Inclusion Rule

Checks if a family of sets fulfills the inclusion rule.

inclusion.rule(A)

Arguments

A	a list of vectors consisting of the stimulus aspects of an elimination-by-aspects model

Details

The inclusion rule is necessary and sufficient for a tree structure on the aspect sets:

Structure theorem. A family \(\{x' | x \in T\}\) of aspect sets is representable by a tree iff either \(x' \cap y' \supset x' \cap z'\) or \(x' \cap z' \supset x' \cap y'\) for all \(x, y, z\) in \(T\). (Tversky and Sattath, 1979, p. 546)

Value

Either TRUE if the inclusion rule holds for A, or FALSE otherwise.

References

Tversky, A., & Sattath, S. (1979). Preference trees. Psychological Review, 86, 542--573. doi: 10.1037/0033-295X.86.6.542

See also

eba, trineq, strans.

Examples

A <- list(c(1, 5), c(2, 5), c(3, 6), c(4, 6))  # tree
inclusion.rule(A)
#> [1] TRUE

B <- list(c(1, 5), c(2, 5, 6), c(3, 6), c(4, 6))  # lattice
inclusion.rule(B)
#> [1] FALSE