Measuring consistency of preferences is very important in decision-making. This paper addresses this key issue for interval-valued reciprocal preference relations. Existing studies implement one of two different measures: the “classical” consistency measure, and the “boundary” consistency measure. The classical consistency degree of an interval-valued reciprocal preference relation is determine...

Incomplete preferences are likely to arise in realworld preference aggregation and voting systems. This paper deals with determining whether an incomplete preference profile is single-peaked. This is essential information since many intractable voting problems become tractable for single-peaked profiles. We prove that for incomplete profiles the problem of determining single-peakedness is NPcom...

This paper studies strict preference relations on product sets induced by “ordinal aggregation methods”. Such methods are interpreted here as performing paired comparisons of alternatives based on the “importance” of attributes favoring each element of the pair: alternative x will be preferred to alternative y if the attributes for which x is better than y are “more important” than the attribut...

This paper studies strict preference relations on product sets induced by “ordinal aggregation methods”. Such methods are interpreted here as performing paired comparisons of alternatives based on the “importance” of attributes favoring each element of the pair: alternative x will be preferred to alternative y if the attributes for which x is better than y are “more important” than the attribut...

In decision-making problems, decision-makers using fuzzy preference relations express their opinions. The values of fuzzy preference relations have been crisp in recent seminar papers. To allow decision makers to give vague or imprecise responses when they are in the process of comparing two alternatives, this paper proposes a new method using fuzzy linguistic assessment variables instead of cr...

The multi-criteria decision-making (MCDM) problem has a solution whose quality can be affected by the experts’ inclinations. Under essential conditions, fuzzy MCDM method provide more acceptable and efficient outcomes to select best alternatives. This work consists of consensus-based technique for selecting evaluating suppliers in an incomplete preference relations (IFPRs) environment utilizing...

Preference relations are the most common representation structures of information used in decision making problems because they are useful tool in modelling decision processes, above all when we want to aggregate experts’ preferences into group preferences. Therefore, to establish rationality properties to be verified by preference relations is very important in the design of good decision maki...

Consistency of preference relations is associated with the study of the transitivity property. In this paper, we analyze the properties to be verified by a function, T , in order to obtain the value of preference of the alternative xi over the alternative xk when we already have the values of the preference of xi over xj , and of xj over xk. As a consequence, we define T -additive transitivity ...

For a set A of n people and a set B of m items, with each person having a preference list that ranks some items in order of preference, we consider the problem of matching every person with a unique item. A matching M is called popular if for any other matching M ′, the number of people who prefer M to M ′ is not less than the number of those who prefer M ′ to M . For given n and m, consider th...