In fuzzy rough sets, the traditional approach primarily employs fuzzy rough approximation operators and fuzzy neighborhood operators to solve attribute reduction problems. However, measures constructed by these operators fail to capture the correlation between attributes, whereas the generalized Shapley value(SHV), as a non-additive measure, takes into account the correlation between attributes from a global perspective. Based on the global attribute correlation problems, SHV for fuzzy neighborhoods utilizing pseudo-overlap functions are proposed to deal with the problem of attribute reduction. Firstly, in the fuzzy β covering approximation spaces( β -FCASs), based on pseudo-overlap functions and their corresponding residual implications(( I PO, PO )), ( I PO, PO )-fuzzy β neighborhood operators ((I PO,PO)−β−FNoperators) and four pairs of ( I PO, PO ) fuzzy β neighborhood measures(( I PO, PO )-fuzzy β−NMs) based on these operators are constructed, thereby extending the representational capacity of fuzzy covering-based rough sets. Secondly, four pairs of SHVs utilize on ( I PO, PO )-fuzzy β−NMs are introduced to evaluate attribute significance from a global perspective. And a new method of attribute reduction of fuzzy β covering information decision tables( β -FCIDTs) based on SHV is proposed. Thirdly, four pairs of Choquet integrals(CHIs) based on SHV are constructed. On this basis, a method for addressing the attribute reduction of β -FCIDT is proposed by considering the correlation of global attributes, and the proposed method is used to deal with the classification problem specifically. Finally, the validity and practicality of the proposed methods are confirmed through the use of several public datasets.