Fuzzy Social Choice Theory

Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

“…To start with, we extend the notions of symmetry and asymmetry. The following definition has been adopted by several authors (see e.g., [7,8,25,26]).…”

“…This question has special relevance. Several authors have already explored this topic with particular decompositions (see, e.g., [7,8]). Other authors have worked under the axiomatic existence of decompositions (see [19]).…”

“…If instead of considering crisp binary relations on the set of alternatives U, we deal with graded membership functions that may take any possible value in the unit interval [0,1], so that the corresponding relations now become fuzzy subsets of the Cartesian product U × U, unlike the crisp approach, it may happen in several contexts that some Arrow-like aggregation of fuzzy preferences is still possible (see e.g., [7,8]). In other words, passing to a fuzzy context gives us the opportunity of looking for good aggregation rules à la Arrow, after all.…”

“…Most Arrow-like models in the fuzzy setting pay attention to the possible generalizations of the restrictions involved in the model and imposed to the aggregation rules (see e.g., [8], where four different extensions of the so-called condition of independence of irrelevant alternatives have been launched).…”

“…Perhaps surprisingly, some of the fuzzy Arrovian models encountered in the specialized literature give rise to possibility theorems, whereas others still generate impossibility results (see e.g., [8,9]). In this direction, the impact of fuzziness in the consideration and handling of this kind of social choice paradoxes has been already discussed in [10] (see also [11][12][13][14][15]).…”