Quantitative Dominance-Based Neighborhood Rough Sets via Fuzzy Preference Relations

Dominance relations exist extensively in decision-making problems. Dominance-based neighborhood rough sets (DNRS) using fuzzy preference relations (FPRs) are presented in this article to deal with attribute reduction in the large-scale decision-making problems. In this model, FPR is elicited to quantify the dominance-based rough set model, which can efficiently deal with the under-fitting problem of classical dominance-based rough sets. First, by formulating a quantified dominance-based neighborhood relation which satisfies reflexivity, the propositions of the quantified DNRSs are analyzed. Second, we propose approaches to attribute reduction based on upper-approximate and lower-approximate discernibility matrices, respectively. Furthermore, we evaluate that the novel model performs efficiently and effectively in time consumption and space storage by experimental analysis. Finally, combining with parallel computing, we demonstrate that the new model can be used to deal with attribute reduction of large-scale datasets effectively.

I. Introduction

Pawlak rough set theory supplies us an effective mathematical method for knowledge representation and acquisition [1], [2]. The rough set approach is constructed based on an equivalence relation, which describes the indiscernibility relationship between arbitrary objects. While in practical decision-making, it is pivotal to consider dominance relationship between objects by a certain order [3], [4] because of preference structures between conditions and decisions. Thus, Greco et al. [42] introduced dominance-based rough set approach (DRSA), which generalizes the rough set approach by a dominance relation. The approach is witnessing an increasing attention in the fields of multicriteria classification [5]–[7], medicine analysis [8], information systems [9]–[12], feature selection [13]–[20], IT business [21], decision-making [22], and so on.