From 06246a89bb33b58a6e03183f59a2fea88179a861 Mon Sep 17 00:00:00 2001 From: Eduardo Julian Date: Sat, 28 Jan 2017 22:22:30 -0400 Subject: - Added support for fuzzy logic. --- stdlib/test/test/lux/math/logic/fuzzy.lux | 175 ++++++++++++++++++++++++++++++ stdlib/test/tests.lux | 3 +- 2 files changed, 177 insertions(+), 1 deletion(-) create mode 100644 stdlib/test/test/lux/math/logic/fuzzy.lux (limited to 'stdlib/test') diff --git a/stdlib/test/test/lux/math/logic/fuzzy.lux b/stdlib/test/test/lux/math/logic/fuzzy.lux new file mode 100644 index 000000000..5b25ecf44 --- /dev/null +++ b/stdlib/test/test/lux/math/logic/fuzzy.lux @@ -0,0 +1,175 @@ +(;module: + lux + (lux [io] + (control monad) + (codata function) + (data (coll [list] + [set]) + [bool "B/" Eq] + [number] + text/format) + ["R" random] + pipe + (math/logic ["&" fuzzy] + continuous)) + lux/test) + +(do-template [ ] + [(test: (format "[" "] " "Triangles") + [x + y + z + sample + #let [[bottom middle top] (case (list;sort (list x y z)) + (^ (list bottom middle top)) + [bottom middle top] + + _ + (undefined)) + triangle ( x y z)]] + ($_ seq + (assert "The middle value will always have maximum membership." + (d.= ~true (&;membership middle triangle))) + + (assert "Boundary values will always have 0 membership." + (and (d.= ~false (&;membership bottom triangle)) + (d.= ~false (&;membership top triangle)))) + + (assert "Values within range, will have membership > 0." + (B/= (d.> ~false (&;membership sample triangle)) + (and ( bottom sample) + ( top sample)))) + + (assert "Values outside of range, will have membership = 0." + (B/= (d.= ~false (&;membership sample triangle)) + (or ( bottom sample) + ( top sample)))) + ))] + + ["Real" R;real &;r.triangle r.< r.<= r.> r.>=] + ["Deg" R;deg &;d.triangle d.< d.<= d.> d.>=] + ) + +(do-template [ ] + [(test: (format "[" "] " "Trapezoids") + [w + x + y + z + sample + #let [[bottom middle-bottom middle-top top] (case (list;sort (list w x y z)) + (^ (list bottom middle-bottom middle-top top)) + [bottom middle-bottom middle-top top] + + _ + (undefined)) + trapezoid ( w x y z)]] + ($_ seq + (assert "The middle values will always have maximum membership." + (and (d.= ~true (&;membership middle-bottom trapezoid)) + (d.= ~true (&;membership middle-top trapezoid)))) + + (assert "Boundary values will always have 0 membership." + (and (d.= ~false (&;membership bottom trapezoid)) + (d.= ~false (&;membership top trapezoid)))) + + (assert "Values within inner range will have membership = 1" + (B/= (d.= ~true (&;membership sample trapezoid)) + (and ( middle-bottom sample) + ( middle-top sample)))) + + (assert "Values within range, will have membership > 0." + (B/= (d.> ~false (&;membership sample trapezoid)) + (and ( bottom sample) + ( top sample)))) + + (assert "Values outside of range, will have membership = 0." + (B/= (d.= ~false (&;membership sample trapezoid)) + (or ( bottom sample) + ( top sample)))) + ))] + + ["Real" R;real &;r.trapezoid r.< r.<= r.> r.>=] + ["Deg" R;deg &;d.trapezoid d.< d.<= d.> d.>=] + ) + +(test: "Gaussian" + #seed +1485654865687 + [deviation R;real + center R;real + #let [gaussian (&;gaussian deviation center)]] + ($_ seq + (assert "The center value will always have maximum membership." + (d.= ~true (&;membership center gaussian))) + )) + +(def: gen-triangle + (R;Random (&;Fuzzy Real)) + (do R;Monad + [x R;real + y R;real + z R;real] + (wrap (&;r.triangle x y z)))) + +(test: "Combinators" + [left gen-triangle + right gen-triangle + sample R;real] + ($_ seq + (assert "Union membership as as high as membership in any of its members." + (let [combined (&;union left right) + combined-membership (&;membership sample combined)] + (and (d.>= (&;membership sample left) + combined-membership) + (d.>= (&;membership sample right) + combined-membership)))) + + (assert "Intersection membership as as low as membership in any of its members." + (let [combined (&;intersection left right) + combined-membership (&;membership sample combined)] + (and (d.<= (&;membership sample left) + combined-membership) + (d.<= (&;membership sample right) + combined-membership)))) + + (assert "Complement membership is the opposite of normal membership." + (d.= (&;membership sample left) + (~not (&;membership sample (&;complement left))))) + + (assert "Membership in the difference will never be higher than in the set being subtracted." + (B/= (d.> (&;membership sample right) + (&;membership sample left)) + (d.< (&;membership sample left) + (&;membership sample (&;difference left right))))) + )) + +(test: "From predicates and sets" + [#let [set-10 (set;from-list number;Hash (list;n.range +0 +10))] + sample (|> R;nat (:: @ map (n.% +20)))] + ($_ seq + (assert "Values that satisfy a predicate have membership = 1. + Values that don't have membership = 0." + (B/= (d.= ~true (&;membership sample (&;from-predicate n.even?))) + (n.even? sample))) + + (assert "Values that belong to a set have membership = 1. + Values that don't have membership = 0." + (B/= (d.= ~true (&;membership sample (&;from-set set-10))) + (set;member? set-10 sample))) + )) + +(test: "Thresholds" + [fuzzy gen-triangle + sample R;real + threshold R;deg + #let [vip-fuzzy (&;cut threshold fuzzy) + member? (&;to-predicate threshold fuzzy)]] + ($_ seq + (assert "Can increase the threshold of membership of a fuzzy set." + (B/= (d.> ~false (&;membership sample vip-fuzzy)) + (d.> threshold (&;membership sample fuzzy)))) + + (assert "Can turn fuzzy sets into predicates through a threshold." + (B/= (member? sample) + (d.> threshold (&;membership sample fuzzy)))) + )) diff --git a/stdlib/test/tests.lux b/stdlib/test/tests.lux index 12601f75b..e3d0e15c3 100644 --- a/stdlib/test/tests.lux +++ b/stdlib/test/tests.lux @@ -53,7 +53,8 @@ ["_;" complex] ## ["_;" random] ["_;" simple] - (logic ["_;" continuous])) + (logic ["_;" continuous] + ["_;" fuzzy])) ## ["_;" macro] (macro ["_;" ast] ["_;" syntax] -- cgit v1.2.3