In this paper we introduce the semi-uninorm based ordered weighted averaging (SUOWA) operators, a new class of aggregation functions that, as WOWA operators, simultaneously generalize weighted means and OWA operators. To do this we take into account that weighted means and OWA operators are particular cases of Choquet integral. So, SUOWA operators are Choquet integral-based operators where their capacities are constructed by using semi-uninorms and the values of the capacities associated to the weighted means and the OWA operators. We also show some interesting properties of these new operators and provide examples showing that SUOWA and WOWA operators are different classes of aggregation operators.
In this paper we point out some interesting properties of a class of decision rules located between simple and unanimous majorities. These majority rules are based on difference of votes: an alternative wins when the difference between the number of votes obtained by this alternative and that obtained by the other is greater than a previously fixed quantity. We also give some characterizations of these majority rules by means of two properties well known in the literature: cancellation and decisiveness.
The finantial support of the Junta de Castilla y León (Consejería de Educación y Cultura, Proyecto VA09/98) is gratefully acknowledged. The authors are indebted to Maurice Salles and two anonymous referees for their valuable comments and helpful suggestions.Abstract. This paper studies by means of reciprocal fuzzy binary relations the aggregation of preferences when individuals show their preferences gradually. We have characterized neutral aggregation rules through functions from powers of the unit interval in the unit interval. Furthermore, we have determined the neutral aggregation rules that are decomposable and anonymous. In this class of rules, the collective intensity of preference is the arithmetic mean of the values assigned by a function to the individual intensities of preference. We have also considered the neutral aggregation rules based on quasiarithmetic means. We have established that this class of rules generalizes the simple majority, when individuals have ordinary preferences and collective preferences are reciprocal.
In this paper a class of voting procedures, located between simple and unanimous majorities, is introduced and characterized. Given two alternatives, the winning alternative is the one with a number of votes exceeding that obtained by the other in a previously fixed quantity. Moreover, a subclass of these voting procedures has been considered, by demanding additionally a number of votes greater than a previously fixed threshold. The main results of this paper are characterizations of these voting procedures through aggregation functions of fuzzy preferences associated with quasiarithmetic means and OWA operators.
a b s t r a c tThere are different ways to allow the voters to express their preferences on a set of candidates. In ranked voting systems, each voter selects a subset of the candidates and ranks them in order of preference. A well-known class of these voting systems are scoring rules, where fixed scores are assigned to the different ranks and the candidates with the highest score are the winners. One of the most important issues in this context is the choice of the scoring vector, since the winning candidate can vary according to the scores used. To avoid this problem, Cook and Kress [W.D. Cook, M. Kress, A data envelopment model for aggregating preference rankings, Management Science 36 (11) (1990) 1302-1310], using a DEA/AR model, proposed to assess each candidate with the most favorable scoring vector for him/her. However, the use of this procedure often causes several candidates to be efficient, i.e., they achieve the maximum score. For this reason, several methods to discriminate among efficient candidates have been proposed. The aim of this paper is to analyze and show some drawbacks of these methods.
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