Matrix‐based method for solving decision domains of neighbourhood multigranulation decision‐theoretic rough sets

Abstract

Abstract It is more and more important to analyse and process complex data for gaining more valuable knowledge and making more accurate decisions. The multigranulation decision theory based on conditional probability and cost loss has the advantage of processing decision‐making problems from multi‐levels and multi‐angles, and the neighbourhood rough set model (NRS) can facilitate the analysis and processing of numerical or mixed type data, and can address the limitation of multigranulation decision‐theoretic rough sets (MG‐DTRS), which is not easy to cope with complex data. Based on the in‐depth study of hybrid‐valued decision systems and MG‐DTRS models, this study analysed neighbourhood MG‐DTRS (NMG‐DTRS) deeply by fusing MG‐DTRS and NRS; a matrix‐based approach for approximation sets of NMG‐DTRS model was proposed on the basis of the matrix representations of concepts; the positive, boundary and negative domains were constructed from the matrix perspective, and the concept of positive decision recognition rate was introduced. Furthermore, the authors explored the related properties of NMG‐DTRS model, and designed and described the corresponding solving algorithms in detail. Finally, some experimental results that were employed not only verified the effectiveness and feasibility of the proposed algorithm, but also showed the relationship between the decision recognition rate and the granularity and threshold.

Keywords

• probability
• approximation theory
• granular computing
• decision theory
• data analysis
• matrix algebra