sugeno | R Documentation |
A factory function for creation of sugeno-integrals.
sugeno( measure, relative = TRUE, strong = FALSE, alg = c("lukasiewicz", "goedel", "goguen") )
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 ( |
alg |
The underlying algebra must be either a string (one from 'lukasiewicz',
'goedel' or 'goguen') or an instance of the S3 class |
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.
Michal Burda
quantifier()
, lingexpr()
# 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)
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