Matching dominance: capture the semantics of dominance for multi-dimensional uncertain objects

Abstract

The dominance operator plays an important role in a wide spectrum of multi-criteria decision making applications. Generally speaking, a dominance operator is a partial order on a set O of objects, and we say the dominance operator has the monotonic property regarding a family of ranking functions F if o₁ dominates o₂ implies f(o₁) ≥ f(o₂) for any ranking function f ∈ F and objects o₁, o₂ ∈ O. The dominance operator on the multi-dimensional points is well defined, which has the monotonic property regarding any monotonic ranking (scoring) function. Due to the uncertain nature of data in many emerging applications, a variety of existing works have studied the semantics of ranking query on uncertain objects. However, the problem of dominance operator against multi-dimensional uncertain objects remains open. Although there are several attempts to propose dominance operator on multi-dimensional uncertain objects, none of them claims the monotonic property on these ranking approaches. Motivated by this, in this paper we propose a novel matching based dominance operator, namely matching dominance, to capture the semantics of the dominance for multi-dimensional uncertain objects so that the new dominance operator has the monotonic property regarding the monotonic parameterized ranking function, which can unify other popular ranking approaches for uncertain objects. Then we develop a layer indexing technique, Matching Dominance based Band (MDB), to facilitate the top k queries on multi-dimensional uncertain objects based on the matching dominance operator proposed in this paper. Efficient algorithms are proposed to compute the MDB index. Comprehensive experiments convincingly demonstrate the effectiveness and efficiency of our indexing techniques.