The information entropy system serves as a fundamental theory of uncertainty description and approximate reasoning, and it has been introduced into rough sets to implement data analyses and intelligence processing. Classical complementary entropy, conditional-entropy and mutual-information can effectively describe roughness and fuzziness, and their system expansion has application significance. In terms of neighborhood rough sets, neighborhood complementary information measures are extendedly constructed, and their heuristic attribute reduction is investigated. According to analytical simulation and granular replacement, neighborhood complementary entropy, conditional-entropy and mutual-information are defined, and their system equation, double bounds and granulation non-monotonicity are achieved. Based on the neighborhood complementary mutual-information, non-monotonic attribute reduction and its heuristic reduction algorithm are proposed. The validity of property and algorithm is verified by decision tables and data experiments. By virtue of neighborhood expansion, relevant information measures and attribute reduction have application prospects.