# operators: And (conjunction) operators In softclassval: Soft Classification Performance Measures

## Description

And operators for the soft performance calculation. The predefined operators are:

 Name Definition `dev`? `postproc`? `hard`? Explanation `gdl` `pmin (r, p)` FALSE FALSE the Gödel-operator (weak conjunction) `luk` `pmax (r + p - 1, 0)` FALSE FALSE Łukasiewicz-operator (strong conjunction) `prd` `r * p` FALSE FALSE product operator `and` `r * p` FALSE TRUE Boolean conjunction: accepts only 0 or 1, otherwise yields `NA` `wMAE` `r * abs (r - p)` TRUE FALSE for weighted mean absolute error `wRMAE` `r * abs (r - p)` TRUE sqrt FALSE for weighted root mean absolute error (bound for RMSE) ##' `wMSE` `r * (r - p)^2` TRUE FALSE for weighted mean squared error `wRMSE` `r * (r - p)^2` TRUE sqrt FALSE for root weighted mean squared error

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```strong(r, p) luk(r, p) weak(r, p) gdl(r, p) prd(r, p) and(r, p) wMAE(r, p) wRMAE(r, p) wMSE(r, p) wRMSE(r, p) ```

## Arguments

 `r` reference vector, matrix, or array with numeric values in [0, 1], for `and` in {0, 1} `p` prediction vector, matrix, or array with numeric values in [0, 1], for `and` in {0, 1}

## Value

numeric of the same size as p

Claudia Beleites

## References

see the literature in `citation ("softclassval")`

Performance measures: `sens`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44``` ```ops <- c ("luk", "gdl", "prd", "and", "wMAE", "wRMAE", "wMSE", "wRMSE") ## make a nice table lastline <- function (f){ body <- body (get (f)) ## function body body <- deparse (body) body [length (body) - 1] ## last line is closing brace } data.frame (source = sapply (ops, lastline), dev = sapply (ops, function (f) dev (get (f))), hard = sapply (ops, function (f) hard (get (f))), postproc = I (lapply (ops, function (f) postproc (get (f)))) ) x <- softclassval:::v x luk (0.7, 0.8) ## The behaviour of the operators ## op (x, 1) cbind (x, sapply (c ("luk", "gdl", "prd", "wMAE", "wRMAE", "wMSE", "wRMSE"), function (op, x) get (op) (x, 1), x)) ## op (x, 0) cbind (x, sapply (c ("luk", "gdl", "prd", "wMAE", "wRMAE", "wMSE", "wRMSE"), function (op, x) get (op) (x, 0), x)) ## op (x, x) cbind (x, sapply (c ("luk", "gdl", "prd", "wMAE", "wRMAE", "wMSE", "wRMSE"), function (op, x) get (op) (x, x), x)) ## Note that the deviation operators are not commutative ## (due to the weighting by reference) zapsmall ( cbind (sapply (c ("luk", "gdl", "prd", "wMAE", "wRMAE", "wMSE", "wRMSE"), function (op, x) get (op) (1, x), x)) - cbind (sapply (c ("luk", "gdl", "prd", "wMAE", "wRMAE", "wMSE", "wRMSE"), function (op, x) get (op) (x, 1), x)) ) ```