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 [v.sub.i].
Saaty [23] 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.
