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(.module:
[lux #*
[abstract
[predicate (#+ Predicate)]]
[data
[collection
["." list]
["." set (#+ Set)]]]
[math
[number
["r" rev]]]]
[//
["&" continuous]])
(type: #export (Fuzzy a)
(-> a Rev))
(def: #export (membership elem set)
(All [a] (-> a (Fuzzy a) Rev))
(set elem))
(def: #export (union left right)
(All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
(function (_ elem)
(&.or (membership elem left)
(membership elem right))))
(def: #export (intersection left right)
(All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
(function (_ elem)
(&.and (membership elem left)
(membership elem right))))
(def: #export (complement set)
(All [a] (-> (Fuzzy a) (Fuzzy a)))
(function (_ elem)
(&.not (membership elem set))))
(def: #export (difference sub base)
(All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
(function (_ elem)
(&.and (membership elem base)
(&.not (membership elem sub)))))
(def: #export (from_predicate predicate)
(All [a] (-> (Predicate a) (Fuzzy a)))
(function (_ elem)
(if (predicate elem)
&.true
&.false)))
(def: #export (from_set set)
(All [a] (-> (Set a) (Fuzzy a)))
(from_predicate (set.member? set)))
(def: (ascending from to)
(-> Rev Rev (Fuzzy Rev))
(function (_ elem)
(cond (r.<= from elem)
&.false
(r.>= to elem)
&.true
## in the middle...
(r./ (r.- from to)
(r.- from elem)))))
(def: (descending from to)
(-> Rev Rev (Fuzzy Rev))
(function (_ elem)
(cond (r.<= from elem)
&.true
(r.>= to elem)
&.false
## in the middle...
(r./ (r.- from to)
(r.- elem to)))))
(def: #export (gradient from to)
(-> Rev Rev (Fuzzy Rev))
(if (r.< to from)
(ascending from to)
(descending from to)))
(def: #export (triangle bottom middle top)
(-> Rev Rev Rev (Fuzzy Rev))
(case (list.sort r.< (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)
(-> Rev Rev Rev Rev (Fuzzy Rev))
(case (list.sort r.< (list bottom middle_bottom middle_top top))
(^ (list bottom middle_bottom middle_top top))
(intersection (ascending bottom middle_bottom)
(descending middle_top top))
_
(undefined)))
(def: #export (cut treshold set)
(All [a] (-> Rev (Fuzzy a) (Fuzzy a)))
(function (_ elem)
(let [membership (set elem)]
(if (r.> treshold membership)
(|> membership (r.- treshold) (r.* &.true))
&.false))))
(def: #export (to_predicate treshold set)
(All [a] (-> Rev (Fuzzy a) (Predicate a)))
(function (_ elem)
(r.> treshold (set elem))))
(type: #export (Fuzzy2 a)
(-> a [Rev Rev]))
(def: #export (type_2 lower upper)
(All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy2 a)))
(function (_ elem)
(let [l_rev (lower elem)
u_rev (upper elem)]
[(r.min l_rev
u_rev)
u_rev])))
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