Possibilistic Similarity Measures

This paper investigates the problem of measuring the similarity degree between two normalized possibility distributions encoding preferences or uncertain knowledge. In a first part, basic natural properties of such similarity measures are proposed. Then a survey of the existing possibilistic similarity indexes is presented and in particular, we analyze which existing similarity measure satisfies the set of basic properties. The second part of this paper goes one step further and provides a set of extended properties that any similarity relation should satisfy. Finally, some definitions of possibilistic similarity measures that involve inconsistency degrees between possibility distributions are discussed.