The further investigation of variable precision intuitionistic fuzzy rough set model

By applying weighted aggregation operator, we firstly define the similarity measure between two intuitionistic fuzzy sets, and we prove that it is also a \(\mathcal {T}\)-equivalence intuitionistic fuzzy relation which is called weighted \(\mathcal {T}\)-equivalence intuitionistic fuzzy relation. However, different attributes have different significance, to measure the importance of each attribute, in this article, we use variable precision intuitionistic fuzzy rough set(VPIFRS) to process the data in decision table and obtain the weight of each condition attribute. Thus, a new \(\mathcal {T}\)-equivalence intuitionistic fuzzy partition is obtained based on the weighted \(\mathcal {T}\)-equivalence intuitionistic fuzzy relation and the weight set of condition attribute, it shows that this partition is more suitable and less sensitive to perturbation. Subsequently, to determine a rational change interval for threshold \(\alpha ,\) we investigate the \(\alpha\)-stable intervals. Simultaneously, we discuss the two types uncertainty of VPIFRS theory, and show that it can be characterized by information entropy and the rough degree. Finally, an example is given to illustrate our results, which show that our method is more feasible and less sensitive to perturbation and misclassification.