Abstract
The paper deals with a problem, the answer to which depends on its chosen logical environment. The solution of the classical Arrow's aggregation problem cannot be obtained within the framework of classical methods. The solution of this problem, as elaborated here, is obtained by exploiting the larger richness of fuzzy logics and expanding the concept of choice functions. Arrow's aggregation problem is formulated for fuzzy environments represented by standard structures. This formulation is surprisingly more transparent than the classic one; the classic problem is merely a special case of our reformulation. This allows the dependence in the system of Arrow's axioms to be more easily studied, thus demonstrating the value of the proposed reformulation. The possible aggregation functions gained from this approach seem to be essential. Nowhere does the framework of interpretations exceed the language of the complete fuzzy calculus of the first order.
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