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... https://en.wikipedia.org/wiki/Fuzzy_logic
(.module:
[library
[lux "*"
[abstract
[predicate {"+" [Predicate]}]
[functor
["." contravariant]]]
[data
[collection
["." list]
["." set {"+" [Set]}]]]
[math
[number
["/" rev]]]]]
["." // "_"
["#" continuous]])
(type: .public (Fuzzy a)
(-> a Rev))
(implementation: .public functor
(contravariant.Functor Fuzzy)
(def: (each f fb)
(|>> f fb)))
(template [<name> <verdict>]
[(def: .public <name>
Fuzzy
(function (_ _)
<verdict>))]
[empty //.false]
[full //.true]
)
(def: .public (membership set elem)
(All (_ a) (-> (Fuzzy a) a Rev))
(set elem))
(template [<set_composition> <membership_composition>]
[(def: .public (<set_composition> left right)
(All (_ a) (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
(function (_ elem)
(<membership_composition> (left elem)
(right elem))))]
[union //.or]
[intersection //.and]
)
(def: .public (complement set)
(All (_ a) (-> (Fuzzy a) (Fuzzy a)))
(|>> set //.not))
(def: .public (difference sub base)
(All (_ a) (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
(..intersection (..complement sub) base))
(def: .public (of_predicate predicate)
(All (_ a) (-> (Predicate a) (Fuzzy a)))
(function (_ elem)
(if (predicate elem)
//.true
//.false)))
(def: .public (predicate treshold set)
(All (_ a) (-> Rev (Fuzzy a) (Predicate a)))
(function (_ elem)
(/.> treshold (set elem))))
(def: .public of_set
(All (_ a) (-> (Set a) (Fuzzy a)))
(|>> set.member? ..of_predicate))
(def: (ascending from to)
(-> Rev Rev (Fuzzy Rev))
(let [measure (/.- from to)]
(function (_ elem)
(cond (/.< from elem)
... below
//.false
(/.< to elem)
... in the middle...
(|> elem
(/.- from)
(/./ measure))
... above
//.true))))
(def: (descending from to)
(-> Rev Rev (Fuzzy Rev))
(..complement (..ascending from to)))
(def: .public (gradient from to)
(-> Rev Rev (Fuzzy Rev))
(if (/.< to from)
(..ascending from to)
(..descending from to)))
(template: (!sort_2 <low> <high>)
[(if (/.> <low> <high>)
[<low> <high>]
[<high> <low>])])
(def: .public (triangle bottom middle top)
(-> Rev Rev Rev (Fuzzy Rev))
(let [[low_0 high_0] (!sort_2 bottom middle)
[bottom' high_1] (!sort_2 low_0 top)
[middle' top'] (!sort_2 high_0 high_1)]
(..intersection (..ascending bottom' middle')
(..descending middle' top'))))
(def: .public (trapezoid bottom middle_bottom middle_top top)
(-> Rev Rev Rev Rev (Fuzzy Rev))
(let [[low_0 high_0] (!sort_2 bottom middle_bottom)
[low_1 high_1] (!sort_2 middle_top top)
[bottom' middle_0] (!sort_2 low_0 low_1)
[middle_1 top'] (!sort_2 high_0 high_1)
[middle_bottom' middle_top'] (!sort_2 middle_0 middle_1)]
(..intersection (..ascending bottom' middle_bottom')
(..descending middle_top' top'))))
(def: .public (cut treshold set)
(All (_ a) (-> Rev (Fuzzy a) (Fuzzy a)))
(function (_ elem)
(let [membership (set elem)]
(if (/.< treshold membership)
//.false
(|> membership (/.- treshold) (/.* //.true))))))
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