1d:T7ed,# A factory function for creation of sugeno-integrals. ```r sugeno( measure, relative = TRUE, strong = FALSE, alg = c("lukasiewicz", "goedel", "goguen") ) ``` ## Arguments - `measure`: A non-decreasing function that assigns a truth value from the $[0, 1]$ interval to the either relative or absolute quantity - `relative`: Whether the measure assumes relative or absolute quantity. Relative quantity is always a number from the $[0,1]$ interval - `strong`: Whether to use the strong conjunction (`TRUE`) or the weak conjunction (`FALSE`) - `alg`: The underlying algebra must be either a string (one from 'lukasiewicz', 'goedel' or 'goguen') or an instance of the S3 class `algebra()`. ## Returns A two-argument function, which expects two numeric vectors of equal length (the vector elements are recycled to ensure equal lengths). The first argument, `x`, is a vector of membership degrees to be measured, the second argument, `w`, is the vector of weights. Let $U$ be the set of input vector indices (1 to `length(x)`). Then the sugeno integral computes the truth values accordingly to the following formula: $\vee_{z \subseteq U} \wedge_{u \in z} (x[u]) CONJ measure(m_z)$, where $m_z = sum(w[z]) / sum(w)$ if `relative==TRUE` or $m_z = sum(w)$ if `relative==FALSE` and where CONJ is a strong conjunction (i.e. `alg$pt`) or a weak conjunction (i.e. `alg$pi`) accordingly to the `strong` parameter. ## Examples ```r # Dvorak <1> "almost all" quantifier q <- sugeno(lingexpr(ctx3(), atomic='bi', hedge='ex')) a <- c(0.9, 1, 1, 0.2, 1) q(x=a, w=1) # Dvorak <1,1> "almost all" quantifier a <- c(0.9, 1, 1, 0.2, 1) b <- c(0.2, 1, 0, 0.5, 0.8) q <- sugeno(lingexpr(ctx3(), atomic='bi', hedge='ex')) q(x=lukas.residuum(a, b), w=1) # Murinová <1,1> "almost all" quantifier a <- c(0.9, 1, 1, 0.2, 1) b <- c(0.2, 1, 0, 0.5, 0.8) q <- sugeno(lingexpr(ctx3(), atomic='bi', hedge='ex')) q(x=lukas.residuum(a, b), w=a) ``` ## See Also `quantifier()`, `lingexpr()` ## Author(s) Michal Burda

sugeno function