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Top1. Introduction
Pawlak (1982) defined the concept of Rough set. And it is aimed at data analysis problems involving uncertain, imprecise or incomplete information, Pattern recognition, machine learning, knowledge acquisition, economic forecasting and data mining. Knowledge classification is a fundamental problem in rough set theory. In Pawlak’s rough set model, the degree of set overlap was not considered, namely, the classification must be totally correct or certain. Therefore, original rough set model cannot effectively deal with data sets which have noisy data and latent useful knowledge in the boundary region may not be fully captured. In order to overcome the limitations, some extended rough set models have been put forward which combine with other available soft computing technologies. Later on Researchers introduced many new concepts of rough set e.g. Probabilistic rough set, 0.5 probabilistic model, symmetric variable precision rough set model, asymmetric variable precision rough set model, statistical rough set model, fuzzy rough set model, covering rough set model, tolerance rough set model, dominance based rough set model . Also depending on the Bayes theorem in 2007 Yiyu Yao (2007) introduced decision theoretic rough set. In 2002 Sleazak and Ziarko (2002) the concept of Bayesian rough set model was introduced and a detail study was done in 2012 (Zhang, Hangyun et al., 2012). After that lots of applications in attribute reduction were investigated by various Researchers.
Variable precision rough set model (VPRSM) (Ziarko, 1993) is one of the most important extensions. In the model, standard inclusion relation is extended to majority inclusion relation, and the novel notion can be able to allow for some degree of misclassification in the largely correct classification. The strict functional or dependent relations between attributes will be softened.
As a result, more general association decision rules including deterministic and probabilistic ones can be obtained in VPRSM.
Subsequently, Ziarko et al. (1994) put forward an asymmetric variable precision rough set model (AVPRSM), and the model becomes more general and flexible. Variable precision rough set models, symmetric or asymmetric, involve some parameters, β. Different parameters will result in different models, and the extracted decision rule sets may be distinct. In the applications, it is not clear how to find out the optimal parameters and their values are often selected based on the decision makers’ previous knowledge of the domain and their intuition or the proposed criteria.
The connections between rough sets and Bayes’ theory were analyzed by Pawlak. Rough set theory offers a new view on Bayes’ theory, and any decision data set in rough set theory will satisfy the total probability theorem and Bayes’ theorem. Based on Bayesian decision procedure with minimum risk, Yao (1990) put forward a new model called decision theoretic rough set model(DTRSM) which brings new insights into the probabilistic approaches to rough set theory. DTRSM provides a general framework for comparing and synthesizing probabilistic rough set approximations. It not only has good theoretical foundation, but also possesses reasonable semantic interpretation. The Pawlak’s rough set model, VPRSM and AVPRSM can be directly derived from DTRSM under relevant loss functions. If the practical decision problems involve cost or risk environments, the DTRSM will be more beneficial for decision making compared with original rough set model.
Moreover, VPRSM and AVPRSM can be considered as an intermediate step when using the decision theoretic approach for rough analysis.