The decision making problem with interval numbers is an important topic of uncertain multiple attribute decision making. A difficulty to solve the interval decision making problems is the ranking method of interval numbers, because among the interval numbers exist cross, it’s difficult to ranking the alternatives directly. This paper studied how to make use of the traditional method for certain...

We identify in this paper two conditions that characterize the domain of single-peaked preferences on the line in the following sense: a preference profile satisfies these two properties if and only if there exists a linear order L over the set of alternatives such that these preferences are single-peaked with respect L. The first property states that for any subset of alternatives the set of a...

Classical voting rules output a winning alternative (or a nonempty set of tied alternatives). Social welfare functions output a ranking over alternatives. There are many practical situations where we have to output a different structure than a winner or a ranking: for instance, a ranked or non-ranked set of k winning alternatives, or an ordered partition of alternatives. We define three classes...

This paper proposes a quadratic programming method (QPM) for ranking alternatives based on multiplicative preference relations (MPRs) and fuzzy preference relations (FPRs). The proposed QPM can be used for deriving a ranking from either a MPR or a FPR, or a group of MPRs, or a group of FPRs, or their mixtures. The proposed approach is tested and examined with two numerical examples, and compara...

We introduce a two-stage ranking of multidimensional alternatives, including uncertain prospects as particular case, when these objects can be given a suitable matrix form. The first stage defines a ranking of rows and a ranking of columns, and the second stage ranks matrices by applying natural monotonicity conditions to these auxiliary rankings. Owing to the Debreu-Gorman theory of additive s...

The new version of the method for the construction of partial order on the set of multicriteria alternatives is presented. This method belongs to the family of Verbal Decision Analysis methods and gives a more efficient means of problem solution. The method is based on psychologically valid operations for information elicitation from a decision maker: comparisons of two distances between the ev...