Description Usage Arguments Details Value Author(s) Examples

By default, the objects created with the `algebra()`

function represent a mathematical
algebra capable to work on the *[0,1]* interval. If `NA`

appears as a value instead,
it is propagated to the result. That is, any operation with `NA`

results in `NA`

, by default.
This scheme of handling missing values is also known as Bochvar's. To change this default
behavior, the following functions may be applied.

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`algebra` |
the underlying algebra object to be modified – see the |

The `sobocinski()`

, `kleene()`

, `nelson()`

, `lowerEst()`

and `dragonfly()`

functions modify the algebra to
handle the `NA`

in a different way than is the default. Sobocinski's algebra simply ignores `NA`

values
whereas Kleene's algebra treats `NA`

as "unknown value". Dragonfly approach is a combination
of Sobocinski's and Bochvar's approach, which preserves the ordering `0 <= NA <= 1`

to obtain from compositions (see `compose()`

)
the lower-estimate in the presence of missing values.

In detail, the behaviour of the algebra modifiers is defined as follows:

Sobocinski's negation for `n`

being the underlying algebra:

a | n(a) |

NA | 0 |

Sobocinski's operation for `op`

being one of `t`

, `pt`

, `c`

, `pc`

, `i`

, `pi`

, `s`

, `ps`

from the underlying algebra:

b | NA | |

a | op(a, b) | a |

NA | b | NA |

Sobocinski's operation for `r`

from the underlying algebra:

b | NA | |

a | r(a, b) | n(a) |

NA | b | NA |

Kleene's negation is identical to `n`

from the underlying algebra.

Kleene's operation for `op`

being one of `t`

, `pt`

, `i`

, `pi`

from the underlying algebra:

b | NA | 0 | |

a | op(a, b) | NA | 0 |

NA | NA | NA | 0 |

0 | 0 | 0 | 0 |

Kleene's operation for `op`

being one of `c`

, `pc`

, `s`

, `ps`

from the underlying algebra:

b | NA | 1 | |

a | op(a, b) | NA | 1 |

NA | NA | NA | 1 |

1 | 1 | 1 | 1 |

Kleene's operation for `r`

from the underlying algebra:

b | NA | 1 | |

a | r(a, b) | NA | 1 |

NA | NA | NA | 1 |

0 | 1 | 1 | 1 |

Dragonfly negation is identical to `n`

from the underlying algebra.

Dragonfly operation for `op`

being one of `t`

, `pt`

, `i`

, `pi`

from the underlying algebra:

b | NA | 0 | 1 | |

a | op(a, b) | NA | 0 | a |

NA | NA | NA | 0 | NA |

0 | 0 | 0 | 0 | 0 |

1 | b | NA | 0 | 1 |

Dragonfly operation for `op`

being one of `c`

, `pc`

, `s`

, `ps`

from the underlying algebra:

b | NA | 0 | 1 | |

a | op(a, b) | a | a | 1 |

NA | b | NA | NA | 1 |

0 | b | NA | 0 | 1 |

1 | 1 | 1 | 1 | 1 |

Dragonfly operation for `r`

from the underlying algebra:

b | NA | 0 | 1 | |

a | r(a, b) | NA | n(a) | 1 |

NA | b | 1 | NA | 1 |

0 | 1 | 1 | 1 | 1 |

1 | b | NA | 0 | 1 |

A list of function of the same structure as is the list returned from the `algebra()`

function

Michal Burda

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