Some Problems Related to Reducts of Consistent Incomplete Decision Tables

Dinh Thu Khanh,Le Hoang Son,Vu Duc Thi,Nguyen Long Giang

doi:10.33889/ijmems.2022.7.2.019

Abstract

In multi-criteria decision making, attribute reduction has attracted the attention of researchers for more than two decades. So far, numerous scientists have proposed algorithms to construct reducts in decision tables. However, most of the suggested algorithms are heuristic which discovers a reduction based on criteria of the attribute set. In fact, studying the properties of reducts to build efficient attribute reduction models is an urgent problem. In this research, we present some properties of reducts in incomplete decision tables by the relational database theory approach. It was found that the properties of reducts in incomplete decision tables are equivalent to properties of the Sperner-systems in the theory of relational database. By studying the properties of the Sperner-systems, the efficient attribute reduction models can be built to improve the efficiency of multi-criteria decision making systems.

Highlights

One of the most important problems in multi-criteria decision making systems is attribute reduction which attracted the consideration of researchers for more than two decades
Various methods have been introduced in order to obtain the reduct of decision tables based on Rough Set (RS) (Pawlak, 1991) or extended RS
We discover the equivalence properties about the reducts obtained from a consistent incomplete decision tables (CIDTs) with Sperner-systems

Summary

Introduction

One of the most important problems in multi-criteria decision making systems is attribute reduction which attracted the consideration of researchers for more than two decades. Results related to the attributes of reduct in decision tables are restricted. By extending the results in the paper (Giang & Son, 2015), all reducts of consistent incomplete decision tables (CIDTs) were calculated by a new method in Demetrovics et al (2013) with a polynomial time.

Results

Conclusion