Generalized granular variable precision approximation operators

摘要

In this paper, as an extension of variable precision (theta, sigma)-fuzzy rough sets, we introduce the notion of the generalized granular variable precision ((R) under bar (beta), (R) over bar (beta))-fuzzy rough sets determined by fuzzy granules with R is an element of L-XxY on a residuated and coresiduated lattice with an involution N. We investigate the properties of (R) under bar (beta) and (R) over bar (beta) with e(L)Y and d(L)Y are (L, circle dot)-fuzzy preorder and (L, circle plus)-fuzzy co-preorder, respectively. Moreover, we investigate Alexander topologies and Alexander cotopologies induced by (R) under bar (perpendicular to) and (R) over bar (perpendicular to), respectively. For an L-fuzzy relation R is an element of L-XxX and (R) under bar (beta), (R) under bar (beta) for each beta is an element of L, we obtain Alexandrov L-fuzzy pretopologies and Alexandrov L-fuzzy precotopologies on X, respectively. We give their examples.