owmax {agop} | R Documentation |
Computes the (Ordered) Weighted Maximum/Minimum.
owmax(x, w = rep(Inf, length(x))) owmin(x, w = rep(-Inf, length(x))) wmax(x, w = rep(Inf, length(x))) wmin(x, w = rep(-Inf, length(x)))
x |
numeric vector to be aggregated |
w |
numeric vector of the same length as |
The OWMax operator is given by
OWMax_w(x) = max_i{ min{w_i, x_(i)} }
where x_(i) denotes the i-th smallest
value in x
.
The OWMin operator is given by
OWMin_w(x) = min_i{ max{w_i, x_(i)} }
The WMax operator is given by
WMax_w(x) = max_i{ min{w_i, x_i} }
The WMin operator is given by
WMin_w(x) = min_i{ max{w_i, x_i} }
OWMax
and WMax
by default return the greatest value in x
and OWMin
and WMin
- the smallest value in x
.
Classically, it is assumed that if we aggregate vectors with elements in [a,b], then the largest weight for OWMax should be equal to b and the smallest for OWMin should be equal to a.
There is a strong connection between the OWMax/OWMin operators and the Sugeno integrals w.r.t. some monotone measures. Additionally, it may be shown that the OWMax and OWMin classes are equivalent.
Moreover, index_h
for integer data
is a particular OWMax operator.
These functions return a single numeric value.
Dubois D., Prade H., Testemale C., Weighted fuzzy pattern matching, Fuzzy Sets and Systems 28, 1988, pp. 313-331.
Dubois D., Prade H., Semantics of quotient operators in fuzzy relational databases, Fuzzy Sets and Systems 78(1), 1996, pp. 89-93.
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
Sugeno M., Theory of fuzzy integrals and its applications, PhD thesis, Tokyo Institute of Technology, 1974.
Other aggregation_operators: owa