This is a talk I’ll be giving myself at ISAS in July this year (shortly after IPMU). I’m very much looking forward to the format of this symposium and of being able to share ideas with the other researchers in attendance.
Title: Elicitation of fuzzy partial orders from incomplete preferences
Author: S. James
Recently we have proposed the framework of fuzzy partial order based preference relations for expression and aggregation of preferences. For a set of n alternatives/options, a FPO-based preference relation is represented as an n × n matrix A where each entry aij represents the degree to which option i is preferred to option j. While this kind of representation has been researched extensively, e.g. with multiplicative and additive relations, the key difference here is that a value of aij = 1 is interpreted as indicating option i is preferred to j, a value of aij = 0 means that option i is not preferred to j and values in-between represent partial preference. We therefore have the restriction that aij > 0 implies aji = 0, and the maximum expression of strength of preference is only crisp preference.
The perceived advantage of such a representation is that the aggregation of such matrices is less susceptible to extreme opinions, corresponding with a fuzzy version of the Kemeny distance. It also should align more with a natural expression of preference that is not as dependent on individual interpretations of a ratings scale.
While we have developed methods for obtaining final rankings of alternatives through aggregation and for repairing inconsistent matrices, a remaining problem is how to deal with large datasets involving many alternatives. In these situations, the elicitation of preferences becomes quite onerous on the decision maker and, on the computation side, the number of corresponding partial orders becomes expensively large. We propose to use a subset of triplets of comparison data, i.e. rankings provided between 3 alternatives, in order to obtain a final ranking of the alternatives. Our goal is to reduce the amount of information and effort required from the decision maker but still be able to obtain an acceptable ranking. Once the theory behind this process is developed, it can be evaluated on human subjects in terms of ease of preference elicitation and their agreement with the final ranking.