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-rw-r--r--stdlib/source/lux/math/logic/fuzzy.lux150
1 files changed, 150 insertions, 0 deletions
diff --git a/stdlib/source/lux/math/logic/fuzzy.lux b/stdlib/source/lux/math/logic/fuzzy.lux
new file mode 100644
index 000000000..12d8b9dc3
--- /dev/null
+++ b/stdlib/source/lux/math/logic/fuzzy.lux
@@ -0,0 +1,150 @@
+(;module:
+ lux
+ (lux (data [number "Deg/" Interval<Deg>]
+ (coll [list]
+ [set])
+ text/format)
+ [math])
+ (.. ["&" continuous]))
+
+(type: #export (Fuzzy a)
+ (-> a Deg))
+
+(def: #export (membership elem set)
+ (All [a] (-> a (Fuzzy a) Deg))
+ (set elem))
+
+(def: #export (union left right)
+ (All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
+ (lambda [elem]
+ (&;~or (membership elem left)
+ (membership elem right))))
+
+(def: #export (intersection left right)
+ (All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
+ (lambda [elem]
+ (&;~and (membership elem left)
+ (membership elem right))))
+
+(def: #export (complement set)
+ (All [a] (-> (Fuzzy a) (Fuzzy a)))
+ (lambda [elem]
+ (&;~not (membership elem set))))
+
+(def: #export (difference sub base)
+ (All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
+ (lambda [elem]
+ (&;~and (membership elem base)
+ (&;~not (membership elem sub)))))
+
+(def: #export (from-predicate predicate)
+ (All [a] (-> (-> a Bool) (Fuzzy a)))
+ (lambda [elem]
+ (if (predicate elem)
+ &;~true
+ &;~false)))
+
+(def: #export (from-set set)
+ (All [a] (-> (set;Set a) (Fuzzy a)))
+ (from-predicate (set;member? set)))
+
+(do-template [<ascending> <descending> <gradient> <type> <lt> <gt> <lte> <gte> <sub> <div> <post>]
+ [(def: (<ascending> from to)
+ (-> <type> <type> (Fuzzy <type>))
+ (lambda [elem]
+ (cond (<lte> from elem)
+ &;~false
+
+ (<gte> to elem)
+ &;~true
+
+ ## in the middle...
+ (<post> (<div> (<sub> from to)
+ (<sub> from elem))))))
+
+ (def: (<descending> from to)
+ (-> <type> <type> (Fuzzy <type>))
+ (lambda [elem]
+ (cond (<lte> from elem)
+ &;~true
+
+ (<gte> to elem)
+ &;~false
+
+ ## in the middle...
+ (<post> (<div> (<sub> from to)
+ (<sub> elem to))))))
+
+ (def: #export (<gradient> from to)
+ (-> <type> <type> (Fuzzy <type>))
+ (if (<lt> to from)
+ (<ascending> from to)
+ (<descending> from to)))]
+
+ [d.ascending d.descending d.gradient Deg d.< d.> d.<= d.>= d.- d./ id]
+ [r.ascending r.descending r.gradient Real r.< r.> r.<= r.>= r.- r./ real-to-deg]
+ )
+
+(do-template [<triangle> <trapezoid> <type> <ascending> <descending> <lt>]
+ [(def: #export (<triangle> bottom middle top)
+ (-> <type> <type> <type> (Fuzzy <type>))
+ (case (list;sort <lt> (list bottom middle top))
+ (^ (list bottom middle top))
+ (intersection (<ascending> bottom middle)
+ (<descending> middle top))
+
+ _
+ (undefined)))
+
+ (def: #export (<trapezoid> bottom middle-bottom middle-top top)
+ (-> <type> <type> <type> <type> (Fuzzy <type>))
+ (case (list;sort <lt> (list bottom middle-bottom middle-top top))
+ (^ (list bottom middle-bottom middle-top top))
+ (intersection (<ascending> bottom middle-bottom)
+ (<descending> middle-top top))
+
+ _
+ (undefined)))]
+
+ [d.triangle d.trapezoid Deg d.ascending d.descending d.<]
+ [r.triangle r.trapezoid Real r.ascending r.descending r.<]
+ )
+
+(def: #export (gaussian deviation center)
+ (-> Real Real (Fuzzy Real))
+ (lambda [elem]
+ (let [scale (|> deviation math;square (r.* 2.0))
+ membership (|> elem
+ (r.- center)
+ math;square
+ (r.* -1.0)
+ (r./ scale)
+ math;exp)]
+ (if (r.= 1.0 membership)
+ &;~true
+ (real-to-deg membership)))))
+
+(def: #export (cut treshold set)
+ (All [a] (-> Deg (Fuzzy a) (Fuzzy a)))
+ (lambda [elem]
+ (let [membership (set elem)]
+ (if (d.> treshold membership)
+ (|> membership (d.- treshold) (d.* &;~true))
+ &;~false))))
+
+(def: #export (to-predicate treshold set)
+ (All [a] (-> Deg (Fuzzy a) (-> a Bool)))
+ (lambda [elem]
+ (d.> treshold (set elem))))
+
+(type: #export (Fuzzy2 a)
+ (-> a [Deg Deg]))
+
+(def: #export (type-2 lower upper)
+ (All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy2 a)))
+ (lambda [elem]
+ (let [l-deg (lower elem)
+ u-deg (upper elem)]
+ [(d.min l-deg
+ u-deg)
+ u-deg])))