The additive consistency of fuzzy preference relation
is a strong condition to assess whether the decision-making judgment is consistent.
Under this assumption, the induced preference relation
is a strict partial order possessing a dominating element.
Herrera Viedma, "Group decision making with incomplete fuzzy linguistic preference relations
," International Journal of Intelligent Systems, vol.
Tabanl, "An integrated multicriteria group decision-making approach to efficient supplier selection and clustering using fuzzy preference relations
," International Journal of Computer Integrated Manufacturing, vol.
For example, CP-nets decompose a complex preference relation
into conditionally independent parts (Boutilier et al.
DR 1: If [v.sup.k.sub.i] - [w.sup.c.sub.i] < -[epsilon] then [e.sub.k] should increase his/her the value of preference relation
Saaty  identified that the multiplicative preference relation
is of acceptable level of consistency when CR < 0.1; otherwise, it is inconsistent and it is necessary to return it to the DMs again for the revision of their preferences until they are acceptable.
Wang, "Deriving the priority weights from incomplete hesitant fuzzy preference relations
in group decision making," Knowledge-Based Systems, vol.
(12.) The level of the interest in Figure 1 represents an order of preference, where ">" stands for the preference relation
: "better than," and "[equivalent to]" stands for the preference relation
: "equal in value to," as specified in the following part of the paper.
Podinovski, "Non-dominance and potential optimality for partial preference relations
," European Journal of Operational Research, vol.
In order to facilitate describing the proposed approach, the definition of fuzzy preference relation
is given firstly.
Since the preference without completeness is a kind of more general order structure, it can make preference relation
and the partial order relation unified completely.