Probabilistic Rough Set Model Multi-attribute And Multi-criteria

Classical rough set model is a very effective data analysis theory and mathematical tools to deal with incomplete and uncertain knowledge. Compared with other mathematical methods processing uncertain problems, the method has a certain degree of superiority. But the classical method’s strict requirements of binary relation and relationship between concepts make the model face many difficulties in practical application. So scholars try to extend classical rough set model from different points of view. Some scholars replace the equivalence relation with similar relation, dominance relation or arbitrary binary relation. Some scholars combine rough set theory with probability theory to propose a variety of extended rough set modal based on probability, such as Variable precision rough set model, Probabilistic rough set model, Bayesian rough set model, etc. The scholars also use different binary relation to deal with different attribution starting from the point of view of attribute classification and propose many models. Multi-attribute and multi-criteria rough set model is such one of the models. However, the Multi-attribute and multi-criteria rough set model is a model based on the completely contained relationship, lacking of fault tolerance. So we can start from the point of view of probability theory to extend Multi-attribute and multi-criteria rough set model. We propose Multi-attribute and multi-criteria probabilistic rough set model, then deeply study the model.Firstly, the paper simply introduces rough set theory and its present state, classical rough set model, several probabilistic rough set models and related knowledge. Starting from the angle of probability, we try to extend Multi-attribute and multi-criteria rough set model. Proposing Variable precision Multi-attribute and multi-criteria rough set model by introducing a misclassification rate parameter, giving the construction process of the model and its application. Then, based on the relationship between the error classification and conditional probability, constructs a Variable precision Multi-attribute and multi-criteria rough set model based on membership function. Next, the paper combines(— )Probabilistic rough set model with Multi-attribute and multi-criteria rough set model to propose Multi-attribute and multi-criteria(— ) probabilistic rough set model by introducing two threshold parameters. In the end, the paper proposes Multi-attribute and multi-criteria decision rough set model from three aspects: interpretation and calculation of two threshold parameters, estimation of conditional probability and the decision rules of positive domains, negative domains, boundary domains, giving the detailed calculation process of two threshold parameters, a complete estimate of conditional probability and decision rules of positive domains, negative domains, boundary domains based on three-way decision and its application.