Distribution reduction of inconsistent formal decision contexts based on information granules

Granular computing and knowledge reduction are two important topics in knowledge discovery and data mining. Based on information granules, this paper studies the definition and method of attribute reduction for inconsistent formal decision contexts. First, a quasi-ordering relation on the object set is defined and its related properties are studied too. Then, a distribution function and a maximum distribution function are defined using the quasi-ordering classes. Moreover, a distribution reduct and a maximum distribution reduct are proposed for the inconsistent formal decision context. Finally, a (maximum) distribution discernibility matrix and the corresponding distribution discernibility functions are introduced into the inconsistent formal decision context. And the judgment theorems of the (maximum) distribution consistent set are given to calculate all the distribution reducts and the maximum distribution reducts.