{
 "cells": [
  {
   "source": [
    "# Tutorial 4 - Certainty factors"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "This tutorial uses the fuzzy inference system developed in Tutorial 1."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import warnings\n",
    "\n",
    "os.chdir('/workspaces/fuzzy-expert')\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "source": [
    "## Fuzzy Variables"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from fuzzy_expert.variable import FuzzyVariable\n",
    "from fuzzy_expert.rule import FuzzyRule\n",
    "from fuzzy_expert.inference import DecompositionalInference\n",
    "\n",
    "variables = {\n",
    "    \"score\": FuzzyVariable(\n",
    "        universe_range=(150, 200),\n",
    "        terms={\n",
    "            \"High\": [(175, 0), (180, 0.2), (185, 0.7), (190, 1)],\n",
    "            \"Low\": [(155, 1), (160, 0.8), (165, 0.5), (170, 0.2), (175, 0)],\n",
    "        },\n",
    "    ),\n",
    "    \"ratio\": FuzzyVariable(\n",
    "        universe_range=(0.1, 1),\n",
    "        terms={\n",
    "            \"Goodr\": [(0.3, 1), (0.4, 0.7), (0.41, 0.3), (0.42, 0)],\n",
    "            \"Badr\": [(0.44, 0), (0.45, 0.3), (0.5, 0.7), (0.7, 1)],\n",
    "        },\n",
    "    ),\n",
    "    #\n",
    "    \"credit\": FuzzyVariable(\n",
    "        universe_range=(0, 10),\n",
    "        terms={\n",
    "            \"Goodc\": [(2, 1), (3, 0.7), (4, 0.3), (5, 0)],\n",
    "            \"Badc\": [(5, 0), (6, 0.3), (7, 0.7), (8, 1)],\n",
    "        },\n",
    "    ),\n",
    "    #\n",
    "    \"decision\": FuzzyVariable(\n",
    "        universe_range=(0, 10),\n",
    "        terms={\n",
    "            \"Approve\": [(5, 0), (6, 0.3), (7, 0.7), (8, 1)],\n",
    "            \"Reject\": [(2, 1), (3, 0.7), (4, 0.3), (5, 0)],\n",
    "        },\n",
    "    ),\n",
    "}"
   ]
  },
  {
   "source": [
    "## Fuzzy rules with certainty factors"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "It is possible to assign a certainty factor (`cf`) to each rule. If this value is not specified, it has assumed to be equal to 1.0. In addition, the `threshold_cf` is the minimum certainty factor required to consider the rule fired; this is, rules with a computed certainty factor below the threshold are not considering for computing the output of the system. The first rule has a certainty factor of `0.9`, while the second rule has a certainty factor of `1.0` (by default)."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "rules = [\n",
    "    FuzzyRule(\n",
    "        cf=0.9,\n",
    "        premise=[\n",
    "            (\"score\", \"High\"),\n",
    "            (\"AND\", \"ratio\", \"Goodr\"),\n",
    "            (\"AND\", \"credit\", \"Goodc\"),\n",
    "        ],\n",
    "        consequence=[(\"decision\", \"Approve\")],\n",
    "    ),\n",
    "    FuzzyRule(\n",
    "        premise=[\n",
    "            (\"score\", \"Low\"),\n",
    "            (\"AND\", \"ratio\", \"Badr\"),\n",
    "            (\"OR\", \"credit\", \"Badc\"),\n",
    "        ],\n",
    "        consequence=[(\"decision\", \"Reject\")],\n",
    "    )\n",
    "]"
   ]
  },
  {
   "source": [
    "## Facts with certainty factors"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "In addition, also it is possible to assign certainty factors to the facts. When a certainty factor not is specified by the user, it has a default value or 1.0. In the following code, the variables `score`, `ratio`, and `credit` have certainty factors of `0.9`, `1.0`, and `0.95` respectively. The conclusion is `decision=8.01` with a certainty factor of `0.95`."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "({'decision': 8.010492631084489}, 0.95)"
      ]
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "from fuzzy_expert.inference import DecompositionalInference\n",
    "\n",
    "model = DecompositionalInference(\n",
    "    and_operator=\"min\",\n",
    "    or_operator=\"max\",\n",
    "    implication_operator=\"Rc\",\n",
    "    composition_operator=\"max-min\",\n",
    "    production_link=\"max\",\n",
    "    defuzzification_operator=\"cog\",\n",
    ")\n",
    "\n",
    "model(\n",
    "    variables=variables,\n",
    "    rules=rules,\n",
    "    score=(190, 0.9),\n",
    "    ratio=(0.39, 1.0),\n",
    "    credit=(1.5, 0.95),\n",
    ")"
   ]
  }
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