Incomplete neighbourhood multi‐granulation decision‐theoretic rough set in the hybrid‐valued decision system

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

“…MG-DTRS models are based on classical DTRS, which uses equivalence relations to partition the target object universe and generate multiple equivalence classes as basic concepts [21]. However, the models based on the equivalence relation are not easy to cope with all kinds of complex data, especially hybridvalued type information system with numerical type and categorical type properties [14,20]. Therefore, the neighbourhood rough set (NRS) was put forward because of the advantage of facilitating the analysis and processing of numerical or mixed type data.…”

“…Among the above achievements, there were few research works on NMG‐DTRS in the complex information system, although literature [22] illustrated the matrix approach for decision‐theoretic rough sets, it is not suitable for neighbourhood information systems in multi‐granularity environment. Literature [14] explored two types of NMG‐DTRS in detail based on the incomplete hybrid ‐valued decision system, however, the knowledge representation based on the models are difficult to understand and has some computational complexity. In this study, in view of the characteristics of matrix in rough set context, we introduced the matrix technique into NMG‐DTRS and proposed a matrix‐based method for solving decision domains of the NMG‐DTRS model for hybrid‐valued decision information systems, the positive, boundary and negative domains were constructed from the matrix perspective.…”

“…In order to address the limitation, Lin et al put forward the neighbourhood rough set models (NRS) in literature [16,17], in the following years, several types of generalised NRS models were widely used in various domains. Literature [18] discussed DTRS model in the neighbourhood system environment, literature [14] deeply analysed the neighbourhood DTRS(NDTRS) and MG-DTRS model, and proposed an incomplete neighbourhood multigranulation decision-theoretic rough set (NMG-DTRS) model; reference [19] investigated neighbourhood multigranulation rough sets (NMRS) and the attribute reduction method for incomplete information systems with symbolic type and numerical type properties. In addition to the mentioned frameworks, some important insights based on these models have been explored, such as the application of matrix technology.…”

“…DTRS and a large number of extended models have been studied to address the corresponding requirements in recent years [9][10][11][12][13]. However, most proposed analysis methods in the light of the classical rough set theory can only be used to process single type of data, such as symbolic data, and there are some limitations in the processing of complex data such as numerical or hybrid-valued type decision systems [14]. Furthermore, with the increasing application of data science and artificial intelligence technology, data from all walks of life are becoming more huge, complex, diverse and uncertain, and people need more comprehensive and diversified analysis and processing of these complex data in order to obtain more valuable knowledge and make more accurate decisions, so the research of multi-granulation decision making methods for numerical data and mixed data has been paid more and more attention.…”