R/fuzzylogic-tnorm.R

In Rexamine/agop: Aggregation Operators and Preordered Sets

## This file is part of the 'agop' library.
##
## Copyleft (c) 2013-2023, Marek Gagolewski <https://www.gagolewski.com/>
##
##
## 'agop' is free software: you can redistribute it and/or modify it under
## the terms of the GNU Lesser General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## 'agop' is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU Lesser General Public License for more details.
##
## A copy of the GNU Lesser General Public License can be downloaded
## from <http://www.gnu.org/licenses/>.


#' @title
#' t-norms
#'
#' @description
#' Various t-norms.
#' Each of these is a fuzzy logic generalization
#' of the classical conjunction operation.
#'
#' @details
#' A function \eqn{T: [0,1]\times [0,1]\to [0,1]}
#' is a \emph{t-norm} if for all \eqn{x,y,z\in [0,1]} it holds:
#' (a) \eqn{T(x,y)=T(y,x)};
#' (b) if \eqn{y\le z}, then \eqn{T(x,y)\le T(x,z)};
#' (c) \eqn{T(x,T(y,z))=T(T(x,y),z)};
#' (d) \eqn{T(x, 1)=x}.
#'
#' The minimum t-norm is given by \eqn{T_M(x,y)=min(x, y)}.
#'
#' The product t-norm is given by \eqn{T_P(x,y)=xy}.
#'
#' The Lukasiewicz t-norm is given by \eqn{T_L(x,y)=max(x+y-1,0)}.
#'
#' The drastic t-norm is given by \eqn{T_D(x,y)=0} iff
#' \eqn{x,y\in [0,1)}, and \eqn{min(x, y)} otherwise.
#'
#' The Fodor t-norm is given by \eqn{T_F(x,y)=0}
#' iff \eqn{x+y \le 1}, and \eqn{min(x, y)} otherwise.
#'
#'
#' @param x numeric vector with elements in \eqn{[0,1]}
#' @param y numeric vector of the same length as \code{x},
#' with elements in \eqn{[0,1]}
#' @return
#' Numeric vector of the same length as \code{x} and \code{y}.
#' The \code{i}th element of the resulting vector gives the result
#' of calculating \code{T(x[i], y[i])}.
#'
#' @rdname fuzzylogic_tnorm
#' @export
#' @family fuzzy_logic
#' @references
#' Klir G.J, Yuan B., \emph{Fuzzy sets and fuzzy logic. Theory and applications},
#' Prentice Hall PTR, New Jersey, 1995.
#'
#' Gagolewski M., Data Fusion: Theory, Methods, and Applications,
#'    Institute of Computer Science, Polish Academy of Sciences, 2015, 290 pp.
#'    isbn:978-83-63159-20-7
tnorm_minimum <- function(x, y) {
   .Call("tnorm_minimum", x, y, PACKAGE="agop")
}


#' @rdname fuzzylogic_tnorm
#' @export
tnorm_product <- function(x, y) {
   .Call("tnorm_product", x, y, PACKAGE="agop")
}

#' @rdname fuzzylogic_tnorm
#' @export
tnorm_lukasiewicz <- function(x, y) {
   .Call("tnorm_lukasiewicz", x, y, PACKAGE="agop")
}

#' @rdname fuzzylogic_tnorm
#' @export
tnorm_drastic <- function(x, y) {
   .Call("tnorm_drastic", x, y, PACKAGE="agop")
}

#' @rdname fuzzylogic_tnorm
#' @export
tnorm_fodor <- function(x, y) {
   .Call("tnorm_fodor", x, y, PACKAGE="agop")
}