Aggregation of fuzzy preferences: Some rules of the mean

Abstract

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.

A new measure of consensus with reciprocal preference relations: The correlation consensus degree

“…The use of aggregation functions to merge inputs into a single output has been extensively analysed in literature [11,28,33,43]. In the Decision Making context, the use of aggregation functions to derive the degree of agreement among a group of experts has been justified (see for example [11,29,31,43,47]).…”

“…This new consensus measure will be developed within assumptions of experts' opinions or preferences being expressed by means of reciprocal preference relations, a framework that is currently of interest to the research community in decision theory under uncertainty [7,27,28,45]. Under reciprocal preference relations, on the one hand and as it was mentioned above, the new proposed approach inherits advantages of previous approaches based on traditional distance/similarity and association measures.…”

Modeling rationality in a linguistic framework

“…Fuzzy and reciprocal preference relations generalize crisp preference relations by allowing individuals to show different degrees of preference among alternatives within the unit interval (see Nurmi [33], Tanino [43], Fodor and Roubens [16], De Baets and Fodor [5], García-Lapresta and Llamazares [18], De Baets and De Meyer [3], and De Baets et al [4], among others).…”

Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support

“…The axiomatic characterization of majorities based on difference in support is introduced in García-Lapresta and Llamazares (2010). Notice that, for other kinds of operators which can be used for the aggregation of reciprocal preferences and their characterizations, the reader is referred to García-Lapresta and Llamazares (2000); Llamazares (2004Llamazares ( , 2007; García-Lapresta (2003, 2008), among others.…”