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

It is an important subject to mine valuable knowledge from complex and massive data in the era of big data. Rough set theory is a new mathematical tool for dealing with uncertain and inaccurate data, decision-theoretic rough set model (DTRS), as an extension of classical rough set model, is used to analyze decision information systems and multi-granulation decision-theoretic rough set model (MG-DTRS) can analyze and process target concepts from different angles and levels. However, the classical DTRS model exists some limitations in dealing numerical or hybrid-valued data. Considering the different influence of numerical features and symbolic features on decision-making, the paper proposes an incomplete neighborhood multi-granulation decision-theoretic rough set model in hybrid-valued decision system through integrating MG-DTRS with neighbourhood rough sets, and two types of neighborhood multi-granulation decision-theoretic set models are emphatically analysed. Furthermore, taking pessimistic and optimistic neighborhood multi-granulation decision-theoretic rough sets as examples, the implementation algorithms and related properties of the two type of models are studied. Finally, the relationship between the proposed model and other models is analyzed through formula derivation. The model proposed in this paper can effectively solve the decision-making problem of hybrid-valued incomplete information system through multi-angle and multi-level analysis.