Axiomatic characterizations of threshold choice functions for comparison functions

Authors:
Somdeb Lahiri
Affiliations:
Indian Institute of Management, Ahmedabad 380 015, India and School of Economic and Business Sciences, University of Witwatersrand at Johannesburg, Private Bag 3, WITS 2050, South Africa
Venue:
Fuzzy Sets and Systems - Possibility theory and fuzzy logic
Year:
2002

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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 ½). 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.