A reciprocal fuzzy preference relation
R = [([r.sub.ij]).sub.nxn] is additive consistency, if, for all i, j, k = 1, 2, ..., n with i < k < j, the condition [r.sub.ik] + [r.sub.kj] = [r.sub.ik] + 0.5.
Therefore, in the preference relation
expressed by the CP-net, we have xyz > xy'z and xyz' > xy'z'.
Wang, "Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations
," Applied Mathematical Modelling, vol.
The ROR approach is the notion of assignment-based weak preference relations
and, analogously to the assignments, new necessary and possible assignment-based relations were established, as well as an estimative of assignment based on pairwise outranking indices.
Second, LPODs use preferences encoded by ordered disjunctions in the heads of individual rules and aggregate them into a global preference relation
on answer sets.
A binary preference relation
is generally assumed to be transitive.
Formally, one can extend the preference relation
over outcomes to a dominance relation over histories and prove the soundness of this notion of dominance, that is, that one can soundly embed any qualitative dominance model in a quantitative decision-theoretic model.
Experts [e.sub.k] whose [pp.sup.k.sub.i] < [pp.sup.A.sub.i] are advised to modify their preference relation
where [[lambda].sub.max] and n are, respectively, the largest eigenvalue and the dimension of the multiplicative preference relation
. The term RI(n) is denoted as random index that completely depends on the value of n.
Ma, "A group decision-making approach to uncertain quality function deployment based on fuzzy preference relation
and fuzzy majority," European Journal of Operational Research, vol.
Before showing how the addressee's communicative inference functions, we specify the speaker's potential goals and the preference relation
for the states of affairs that make the various meanings of (3) plausible:
Ok, "On the multi-utility representation of preference relations
," Journal of Mathematical Economics, vol.