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...

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 ...

One of the key tasks in data mining and information retrieval is to learn preference relations between objects. Approaches reported in the literature mainly aim at learning preference relations between objects represented according to the classical attribute-value representation. However, the growing interest in data mining techniques able to directly mine data represented according to more sop...

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 article develops a group decision framework with intuitionistic preference relations. An approach is first devised to rectify an inconsistent intuitionistic preference relation to derive an additive consistent one. A new aggregation operator, the so-called induced intuitionistic ordered weighted averaging (IIOWA) operator, is proposed to aggregate individual intuitionistic fuzzy judgments....

We explore the notion of duality for defeasible entailment relations induced by preference orderings on states. We then show that such preferential entailment relations may be used to characterise Peircean inductive and abductive reasoning. Interpreting the preference relations as accessibility relations establishes modular Gödel-Löb logic as the modal logic of inductive and abductive reasoning. §

A multiperson decision making problem, where the information about the alternatives provided by the experts can be presented by means of diierent preference representation structures (preference orderings, utility functions and multiplicative preference relations) is studied. Assuming the multiplicative preference relation as the uniform element of the preference representation, a multiplicativ...