Twenty years of fuzzy preference structures (1978–1997)

The aim of this paper is to summarize the historical development of the concept of a fuzzy preference structure and to present the resulting material in a logical manner. Roughly speaking, three phases can be distinguished. In the first phase, different proposals for constructing fuzzy strict preference and indifference relations emerge. In the second one, this construction is approached in an axiomatic way, by imposing conditions on the fuzzy strict preference, indifference and incomparability relations, leading to functional equations identifying suitable strict preference, indifference and incomparability generators. Surprisingly, the definition of a fuzzy preference structure was only given in the third phase, leading to the study of additive fuzzy preference structures. Combined with results from the axiomatic approach, this has finally led to the discovery of characterizable fuzzy preference structures.