Safe Haskell | Safe-Inferred |
---|---|

Language | Haskell2010 |

# Documentation

Interval Type-2 Fuzzy sets. Defined entirely by the footprint of uncertainty, lmf and umf are the bounds of this area.

FSet (IT2Set a) | Enables use of support, hedge and |

Fuzzy (IT2Set a) | Interval Type-2 fuzzy sets allow us to work in type-1 concepts. Operators are defined through application to lower and upper membership functions. |

Defuzzifier (IT2Set Double) | |

FRule (IT2Set a) | |

type Value (IT2Set a) = a | |

type Support (IT2Set a) = [(a, a)] | |

type Returned (IT2Set a) = (Double, Double) | |

type Result (IT2Set Double) = (Double, Double) | |

type Antecedent (IT2Set a) = (Double, Double) |

Standard operations on fuzzy sets. Instantiated for each kind of fuzzy set. If you want to overload with a t-norm, instantiate against a newtype or instantiated set.

(?&&) :: a -> a -> a infixr 3 Source

Union over fuzzy values.

(?||) :: a -> a -> a infixr 2 Source

Intersection over fuzzy values.

Fuzzy complement.

Fuzzy Double | Standard definitions for operations as defined by Zadeh (1965) |

Fuzzy (MF a) | |

Fuzzy (T1Set a) | Fuzzy operators are supported on T1Sets. Applies operator to membership functions inside T1Set type. |

Fuzzy (IT2Set a) | Interval Type-2 fuzzy sets allow us to work in type-1 concepts. Operators are defined through application to lower and upper membership functions. |

Fuzzy (T2ZSet a) | Operations on zSlices fuzzy sets are simply defined as higher order funcitons over the list of zSlices. |

Fuzzy b => Fuzzy (a -> b) | Fuzzy operators for membership functions. |

(Fuzzy a, Fuzzy b) => Fuzzy (a, b) | Instance for tuple needed for interval type-2 fuzzy sets. |

Specifically for fuzzy sets, as opposed to fuzzy values.
Support is all elements of domain for which membership is non-zero.
Hedge is a modifier of fuzzy sets.
`is`

is for application of a value to a fuzzy set.

A single value of the domain.

A list of values from the domain for which membership is non-zero.

Degree of membership from applying a value to membership function.

contIT2 :: (Num a, Enum a) => a -> a -> a -> MF a -> MF a -> IT2Set a Source

Smart constructor for continuos interval type-2 membership functions. Watch that resolution!

discIT2 :: [a] -> MF a -> MF a -> IT2Set a Source

Smart constructor for discrete interval type-2 membership functions. Be wary of domain size.

unsafeMkIT2 :: [a] -> MF a -> MF a -> IT2Set a Source

Only use this if you trust your functions or have no other recourse.