGHTS*df_, axis=1)\n",
    "df[\"ranking\"] = (\n",
    "    df[\"score\"]\n",
    "    .rank(ascending=False, method=\"first\")\n",
    "    .astype(int)\n",
    ")\n",
    "\n",
    "(\n",
    "    df.sort_values(\"ranking\")\n",
    "    .style.background_gradient(\n",
    "        subset=list(ORDER)\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ambient-vacation",
   "metadata": {},
   "source": [
    "## 3. Examples\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "assigned-residence",
   "metadata": {},
   "source": [
    "### 3.1. Device priorization\n",
    "---\n",
    "As an example, let's priorize devices based on their attributes. The data was taken from [dxomark](https://www.dxomark.com/smartphones/) and we will consider 5 criteria: **price**, **camera**, **audio**, **display** and **battery**. The _price_ is a value we want to **minimize** so we have to prepare this feature before calculating the score. The other criteria are scores and we will maximize as usual."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "unsigned-funds",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table id=\"T_3ba0a_\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th class=\"col_heading level0 col0\" >device</th>\n",
       "      <th class=\"col_heading level0 col1\" >price</th>\n",
       "      <th class=\"col_heading level0 col2\" >camera</th>\n",
       "      <th class=\"col_heading level0 col3\" >audio</th>\n",
       "      <th class=\"col_heading level0 col4\" >display</th>\n",
       "      <th class=\"col_heading level0 col5\" >battery</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_3ba0a_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_3ba0a_row0_col0\" class=\"data row0 col0\" >Apple iPhone 15 Pro Max</td>\n",
       "      <td id=\"T_3ba0a_row0_col1\" class=\"data row0 col1\" >1199</td>\n",
       "      <td id=\"T_3ba0a_row0_col2\" class=\"data row0 col2\" >154</td>\n",
       "      <td id=\"T_3ba0a_row0_col3\" class=\"data row0 col3\" >143</td>\n",
       "      <td id=\"T_3ba0a_row0_col4\" class=\"data row0 col4\" >151</td>\n",
       "      <td id=\"T_3ba0a_row0_col5\" class=\"data row0 col5\" >134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3ba0a_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_3ba0a_row1_col0\" class=\"data row1 col0\" >Apple iPhone 15 Pro</td>\n",
       "      <td id=\"T_3ba0a_row1_col1\" class=\"data row1 col1\" >999</td>\n",
       "      <td id=\"T_3ba0a_row1_col2\" class=\"data row1 col2\" >154</td>\n",
       "      <td id=\"T_3ba0a_row1_col3\" class=\"data row1 col3\" >142</td>\n",
       "      <td id=\"T_3ba0a_row1_col4\" class=\"data row1 col4\" >151</td>\n",
       "      <td id=\"T_3ba0a_row1_col5\" class=\"data row1 col5\" >114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3ba0a_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_3ba0a_row2_col0\" class=\"data row2 col0\" >Google Pixel 8 Pro</td>\n",
       "      <td id=\"T_3ba0a_row2_col1\" class=\"data row2 col1\" >999</td>\n",
       "      <td id=\"T_3ba0a_row2_col2\" class=\"data row2 col2\" >153</td>\n",
       "      <td id=\"T_3ba0a_row2_col3\" class=\"data row2 col3\" >142</td>\n",
       "      <td id=\"T_3ba0a_row2_col4\" class=\"data row2 col4\" >154</td>\n",
       "      <td id=\"T_3ba0a_row2_col5\" class=\"data row2 col5\" >111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3ba0a_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_3ba0a_row3_col0\" class=\"data row3 col0\" >Google Pixel 7 Pro</td>\n",
       "      <td id=\"T_3ba0a_row3_col1\" class=\"data row3 col1\" >899</td>\n",
       "      <td id=\"T_3ba0a_row3_col2\" class=\"data row3 col2\" >147</td>\n",
       "      <td id=\"T_3ba0a_row3_col3\" class=\"data row3 col3\" >137</td>\n",
       "      <td id=\"T_3ba0a_row3_col4\" class=\"data row3 col4\" >148</td>\n",
       "      <td id=\"T_3ba0a_row3_col5\" class=\"data row3 col5\" >102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3ba0a_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_3ba0a_row4_col0\" class=\"data row4 col0\" >Huawei Mate 50 Pro</td>\n",
       "      <td id=\"T_3ba0a_row4_col1\" class=\"data row4 col1\" >1299</td>\n",
       "      <td id=\"T_3ba0a_row4_col2\" class=\"data row4 col2\" >149</td>\n",
       "      <td id=\"T_3ba0a_row4_col3\" class=\"data row4 col3\" >144</td>\n",
       "      <td id=\"T_3ba0a_row4_col4\" class=\"data row4 col4\" >133</td>\n",
       "      <td id=\"T_3ba0a_row4_col5\" class=\"data row4 col5\" >103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3ba0a_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_3ba0a_row5_col0\" class=\"data row5 col0\" >Huawei P50 Pro</td>\n",
       "      <td id=\"T_3ba0a_row5_col1\" class=\"data row5 col1\" >907</td>\n",
       "      <td id=\"T_3ba0a_row5_col2\" class=\"data row5 col2\" >143</td>\n",
       "      <td id=\"T_3ba0a_row5_col3\" class=\"data row5 col3\" >119</td>\n",
       "      <td id=\"T_3ba0a_row5_col4\" class=\"data row5 col4\" >134</td>\n",
       "      <td id=\"T_3ba0a_row5_col5\" class=\"data row5 col5\" >123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3ba0a_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_3ba0a_row6_col0\" class=\"data row6 col0\" >Samsung Galaxy S24 Ultra</td>\n",
       "      <td id=\"T_3ba0a_row6_col1\" class=\"data row6 col1\" >1299</td>\n",
       "      <td id=\"T_3ba0a_row6_col2\" class=\"data row6 col2\" >144</td>\n",
       "      <td id=\"T_3ba0a_row6_col3\" class=\"data row6 col3\" >139</td>\n",
       "      <td id=\"T_3ba0a_row6_col4\" class=\"data row6 col4\" >155</td>\n",
       "      <td id=\"T_3ba0a_row6_col5\" class=\"data row6 col5\" >130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3ba0a_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "      <td id=\"T_3ba0a_row7_col0\" class=\"data row7 col0\" >Samsung Galaxy S23 Ultra</td>\n",
       "      <td id=\"T_3ba0a_row7_col1\" class=\"data row7 col1\" >1199</td>\n",
       "      <td id=\"T_3ba0a_row7_col2\" class=\"data row7 col2\" >140</td>\n",
       "      <td id=\"T_3ba0a_row7_col3\" class=\"data row7 col3\" >139</td>\n",
       "      <td id=\"T_3ba0a_row7_col4\" class=\"data row7 col4\" >148</td>\n",
       "      <td id=\"T_3ba0a_row7_col5\" class=\"data row7 col5\" >142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3ba0a_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_3ba0a_row8_col0\" class=\"data row8 col0\" >Xiaomi Mi 11 Ultra</td>\n",
       "      <td id=\"T_3ba0a_row8_col1\" class=\"data row8 col1\" >1200</td>\n",
       "      <td id=\"T_3ba0a_row8_col2\" class=\"data row8 col2\" >141</td>\n",
       "      <td id=\"T_3ba0a_row8_col3\" class=\"data row8 col3\" >119</td>\n",
       "      <td id=\"T_3ba0a_row8_col4\" class=\"data row8 col4\" >125</td>\n",
       "      <td id=\"T_3ba0a_row8_col5\" class=\"data row8 col5\" >108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3ba0a_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "      <td id=\"T_3ba0a_row9_col0\" class=\"data row9 col0\" >Xiaomi 13 Ultra</td>\n",
       "      <td id=\"T_3ba0a_row9_col1\" class=\"data row9 col1\" >908</td>\n",
       "      <td id=\"T_3ba0a_row9_col2\" class=\"data row9 col2\" >140</td>\n",
       "      <td id=\"T_3ba0a_row9_col3\" class=\"data row9 col3\" >140</td>\n",
       "      <td id=\"T_3ba0a_row9_col4\" class=\"data row9 col4\" >130</td>\n",
       "      <td id=\"T_3ba0a_row9_col5\" class=\"data row9 col5\" >133</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x271f496d288>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_ex1 = pd.DataFrame({\n",
    "    \"device\": [\n",
    "        \"Apple iPhone 15 Pro Max\", \n",
    "        \"Apple iPhone 15 Pro\",\n",
    "        \"Google Pixel 8 Pro\",\n",
    "        \"Google Pixel 7 Pro\",\n",
    "        \"Huawei Mate 50 Pro\",\n",
    "        \"Huawei P50 Pro\",\n",
    "        \"Samsung Galaxy S24 Ultra\",\n",
    "        \"Samsung Galaxy S23 Ultra\",\n",
    "        \"Xiaomi Mi 11 Ultra\",\n",
    "        \"Xiaomi 13 Ultra\",\n",
    "    ],\n",
    "    # criteria we want to minimize\n",
    "    \"price\": [1199, 999, 999, 899, 1299, 907, 1299, 1199, 1200, 908],\n",
    "    # criteria we want to maximize\n",
    "    \"camera\": [154, 154, 153, 147, 149, 143, 144, 140, 141, 140],\n",
    "    \"audio\": [143, 142, 142, 137, 144, 119, 139, 139, 119, 140],\n",
    "    \"display\": [151, 151, 154, 148, 133, 134, 155, 148, 125, 130],\n",
    "    \"battery\": [134, 114, 111, 102, 103, 123, 130, 142, 108, 133]\n",
    "})\n",
    "\n",
    "df_ex1.style.background_gradient()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "outer-funds",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_7df10_row0_col1, #T_7df10_row1_col1 {\n",
       "  background-color: #fcf4fa;\n",
       "  color: #000000;\n",
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       "#T_7df10_row0_col2, #T_7df10_row1_col3, #T_7df10_row2_col1, #T_7df10_row2_col5, #T_7df10_row6_col2, #T_7df10_row8_col3, #T_7df10_row8_col4 {\n",
       "  background-color: #fff7fb;\n",
       "  color: #000000;\n",
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       "  background-color: #046096;\n",
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       "  background-color: #e3e0ee;\n",
       "  color: #000000;\n",
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       "  background-color: #056ba9;\n",
       "  color: #f1f1f1;\n",
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       "#T_7df10_row1_col2 {\n",
       "  background-color: #d9d8ea;\n",
       "  color: #000000;\n",
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       "#T_7df10_row1_col4, #T_7df10_row3_col5 {\n",
       "  background-color: #c0c9e2;\n",
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       "  background-color: #67a4cc;\n",
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       "#T_7df10_row3_col1, #T_7df10_row4_col1 {\n",
       "  background-color: #d0d1e6;\n",
       "  color: #000000;\n",
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       "#T_7df10_row3_col2, #T_7df10_row5_col2, #T_7df10_row6_col5, #T_7df10_row7_col1, #T_7df10_row7_col4, #T_7df10_row9_col1, #T_7df10_row9_col3 {\n",
       "  background-color: #023858;\n",
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       "#T_7df10_row3_col3, #T_7df10_row4_col3 {\n",
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       "  background-color: #034b76;\n",
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       "  background-color: #d6d6e9;\n",
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       "#T_7df10_row5_col1, #T_7df10_row6_col1, #T_7df10_row8_col1 {\n",
       "  background-color: #056faf;\n",
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       "  background-color: #034369;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_7df10_row5_col5, #T_7df10_row6_col3, #T_7df10_row7_col3 {\n",
       "  background-color: #0567a2;\n",
       "  color: #f1f1f1;\n",
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       "#T_7df10_row7_col2 {\n",
       "  background-color: #c4cbe3;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_7df10_row7_col5 {\n",
       "  background-color: #187cb6;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_7df10_row8_col2 {\n",
       "  background-color: #f4eef6;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_7df10_row8_col5 {\n",
       "  background-color: #e7e3f0;\n",
       "  color: #000000;\n",
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       "#T_7df10_row9_col2 {\n",
       "  background-color: #2f8bbe;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_7df10_row9_col4 {\n",
       "  background-color: #cacee5;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_7df10_row9_col5 {\n",
       "  background-color: #fbf4f9;\n",
       "  color: #000000;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_7df10_\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th class=\"col_heading level0 col0\" >device</th>\n",
       "      <th class=\"col_heading level0 col1\" >price</th>\n",
       "      <th class=\"col_heading level0 col2\" >camera</th>\n",
       "      <th class=\"col_heading level0 col3\" >audio</th>\n",
       "      <th class=\"col_heading level0 col4\" >display</th>\n",
       "      <th class=\"col_heading level0 col5\" >battery</th>\n",
       "      <th class=\"col_heading level0 col6\" >score</th>\n",
       "      <th class=\"col_heading level0 col7\" >ranking</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_7df10_level0_row0\" class=\"row_heading level0 row0\" >9</th>\n",
       "      <td id=\"T_7df10_row0_col0\" class=\"data row0 col0\" >Xiaomi 13 Ultra</td>\n",
       "      <td id=\"T_7df10_row0_col1\" class=\"data row0 col1\" >908</td>\n",
       "      <td id=\"T_7df10_row0_col2\" class=\"data row0 col2\" >140</td>\n",
       "      <td id=\"T_7df10_row0_col3\" class=\"data row0 col3\" >140</td>\n",
       "      <td id=\"T_7df10_row0_col4\" class=\"data row0 col4\" >130</td>\n",
       "      <td id=\"T_7df10_row0_col5\" class=\"data row0 col5\" >133</td>\n",
       "      <td id=\"T_7df10_row0_col6\" class=\"data row0 col6\" >0.631900</td>\n",
       "      <td id=\"T_7df10_row0_col7\" class=\"data row0 col7\" >1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_7df10_level0_row1\" class=\"row_heading level0 row1\" >5</th>\n",
       "      <td id=\"T_7df10_row1_col0\" class=\"data row1 col0\" >Huawei P50 Pro</td>\n",
       "      <td id=\"T_7df10_row1_col1\" class=\"data row1 col1\" >907</td>\n",
       "      <td id=\"T_7df10_row1_col2\" class=\"data row1 col2\" >143</td>\n",
       "      <td id=\"T_7df10_row1_col3\" class=\"data row1 col3\" >119</td>\n",
       "      <td id=\"T_7df10_row1_col4\" class=\"data row1 col4\" >134</td>\n",
       "      <td id=\"T_7df10_row1_col5\" class=\"data row1 col5\" >123</td>\n",
       "      <td id=\"T_7df10_row1_col6\" class=\"data row1 col6\" >0.622708</td>\n",
       "      <td id=\"T_7df10_row1_col7\" class=\"data row1 col7\" >2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_7df10_level0_row2\" class=\"row_heading level0 row2\" >3</th>\n",
       "      <td id=\"T_7df10_row2_col0\" class=\"data row2 col0\" >Google Pixel 7 Pro</td>\n",
       "      <td id=\"T_7df10_row2_col1\" class=\"data row2 col1\" >899</td>\n",
       "      <td id=\"T_7df10_row2_col2\" class=\"data row2 col2\" >147</td>\n",
       "      <td id=\"T_7df10_row2_col3\" class=\"data row2 col3\" >137</td>\n",
       "      <td id=\"T_7df10_row2_col4\" class=\"data row2 col4\" >148</td>\n",
       "      <td id=\"T_7df10_row2_col5\" class=\"data row2 col5\" >102</td>\n",
       "      <td id=\"T_7df10_row2_col6\" class=\"data row2 col6\" >0.622147</td>\n",
       "      <td id=\"T_7df10_row2_col7\" class=\"data row2 col7\" >3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_7df10_level0_row3\" class=\"row_heading level0 row3\" >1</th>\n",
       "      <td id=\"T_7df10_row3_col0\" class=\"data row3 col0\" >Apple iPhone 15 Pro</td>\n",
       "      <td id=\"T_7df10_row3_col1\" class=\"data row3 col1\" >999</td>\n",
       "      <td id=\"T_7df10_row3_col2\" class=\"data row3 col2\" >154</td>\n",
       "      <td id=\"T_7df10_row3_col3\" class=\"data row3 col3\" >142</td>\n",
       "      <td id=\"T_7df10_row3_col4\" class=\"data row3 col4\" >151</td>\n",
       "      <td id=\"T_7df10_row3_col5\" class=\"data row3 col5\" >114</td>\n",
       "      <td id=\"T_7df10_row3_col6\" class=\"data row3 col6\" >0.615029</td>\n",
       "      <td id=\"T_7df10_row3_col7\" class=\"data row3 col7\" >4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_7df10_level0_row4\" class=\"row_heading level0 row4\" >2</th>\n",
       "      <td id=\"T_7df10_row4_col0\" class=\"data row4 col0\" >Google Pixel 8 Pro</td>\n",
       "      <td id=\"T_7df10_row4_col1\" class=\"data row4 col1\" >999</td>\n",
       "      <td id=\"T_7df10_row4_col2\" class=\"data row4 col2\" >153</td>\n",
       "      <td id=\"T_7df10_row4_col3\" class=\"data row4 col3\" >142</td>\n",
       "      <td id=\"T_7df10_row4_col4\" class=\"data row4 col4\" >154</td>\n",
       "      <td id=\"T_7df10_row4_col5\" class=\"data row4 col5\" >111</td>\n",
       "      <td id=\"T_7df10_row4_col6\" class=\"data row4 col6\" >0.611794</td>\n",
       "      <td id=\"T_7df10_row4_col7\" class=\"data row4 col7\" >5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_7df10_level0_row5\" class=\"row_heading level0 row5\" >0</th>\n",
       "      <td id=\"T_7df10_row5_col0\" class=\"data row5 col0\" >Apple iPhone 15 Pro Max</td>\n",
       "      <td id=\"T_7df10_row5_col1\" class=\"data row5 col1\" >1199</td>\n",
       "      <td id=\"T_7df10_row5_col2\" class=\"data row5 col2\" >154</td>\n",
       "      <td id=\"T_7df10_row5_col3\" class=\"data row5 col3\" >143</td>\n",
       "      <td id=\"T_7df10_row5_col4\" class=\"data row5 col4\" >151</td>\n",
       "      <td id=\"T_7df10_row5_col5\" class=\"data row5 col5\" >134</td>\n",
       "      <td id=\"T_7df10_row5_col6\" class=\"data row5 col6\" >0.567062</td>\n",
       "      <td id=\"T_7df10_row5_col7\" class=\"data row5 col7\" >6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_7df10_level0_row6\" class=\"row_heading level0 row6\" >7</th>\n",
       "      <td id=\"T_7df10_row6_col0\" class=\"data row6 col0\" >Samsung Galaxy S23 Ultra</td>\n",
       "      <td id=\"T_7df10_row6_col1\" class=\"data row6 col1\" >1199</td>\n",
       "      <td id=\"T_7df10_row6_col2\" class=\"data row6 col2\" >140</td>\n",
       "      <td id=\"T_7df10_row6_col3\" class=\"data row6 col3\" >139</td>\n",
       "      <td id=\"T_7df10_row6_col4\" class=\"data row6 col4\" >148</td>\n",
       "      <td id=\"T_7df10_row6_col5\" class=\"data row6 col5\" >142</td>\n",
       "      <td id=\"T_7df10_row6_col6\" class=\"data row6 col6\" >0.549702</td>\n",
       "      <td id=\"T_7df10_row6_col7\" class=\"data row6 col7\" >7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_7df10_level0_row7\" class=\"row_heading level0 row7\" >6</th>\n",
       "      <td id=\"T_7df10_row7_col0\" class=\"data row7 col0\" >Samsung Galaxy S24 Ultra</td>\n",
       "      <td id=\"T_7df10_row7_col1\" class=\"data row7 col1\" >1299</td>\n",
       "      <td id=\"T_7df10_row7_col2\" class=\"data row7 col2\" >144</td>\n",
       "      <td id=\"T_7df10_row7_col3\" class=\"data row7 col3\" >139</td>\n",
       "      <td id=\"T_7df10_row7_col4\" class=\"data row7 col4\" >155</td>\n",
       "      <td id=\"T_7df10_row7_col5\" class=\"data row7 col5\" >130</td>\n",
       "      <td id=\"T_7df10_row7_col6\" class=\"data row7 col6\" >0.512038</td>\n",
       "      <td id=\"T_7df10_row7_col7\" class=\"data row7 col7\" >8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_7df10_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_7df10_row8_col0\" class=\"data row8 col0\" >Xiaomi Mi 11 Ultra</td>\n",
       "      <td id=\"T_7df10_row8_col1\" class=\"data row8 col1\" >1200</td>\n",
       "      <td id=\"T_7df10_row8_col2\" class=\"data row8 col2\" >141</td>\n",
       "      <td id=\"T_7df10_row8_col3\" class=\"data row8 col3\" >119</td>\n",
       "      <td id=\"T_7df10_row8_col4\" class=\"data row8 col4\" >125</td>\n",
       "      <td id=\"T_7df10_row8_col5\" class=\"data row8 col5\" >108</td>\n",
       "      <td id=\"T_7df10_row8_col6\" class=\"data row8 col6\" >0.494595</td>\n",
       "      <td id=\"T_7df10_row8_col7\" class=\"data row8 col7\" >9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_7df10_level0_row9\" class=\"row_heading level0 row9\" >4</th>\n",
       "      <td id=\"T_7df10_row9_col0\" class=\"data row9 col0\" >Huawei Mate 50 Pro</td>\n",
       "      <td id=\"T_7df10_row9_col1\" class=\"data row9 col1\" >1299</td>\n",
       "      <td id=\"T_7df10_row9_col2\" class=\"data row9 col2\" >149</td>\n",
       "      <td id=\"T_7df10_row9_col3\" class=\"data row9 col3\" >144</td>\n",
       "      <td id=\"T_7df10_row9_col4\" class=\"data row9 col4\" >133</td>\n",
       "      <td id=\"T_7df10_row9_col5\" class=\"data row9 col5\" >103</td>\n",
       "      <td id=\"T_7df10_row9_col6\" class=\"data row9 col6\" >0.479198</td>\n",
       "      <td id=\"T_7df10_row9_col7\" class=\"data row9 col7\" >10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x271f49937c8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Criteria order of importance\n",
    "ORDER_ex1 = {\n",
    "    \"price\": 1,\n",
    "    \"camera\": 2,\n",
    "    \"audio\": 5,\n",
    "    \"display\": 4,\n",
    "    \"battery\": 3\n",
    "}\n",
    "\n",
    "# Criteria weights method\n",
    "m = len(ORDER_ex1)\n",
    "K = np.arange(m) + 1\n",
    "\n",
    "WEIGHTS_ex1 = pd.Series({\n",
    "    k: 1/m*(1/K[o-1:]).sum()\n",
    "    for k, o in ORDER_ex1.items()\n",
    "})\n",
    "\n",
    "# Data preparation and price minimization\n",
    "df_ex1_ = df_ex1[list(ORDER_ex1)]\n",
    "df_ex1_ = df_ex1_/df_ex1_.max()\n",
    "df_ex1_[\"price\"] = 1 - df_ex1_[\"price\"]\n",
    "\n",
    "# Score and Ranking\n",
    "df_ex1[\"score\"] = np.sum(WEIGHTS_ex1*df_ex1_, axis=1)\n",
    "df_ex1[\"ranking\"] = (\n",
    "    df_ex1[\"score\"]\n",
    "    .rank(ascending=False, method=\"first\")\n",
    "    .astype(int)\n",
    ")\n",
    "\n",
    "# Output\n",
    "(\n",
    "    df_ex1.sort_values(\"ranking\")\n",
    "    .style.background_gradient(\n",
    "        subset=list(ORDER_ex1)\n",
    "    )\n",
    ")"
   ]
  }
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