algebraNA: Modify algebra's way of computing with 'NA' values. In lfl: Linguistic Fuzzy Logic

Description

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.

Usage

 1 2 3 4 5 6 7 8 9 sobocinski(algebra) kleene(algebra) dragonfly(algebra) nelson(algebra) lowerEst(algebra)

Arguments

 algebra the underlying algebra object to be modified – see the algebra() function

Details

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 behavior 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

Value

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

Michal Burda

Examples

 1 2 3 4 5 a <- algebra('lukas') b <- sobocinski(a) a\$t(0.3, NA) # NA b\$t(0.3, NA) # 0.3

lfl documentation built on Aug. 23, 2021, 5:09 p.m.