Reductions in inconsistent decision systems based on dominance relations

By incorporating domination principle in inconsistent decision systems based on dominance relations, we define the concept of distribution function for a decision system to directly reflect the inconsistent degree of this system. A new type of distribution reduction and maximum distribution reduction are correspondingly introduced. The relationships between these two reductions are discussed, and their judgment theorems are given. In addition, this article also discusses the relations of several existing reductions, including compatible reduction, absolute reduction, and the proposed distribution reduction and maximum distribution reduction.