Fuzzy Python.ipynb

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      "#What is Fuzzy Logic?\n",
      "Everything is true to Degrees.\n",
      "\n",
      "The chief but superficial similarity is that both describe uncertainty with the numbers in the unit interval $[0,1]$\n",
      "\n",
      "##What is Logic?\n",
      "1. Is it always true that $A \\cap A^{c} = \\emptyset$\n",
      "\n",
      "Why does that even matter?\n",
      "\n",
      "Because everything in the world that isn't classical mathematics is Fuzzy. Fuzzy veganism, fuzzy politics. \n",
      "\n",
      "##Paradox\n",
      "Remember the yoga teacher paradox:\n",
      "In a village there is ONE yoga teacher rules are:\n",
      "\n",
      "1. (Everyone who does not teach themselves yoga) [Group A], is (taught by the yoga teacher) [Group B].\n",
      "2. (Everyone who is taught by the Yoga teacher) [Group B] does (not teach themselves) [Group A].\n",
      "\n",
      "Question: Who teaches the Yoga Teacher? \n",
      "or __Does the Yoga Teacher Teach Themselves?__\n",
      "\n",
      "Let's assume True -> False\n",
      "\n",
      "Lets assume False -> True\n",
      "\n",
      "## Paradox is the maximally Fuzzy value\n",
      "\n",
      "$ T \\rightarrow F$\n",
      "and $F \\rightarrow T$\n",
      "\n",
      "So. $T = F$\n",
      "\n",
      "And classical logic says $F = 1 - T$\n",
      "\n",
      "Thus $T = 1 - T$\n",
      "\n",
      "or $2T = 1$\n",
      "\n",
      "Finally $T = \\frac{1}{2}$\n",
      "\n",
      "The __truthiness is one-half__.\n",
      "\n",
      "##Fuzzy Rice Cooker\n",
      "```\n",
      "IF temperature IS very cold THEN stop fan\n",
      "IF temperature IS cold THEN turn down fan\n",
      "IF temperature IS normal THEN maintain fan\n",
      "IF temperature IS hot THEN speed up fan\n",
      "```\n",
      "##What is operator overloading?\n",
      "\n",
      "How to add a hobbit an apple. \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "True & False"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 66,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "True | False"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 67,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "not True"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 68,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "int(True), int(False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "if '':\n",
      "    print \"'' is False\"\n",
      "\n",
      "if ' ':\n",
      "    print \"' ' is True\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "'a' & 'b'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class fuzzy:\n",
      "    value = 0\n",
      "    \n",
      "    def __init__(self, value):\n",
      "        if (value >= 0) and (value <= 1):\n",
      "            self.value = value\n",
      "        else:\n",
      "            raise ValueError('{} not in range [0,1]'.format(value))\n",
      "            \n",
      "    def __and__(self, other):\n",
      "        if isinstance(other, fuzzy):\n",
      "            return min(self.value, other.value)\n",
      "        if isinstance(other, float):\n",
      "            return min(self.value, other)\n",
      "    \n",
      "    def __or__(self, other):\n",
      "        return max(self.value, other.value)\n",
      "    \n",
      "    def __neg__(self):\n",
      "        return 1-self.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 91
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pretty_warm = fuzzy(0.1)\n",
      "ice_cold = fuzzy(0.8)\n",
      "absolute_zero = fuzzy(1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 92
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pretty_warm | ice_cold"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 79,
       "text": [
        "0.8"
       ]
      }
     ],
     "prompt_number": 79
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "absolute_zero & ice_cold"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 80,
       "text": [
        "0.8"
       ]
      }
     ],
     "prompt_number": 80
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "-pretty_warm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 81,
       "text": [
        "0.9"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "temp = 0.2 and pretty_warm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 95
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "isinstance(temp, fuzzy)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 99,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 99
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "isinstance(pretty_warm, fuzzy)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class FuzzyObj:\n",
      "    \n",
      "    def __init__(self, value):\n",
      "        self.value = value\n",
      "    \n",
      "    def fuzzy_and(self, fo):\n",
      "        return min(self.value, fo.value)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = FuzzyObj(1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 74
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b = FuzzyObj(0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 75
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a.fuzzy_and(b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 76,
       "text": [
        "0.5"
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a & b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "TypeError",
       "evalue": "unsupported operand type(s) for &: 'instance' and 'instance'",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-77-ed983a5ba089>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0ma\u001b[0m \u001b[1;33m&\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;31mTypeError\u001b[0m: unsupported operand type(s) for &: 'instance' and 'instance'"
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "code",
     "collapsed": false,
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     "language": "python",
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