Defuzzify

CHANGELOG.md

@@ -6,3 +6,7 @@
 
 ## 1.0.1 -- 2025-05-01
 * Changed constrains for dependencies in .cabal file to allow for more flexibility in package versions.
+
+## 1.0.2 -- 2025-03-28
+* Added deffuzzification function to the library, allowing users to convert fuzzy sets (Lset Double l) back into numbers. 
+* This update is prepared for the next major release, which will include fuzzy control systems, if than rules and more.

fuzzySets.cabal

@@ -1,6 +1,6 @@
 cabal-version:      2.4
 name:               fuzzySets
-version:            1.0.1
+version:            1.0.2
 category:           Math
 license:            BSD-3-Clause
 author:             Lukas Balog <lukasbalog66@gmail.com>
@@ -17,7 +17,7 @@ description:
 
     This package provide functions for working with fuzzy sets and fuzzy relations.
 
-extra-source-files: CHANGELOG.md
+extra-doc-files: CHANGELOG.md
 
 source-repository head
     type:           git
@@ -33,6 +33,7 @@ library
         Fuzzy.Sets.MembershipFunctions
         Fuzzy.Sets.Cardinality
         Fuzzy.Sets.Properties
+        Fuzzy.Control.Defuzzification
         Fuzzy.Relations.LRelation
         Fuzzy.Relations.MembershipFunctions
         Fuzzy.Relations.RelationComposition
@@ -77,3 +78,4 @@ test-suite test
         Fuzzy.Sets.PropertiesTest
         Fuzzy.Relations.LRelationTest
         Fuzzy.Relations.PropertiesTest
+        Fuzzy.Control.DefuzzificationTest

src/Fuzzy/Control/Defuzzification.hs

@@ -0,0 +1,55 @@
+module Fuzzy.Control.Defuzzification where
+
+import Fuzzy.Sets.LSet (LSet, toList)
+import Fuzzy.Sets.Cardinality
+import Lattices.ResiduatedLattice (ResiduatedLattice)
+import FuzzySet
+import Data.List (maximumBy)
+import Data.Ord (comparing)
+
+-- | Defuzzify a fuzzy set using the center of gravity (centroid) method.
+-- 
+-- Returns 0 for an empty universe.
+centerOfGravity ::  ResiduatedLattice l => LSet Double l -> Double
+centerOfGravity  = centerOfGravityMod id
+
+-- | Defuzzify with a membership modifier function 'c'.
+--
+-- The modifier is applied to each membership value before computing the weighted mean.
+-- Returns 0 when the modified sigma count is 0.
+centerOfGravityMod :: ResiduatedLattice l => (l -> l) -> LSet Double l -> Double
+centerOfGravityMod c set = if card == 0 then 0 else numer / card
+    where 
+        pairs = toList set
+        card = sigmaCountMod c set
+        numer = sum [x * realToFrac mem | (x, mem) <- pairs]
+
+-- | Defuzzify by taking the midpoint of the maximum interval.
+--
+-- For a non-empty set returns (max + min) / 2 based on the universe support.
+centerOfMaxima :: ResiduatedLattice l => LSet Double l -> Double
+centerOfMaxima set = (sup + inf) / 2 
+    where 
+        sup = maximum $ universe set
+        inf = minimum $ universe set
+
+-- | Mean of maxima with a modifier function.
+--
+-- Uses 'sigmaCountMod' for total modified membership and normalizes by universe size.
+-- Returns 0 for empty universes.
+meanOfMaximaMod :: ResiduatedLattice l => (l -> l) -> LSet Double l -> Double
+meanOfMaximaMod c set = if sizeUniverse == 0 then 0 else card / sizeUniverse
+    where 
+        card = sigmaCountMod c set
+        sizeUniverse = fromIntegral $ universeCardinality set
+
+-- | Return the universe element with maximal membership degree.
+--
+-- If multiple elements have the same maximal degree, the first encountered is returned.
+-- For an empty set, returns 0.
+maxMembership :: ResiduatedLattice l => LSet Double l -> Double
+maxMembership set
+    | null pairs = 0
+    | otherwise  = fst $ maximumBy (comparing snd) pairs
+    where
+        pairs = toList set

src/Fuzzy/Sets/Cardinality.hs

@@ -2,7 +2,7 @@ module Fuzzy.Sets.Cardinality(
     sigmaCount,
     thresholdSigmaCount,
     normalizedSigmaCount,
-    sigmaCountWithModifier,
+    sigmaCountMod,
     -- * Modifier functions
     modifierFunction,
     sigmoidModifier,
@@ -41,11 +41,11 @@ For a fuzzy set A, |A| = Σ c(A(u)) for all u ∈ U
 
 >>> let set = fromPairs [(1, 0.2), (2, 0.7), (3, 0.5)] :: LSet Int UILukasiewicz
 >>> let modifier = sigmoidModifier 2.0 0.5
->>> sigmaCountWithModifier modifier set
+>>> sigmaCountMod modifier set
 1.4
 -}
-sigmaCountWithModifier :: (FuzzySet set a l) => (l -> l) -> set -> Double
-sigmaCountWithModifier c set = sum [realToFrac $ (c . f) x | x <- universe set]
+sigmaCountMod :: (FuzzySet set a l) => (l -> l) -> set -> Double
+sigmaCountMod c set = sum [realToFrac $ (c . f) x | x <- universe set]
     where f = member set
 
 

test/Fuzzy/Control/DefuzzificationTest.hs

@@ -0,0 +1,38 @@
+module Fuzzy.Control.DefuzzificationTest (
+    defuzzificationTests
+) where
+
+import Test.Tasty
+import Test.Tasty.HUnit
+import Fuzzy.Control.Defuzzification
+import Fuzzy.Sets.LSet
+import Fuzzy.Sets.Cardinality
+import Lattices.UnitIntervalStructures.Godel
+
+-- Test data
+sampleSet :: LSet Double UIGodel
+sampleSet = fromList [(1, 0.2), (2, 0.8)]
+
+emptySet :: LSet Double UIGodel
+emptySet = mkEmptySet
+
+-- Test group
+defuzzificationTests :: TestTree
+defuzzificationTests = testGroup "Defuzzification Tests" [
+    testCase "centerOfGravity on non-empty set" $
+        assertEqual "centroid correct" 1.8 (centerOfGravity sampleSet),
+    testCase "centerOfGravity on empty set" $
+        assertEqual "empty set yields 0" 0.0 (centerOfGravity emptySet),
+    testCase "centerOfGravityMod with alpha-cut" $
+        assertEqual "modifier influences denominator only" 1.8 (centerOfGravityMod (alphaCutModifier 0.5) sampleSet),
+    testCase "centerOfMaxima uses universe bounds" $
+        assertEqual "midpoint between min and max" 1.5 (centerOfMaxima sampleSet),
+    testCase "meanOfMaximaMod with identity modifier" $
+        assertEqual "normalized sigma count" 0.5 (meanOfMaximaMod (\x -> x) sampleSet),
+    testCase "meanOfMaximaMod with alpha-cut modifier" $
+        assertEqual "alpha-cut count over universe size" 0.5 (meanOfMaximaMod (alphaCutModifier 0.5) sampleSet),
+    testCase "maxMembership on non-empty set" $
+        assertEqual "highest membership element" 2.0 (maxMembership sampleSet),
+    testCase "maxMembership on empty set" $
+        assertEqual "empty set returns 0" 0.0 (maxMembership emptySet)
+    ]

test/Tests.hs

@@ -10,6 +10,7 @@ import Fuzzy.Sets.PropertiesTest
 import Fuzzy.Sets.MembershipFunctionsTest
 import Fuzzy.Relations.LRelationTest
 import Fuzzy.Relations.PropertiesTest
+import Fuzzy.Control.DefuzzificationTest
 
 -- Run all tests
 main :: IO ()
@@ -21,5 +22,6 @@ main = defaultMain $ testGroup "All Tests" [
     membershipFunctionsTests,
     propertiesTests,
     lrelationTests,
-    relPropertiesTests
+    relPropertiesTests,
+    defuzzificationTests
     ]