Fuzzy

This module contains bunch of factory methods for Fuzzy type

Functions and values

Function or value	Description
`alpha total level` Signature:total:int -> level:int -> decimal<1>	Converts number of the level in \(\alpha\)-cut array to the value of membership function \(\mu\)
`binary f a b` Signature:f:(Interval * Interval -> decimal) -> a:Fuzzy -> b:Fuzzy -> decimal	Binary function for defuzzification of the result of operation `f` applied to each pair of corresponding \(\alpha\)-cuts taken from `a` and `b` weighted by value of \(\mu\). For example, useful for calcualtion of the `distance` between two fuzzy sets: \({\Delta }_{\bar{A}-\bar{B}} = \frac{\sum_{\alpha}\alpha \Delta_{A_\alpha-B_\alpha}}{\sum_{\alpha}\alpha}\) Note that \(\sum_{\alpha}\alpha = \frac{n}{2}\) where \(n\) - number of \(\alpha\)-cuts Important! `a` and `b` should have same number of \(\alpha\)-cuts
`distance a b` Signature:a:Fuzzy -> b:Fuzzy -> decimal	Calculates distance between two fuzzy sets `a` and `b`
`interval (a, b, c, d)` Signature:(a:decimal * b:decimal * c:decimal * d:decimal) -> Fuzzy	Creates trapezoid with 11 \(\alpha\)-cuts which gives increment of 0.1 in \(\mu\) from one \(\alpha\)-cut to the next
`number (a, b, c)` Signature:(a:decimal * b:decimal * c:decimal) -> Fuzzy	Creates triangular fuzzy set with bottom \(\alpha\)-cut `{a,c}` and zero-length top \(\alpha\)-cut `b`
`plot a` Signature:a:Fuzzy -> (decimal * decimal<1>) []	Represents fuzzy set `a` for drawing a chart
`point a` Signature:a:decimal -> Fuzzy	Creates fuzzy representation of zero-length interval
`risk a` Signature:a:Fuzzy -> decimal	Calculates weighted risk of fuzzy set `a`, i.e. the ratio between its width and the middle on each \(\alpha\)-cut
`trapezoid levels (a, b, c, d)` Signature:levels:int -> (a:decimal * b:decimal * c:decimal * d:decimal) -> Fuzzy	Creates trapezoid fuzzy set with bottom \(\alpha\)-cut `{a,d}` and top \(\alpha\)-cut `{b,c}`
`unary f a` Signature:f:(Interval -> decimal) -> a:Fuzzy -> decimal	Unary function for defuzzification of the result of operation `f` applied to each \(\alpha\)-cut of `a` weighted by corresponding value of \(\mu\). \(W f = \frac{\sum_{\alpha}\alpha f}{\sum_{\alpha}\alpha}\) Note that \(\sum_{\alpha}\alpha = \frac{n}{2}\) where \(n\) - number of \(\alpha\)-cuts
`width a` Signature:a:Fuzzy -> decimal	Calculates weighted width of fuzzy set `a`

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