Notes on bipolar concordance relations
نویسنده
چکیده
Remark 1 In this text, we always work between 0 and 1 with 1/2 playing the rôle of the midpoint. A simple rescaling allows to work between −1 and 1 with 0 playing the rôle of a midpoint. • A valued relation T is said to be reflexive if T (x, x) = 1, for all x ∈ X. A valued relation T on X such that T (x, y) ∈ {0, 1}, for all x, y ∈ X, is said to be crisp. As is usual, we write x T y instead of T (x, y) = 1 when T is a crisp relation. A crisp relation T on a set X is said to be:
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Notes on strict concordance relations
The idea of concordance is central to many MCDM techniques. It leads to comparing alternatives by pairs on the basis of a comparison in terms of importance of the coalitions of attributes favoring each element of the pair. Such a way of comparing alternatives has a definite “ordinal” flavor. It is well-know that it may lead to relations that do not possess any remarkable transitivity properties...
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