Reaching a high level of consensus among experts is critical in group decision making problems. Usually, it is the moderator task to assure that the consensus process is carried out properly and, if possible, to offer recommendations to the expert in order to change their opinions and narrow their differences. In this paper we present an implemented web based consensus support system that is ab...

We present here a formal foundation for an iterative and incremental approach to constructing and evaluating preference queries. Our main focus is query modification: a query transformation approach which works by revising the preference relation in the query. We provide a detailed analysis of the cases where the order-theoretic properties of the preference relation are preserved in the revisio...

Rechenauer (2008) claims that weak preference is a better starting point for preference relations than strict preferences. This contention is challenged. Definitional connections between weak and strict preference are suggested that lead to the opposite conclusion. This is not taken as a justification of the superiority of strict over weak preference as the primitive preference relation, but ju...

Several methods for the processing of incomplete preference information in additive preference models have been proposed. Due to the lack of adequate decision aiding tools, however, only a few case studies have been reported so far. In this paper, we present PRIME Decisions, a decision aiding tool which supports the analysis of incomplete preference information with the PRIME method. PRIME Deci...

Preference relations are very useful to express decision makers’ preferences over alternatives in the process of group decision-making. However, the multiple self-confidence levels are not considered in existing preference relations. In this study, we define the preference relation with self-confidence by taking multiple self-confidence levels into consideration, and we call it the preference r...

Useful decision recommendations can often be provided even if the model parameters are not exactly specified. The recognition of this fact has spurred the development of multicriteria methods which are capable of admitting and synthesizing incomplete preference information in hierarchical weighting models. These methods share similarities in that they (i) accommodate incomplete preference infor...

Topological separability is crucial for the utility representation of a complete preference relation. When preferences are incomplete, this axiom has suitably de…ned counterparts: upper separability and lower separability (Ok (2002)). We consider the problem of representing an incomplete preference relation by means of a vector-valued utility function; we obtain representation results under the...

Methods for dealing with incomplete preference information in hierarchical weighting models have continued to attract attention in the literature on multi-criteria decision analysis (MCDA). In this paper, we give a structured overview of several such methods which (i) accommodate incomplete preference information, (ii) offer dominance concepts and decision rules for the generation of decision r...

Incomplete relations are relations which contain null values, whose meaning is \value is at present unknown". Such relations give rise to two types of functional dependency (FD). The rst type, called the strong FD (SFD), is satissed in an incomplete relation if for all possible worlds of this relation the FD is satissed in the standard way. The second type, called the weak FD (WFD), is satissed...