Attribute reduction relies on knowledge granulation and uncertainty measurement， thus facilitating intelligent recognition. For incomplete continuous data， neighborhood decision rough sets induce attribute reduction. However， the related neighborhood relation deserves optimal improvements， while the existing decision cost deserves integrated reinforcements. In this paper， a new neighborhood relation is proposed， and three decision-cost fusion measures are constructed， so new incomplete neighborhood decision rough sets are established and the attribute reduction is systematically researched. At first， an improved distance is introduced to produce an incomplete neighborhood relation， so improved rough sets on incomplete neighborhood are proposed. Then， the dependence degree and neighborhood entropy are introduced based on decision costs， so three fusion measures on decision costs are obtained by multiplication fusion， thus acquiring granulation non-monotonicity. Furthermore， eight heuristic reduction algorithms based on attribute importances are designed from two neighborhood relations and four relevant measures of decision costs. As finally verified by data experiments， the five algorithms out of the seven new algorithms have good performance of classification learning， thus improving the basic reduction algorithm.