A distance for evidential preferences with application to group decision making

Abstract

In this paper, we focus on measuring the dissimilarity between preferences with uncertainty and imprecision, modelled by evidential preferences based on the theory of belief functions. Two issues are targeted: The first concerns the conflicting interpretations of incomparability, leading to a lack of consensus within the preference modelling community. This discord affects the value settings of dissimilarity measures between preference relations. After reviewing the state of the art, we propose to distinguish between two cases: indecisive and undecided, respectively modelled by a binary relation and union of all relations. The second concerns a flaw that becomes apparent when measuring the dissimilarity in the theory of belief functions. Existing dissimilarity functions in the theory of belief functions are not suitable for evidential preferences, because they measure the dissimilarity between preference relations as being identical. This is counter-intuitive and conflicting with almost all the related works. We propose a novel distance named Unequal Singleton Pair (USP) distance, able to discriminate specific singletons from others when measuring the dissimilarity. The advantages of USP distances are illustrated by the evidential preference aggregation and group decision-making applications. The experiments show that USP distance effectively improves the quality of decision results.

Unequal Singleton Pair Distance for Evidential Preference Clustering

“…With the combination rules in the framework of BFT, the evidential preference model is effective in group decision-making with imperfect preference information sources, as systematically discussed in [19].…”

“…In this work, we take the extreme value as in [19], shown in Table 1, with which the similarity matrix Sim over 2 Ω can be obtained by Equation (12).…”

“…Naturally, dissimilarity measure methods in BFT come into the focus for evidential preferences. Even though many dissimilarity measures have been proposed in BFT, they are proved not suitable for evidential preference in [19] because of the conflicts between inherent properties of preference relations. An important one is the equal dissimilarity value between singletons.…”

“…al. [19] discussed negative consequences of such valuation in preference aggregation application and proposed Unequal Singleton Pair (USP) distance, solving the issue by discriminating the dissimilarity between different singleton pairs with other important properties in BFT still guaranteed.…”

“…The effectiveness of USP distance in evidential preference aggregation has already been demonstrated [19], while not applied in evidential preference clustering.…”