Axiomatic characterizations of threshold choice functions for comparison functions

Abstract

In this paper we characterize the threshold choice functions associated with comparison functions (= reciprocal fuzzy relations), a special of which is the Orlovsky choice function (with threshold 1/2). Our family of threshold choice functions is somewhat larger than the family of choice functions which select only those alternatives that secure a certain pre-specified proportion of the votes against all other alternatives. Our family of threshold choice functions also include ones which select only those alternatives that exceed a certain pre-specified proportion of the votes against all other alternatives. This is the price we pay for omitting continuity from our axiomatic characterizations. © 2001 Elsevier Science B.V. All rights reserved.