Some variants and extensions of dominance network analysis Abstract   The aim of this paper is to extend Dominance Network (DN) analysis, a methodology that evaluates the dominance relationships among a sample of homogeneous operating units (OUs) based on the inputs they consume and the outputs they produce. The relative efficiencies of the OUs are commonly assessed using Data Envelopment Analysis (DEA). DN complements DEA providing indicators to assess the performance of not only each OU individually but also the whole set of OUs. DN also allows visualisation of multidimensional datasets that in conventional DEA can only be done for lowdimensional datasets. The methodology builds a weighted directed acyclic network, the nodes of which are the observed OUs and the links represent all the dominance relationships among the OUs. The weight of these links measures the relative inefficiency among the linked OUs. Complex Network Analysis (CNA) techniques can be applied to this type of layered network. This provides many interesting measures and indexes to characterise the individual nodes as well as the whole sample. However, existing DN applications only involve the existing OUs and hence use a nonconvex DEA technology. In this paper, an approach to overcome this limitation and use other DEA technologies is proposed. Also, as a secondary objective, how the use of different inefficiency metrics affects the results of the analysis is studied.

An Acceleration Method for Computing Dominace Classes in Ordered Information System In rough set theory, two crisp sets (i.e., the lower and upper approximates of a target concept) is used to describe uncertainties in given information systems. However, the traditional rough set models are built based on equivalence relations which do not consider the preference relationship of attribute values. Dominance relationbased rough set approach effectively solve this problem which uses dominance relations to substitute equivalence relations to deal with ordered data. In this kind of approach, the computing of dominance class is a necessary step to attribute reduction which is very timeconsuming. In order to reduce the computational cost in calculating dominance classes, this paper presents a method to compute dominance classes by gradually reducing the search space in the domain. The corresponding algorithm is proposed. In each step of the algorithm, the inferior classes of the objects in a given information system are removed in the universe with the increase of the attributes. Experiments using six UCI data show that the proposed method improves the efficiency of computing dominance classes with the increasing of attributes and objects.