simple_disjoint_sum

Author: amogorkon

Showcase.ipynb

@@ -134,18 +134,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 29,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "<function all>"
+       "False"
       ]
      },
-     "execution_count": 28,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }

fuzzy/classes.py

@@ -6,7 +6,7 @@
 import pickle
 
 from fuzzy.functions import inv, normalize
-from fuzzy.combinators import MAX, MIN, product, bounded_sum
+from fuzzy.combinators import MAX, MIN, product, bounded_sum, simple_disjoint_sum
 
 class FuzzyWarning(UserWarning):
     pass
@@ -174,6 +174,9 @@ def __mul__(self, other):
 
     def __add__(self, other):
         return Set(bounded_sum(self.func, other.func))
+    
+    def __xor__(self, other):
+        return Set(simple_disjoint_sum(self.func, other.func))
 
     def __pow__(self, power):
         """pow is used with hedges"""
@@ -218,9 +221,18 @@ def __gt__(self, other):
 
     def __len__(self):
         if self.domain is None:
-            raise FuzzyWarning("No domain, can't determine length.")
+            raise FuzzyWarning("No domain.")
         return len(self.array())
-        
+    
+    def cardinality(self):
+        if self.domain is None:
+            raise FuzzyWarning("No domain.")
+        return sum(self.array())
+
+    def relative_cardinality(self):
+        if self.domain is None:
+            raise FuzzyWarning("No domain.")
+        return self.cardinality() / len(self)
 
     def plot(self, low=None, high=None, res=None):
         """Graph the set.

fuzzy/combinators.py

@@ -120,4 +120,13 @@ def f(z):
             x, y = a(z), b(z)
             return (x * y) ** (1 - g) * ((1 - x) * (1 - y)) ** g
         return f
-    return e
+    return e
+
+def simple_disjoint_sum(a, b):
+    """Implements a simple fuzzy XOR operation.
+    (A AND ~B) OR (~A AND B)
+    """
+    def f(z):
+        x, y = a(z), b(z)
+        return max(min(x, 1-y), min(1-x, y))
+    return f

test_fuzzy_units.py

@@ -278,6 +278,12 @@ def test_gamma_op(self, x, g):
         f = g(a, b)
         assert (0 <= f(x) <= 1)
 
+    @given(st.floats(min_value=0, max_value=1))
+    def test_hamacher_sum(self, x):
+        a = fun.noop()
+        b = fun.noop()
+        f = combi.simple_disjoint_sum(a, b)
+        assert (0 <= f(x) <= 1)
 
 class Test_Set(TestCase):
     @skip("repr is complicated")