Fuzzy

Fuzzy type This type implements subset of fuzzy intervals described by convex membership function \(\mu\) with values changing from 0 to 1. Accepts array of intervals comprising \(\alpha\)-cuts, starting from Bottom level up to the Top.

Constructors

Constructor	Description
`new(a)` Signature:a:seq<Interval> -> Fuzzy

Instance members

Instance member	Description
`alphaCuts` Signature:Interval []	Exposes raw list of \(\alpha\)-cuts
`Bottom` Signature:Interval	\(\alpha\)-cut with \(\mu\) = 0
`Top` Signature:Interval	\(\alpha\)-cut with \(\mu\) = 1

Static members

Static member	Description
`( - )(x, y)` Signature:(x:decimal * y:Fuzzy) -> Fuzzy	Subtract `y` from `x`, uses `map`
`( - )(x, y)` Signature:(x:Fuzzy * y:decimal) -> Fuzzy	Subtract `y` from `x`, uses `map`
`( - )(x, y)` Signature:(x:Fuzzy * y:Fuzzy) -> Fuzzy	Subtract `y` from `x`, uses `operation`
`( * )(x, y)` Signature:(x:decimal * y:Fuzzy) -> Fuzzy	Multiply `x` by `y`, uses `map`
`( * )(x, y)` Signature:(x:Fuzzy * y:decimal) -> Fuzzy	Multiply `x` by `y`, uses `map`
`( * )(x, y)` Signature:(x:Fuzzy * y:Fuzzy) -> Fuzzy	Multiply `x` by `y`, uses `operation`
`( / )(x, y)` Signature:(x:decimal * y:Fuzzy) -> Fuzzy	Divide `x` by `y`, uses `map`
`( / )(x, y)` Signature:(x:Fuzzy * y:decimal) -> Fuzzy	Divide `x` by `y`, uses `map`
`( / )(x, y)` Signature:(x:Fuzzy * y:Fuzzy) -> Fuzzy	Divide `x` by `y`, uses `operation`
`( + )(x, y)` Signature:(x:decimal * y:Fuzzy) -> Fuzzy	Add `x` to `y`, uses `map`
`( + )(x, y)` Signature:(x:Fuzzy * y:decimal) -> Fuzzy	Add `x` to `y`, uses `map`
`( + )(x, y)` Signature:(x:Fuzzy * y:Fuzzy) -> Fuzzy	Add `x` to `y`, uses `operation`
`map(f a)` Signature:(f:(Interval -> Interval)) -> a:Fuzzy -> Fuzzy	Generic unary operation overa set implemented as an application of `f` on each \(\alpha\)-cut
`operation(f a b)` Signature:(f:(Interval -> Interval -> Interval)) -> a:Fuzzy -> b:Fuzzy -> Fuzzy	Generic binary operation over two fuzzy sets implemented as a sum of operations over each \(\alpha\)-cut
`pow(x, p)` Signature:(x:Fuzzy * p:double) -> Fuzzy	Rises `x` to the power of `p`, uses `map`
`Zero` Signature:Fuzzy	Fuzzy set comprized from 11 zero \(\alpha\)-cuts

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