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Aiming at the lager rule redundancy problems in traditional association rules, this article proposes minimum monotonous constraint closure Hadoop parallel association rules. First, basing on closure operator constraint rule equivalence relation set, this article gives satisfying minimum monotonous constraint rule set which can effectively divide the constraint rule set into disjoint equivalence rule class to reduce the rate of redundancy rule. Second, aiming at the big data problems, this article adopts Mapreduce parallel computation model under Hadoop framework to realize the parallelization computation of minimum monotonous constraint association rules which effectively promote the expansibility of algorithm to big data treatment. At last, through experimental comparison on standard test set, this article shows the effectiveness of the proposed algorithm. Correlation Studies In order to reduce the storage and computation time of big data, the technology of reducing data mining algorithm redundancy basing on constraint limit has obtained extensive research and application. In the initial stage of studying this technology, the research direction is to use original constraint for the data mining algorithm. The most typical example is to reduce redundancy of discovered frequent item set through finding the constraint with lowest frequency in the transaction database, and then implement constraint to the frequent item set of association rules through minimum confidence degrees to effectively reduce association rules algorithm redundancy and increase algorithm efficiency. For model ( , , ) m T O A R  , when using traditional association rules for computation, if the Tm value is large, then the algorithm has a low operation efficiency. In addition, only implementing constraint with confidence degrees and support degrees, the users cannot locate interest subset quickly and the algorithm efficiency is low. So scholars propose a more complicated constraint limit to simulate the real demands of users to further reduce cost of algorithm. For example, literature [4] designed monotonous and anti-monotonous characteristic constraint which are Cm and Cam respectively. Basing on the above research achievements, this article also proposes to adopt association rules equivalence relation set of closure constraint rules from algorithm constraint point, comprehensively considers maximum confidence degrees and support degrees threshold value as well as minimum monotonous constraint which implement disjoint division of equivalence rules class to constraint rules set 0 0 , 0 1 0 1 ARS ( , , , ) L R s s c c   . Problem Description of Association Rules For model Tm ( , , ) O A R  , O is non-empty object constraint. A is object characteristic attribute, R is binary relation set O A  . The base numbers of O and A can be indicated as n O  and m A  . X A  is item set whose support set is supp( ) X . Let the upper and lower limit of support threshold values as 0 s and 1 s respectively. Among them, 0 1 0 1 1 n s s     , n O  . If A is non-empty 4th International Conference on Computer, Mechatronics, Control and Electronic Engineering (ICCMCEE 2015) © 2015. The authors Published by Atlantis Press 799 frequency item set and satisfies the condition 0 1 sup p( ) s A s   , then non-empty proper subset L can be extracted from any frequency item set S  and L S      , R S L     . Establish rule relation L R    basing on subset L , the computation mode of confidence degree and support degree of R is: supp( ) supp( ) conf( ) supp( ) supp( ) r L r S L         (1) The upper limit and lower limit of confidence threshold values are 0 c and 1 c respectively and satisfy the condition 0 1 0 1 c c    , the under the conditions of 0 conf( ) c r  and   0 supp s r  , the association rules set is

Minimum Monotonous Constraint Closure Hadoop Parallel Association Rules Under Big Data Environment