{
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  {
   "cell_type": "markdown",
   "id": "7a7ff013",
   "metadata": {},
   "source": [
    "# Zadeh operators by using operator overloading"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cada993c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aed07c67",
   "metadata": {},
   "source": [
    "## Fuzzy value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "59aaa0e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Zadeh:\n",
    "    \"\"\"\n",
    "    Represents a fuzzy value\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, value):\n",
    "        self.value = value\n",
    "\n",
    "    @property\n",
    "    def value(self):\n",
    "        return self._value\n",
    "\n",
    "    @value.setter\n",
    "    def value(self, value):\n",
    "        if 0 <= value <= 1:\n",
    "            self._value = value\n",
    "        else:\n",
    "            raise ValueError(f'The fuzzy value {value} is invalid!')\n",
    "    \n",
    "    def __and__(self, other):\n",
    "        \"\"\"\n",
    "        T-norm\n",
    "        \"\"\"\n",
    "        if self.value < other.value:\n",
    "            return Zadeh(self.value)\n",
    "        else:\n",
    "            return Zadeh(other.value)\n",
    "\n",
    "    def __or__(self, other):\n",
    "        \"\"\"\n",
    "        S-norm\n",
    "        \"\"\"\n",
    "        if self.value > other.value:\n",
    "            return Zadeh(self.value)\n",
    "        else:\n",
    "            return Zadeh(other.value)\n",
    "\n",
    "    def __str__(self):\n",
    "        return f'{self.value}'\n",
    "\n",
    "    def __repr__(self):\n",
    "        return f'Zadeh({self.value})'\n",
    "\n",
    "def not_(z):\n",
    "    \"\"\"\n",
    "    Negation\n",
    "    \"\"\"\n",
    "    return Zadeh(1 - z.value)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b94b9098",
   "metadata": {},
   "source": [
    "Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a0b864e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = Zadeh(0.37)\n",
    "b = Zadeh(0.23)\n",
    "c = Zadeh(0.81)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ea34fdfc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Zadeh(0.18999999999999995)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a or b) and not_(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb89a26a",
   "metadata": {},
   "source": [
    "## Membership function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b3865c87",
   "metadata": {},
   "outputs": [],
   "source": [
    "class MembershipFunction:\n",
    "\n",
    "    def __init__(self, table, value=None):\n",
    "        self._table = table\n",
    "        self.value = value\n",
    "\n",
    "    def __eq__(self, other):\n",
    "        if other not in self._table:\n",
    "            raise ValueError(f'Undefined language variable! \"{other}\"')\n",
    "        full_table = self._table | {'-inf': -math.inf, '+inf': math.inf}\n",
    "        intervals = sorted(list(full_table.items()), key=lambda item: item[1])\n",
    "        index = None\n",
    "        i = 1\n",
    "        while index is None:\n",
    "            if intervals[i][0] == other:\n",
    "                index = i\n",
    "            i += 1\n",
    "        m = 0\n",
    "        if index == 1 and self.value <= intervals[1][1]:\n",
    "            m = 1\n",
    "        elif index == len(intervals) - 2 and self.value >= intervals[index][1]:\n",
    "            m = 1\n",
    "        elif intervals[index - 1][1] <= self.value < intervals[index][1]:\n",
    "            m = (intervals[index][1] - self.value) / (intervals[index][1] - intervals[index - 1][1])\n",
    "        elif intervals[index][1] <= self.value < intervals[index + 1][1]:\n",
    "            m = (self.value - intervals[index][1]) / (intervals[index + 1][1] - intervals[index][1])\n",
    "        return Zadeh(m)\n",
    "\n",
    "    @property\n",
    "    def value(self):\n",
    "        return self._value\n",
    "\n",
    "    @value.setter\n",
    "    def value(self, value):\n",
    "        self._value = value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77f5f599",
   "metadata": {},
   "source": [
    "Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "576260bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "battery = MembershipFunction({\n",
    "    'empty': 0,\n",
    "    'full': 100\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bd39e9dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "distance = MembershipFunction({\n",
    "    'close': 0,\n",
    "    'near': 5,\n",
    "    'far': 20\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f53baf2d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.45\n"
     ]
    }
   ],
   "source": [
    "battery.value = 45\n",
    "distance.value = 12\n",
    "speed = (battery == 'empty') or (distance == 'close')\n",
    "print(speed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "22e27f0b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4\n"
     ]
    }
   ],
   "source": [
    "battery.value = 70\n",
    "distance.value = 3\n",
    "speed = (battery == 'full') and not_(distance == 'close')\n",
    "print(speed)"
   ]
  }
 ],
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