不同信任结构下约简的证据特征及其一致性

Evidence Characteristic and Consistency of Attribute Reduction in Different Belief Structures

不一致性决策表中广义决策约简与相对约简不完全一致.文中给出划分和覆盖2种信任结构下的广义决策约简和相对约简的概念,研究这2种约简的证据结构特征,分别证明广义决策约简和相对约简是保持广义决策值的似然函数之和与信任函数之和不变的最小属性集合.在此基础上,提出划分和覆盖结构中的广义信任约简,进而分析这2种结构中广义决策约简、广义信任约简及相对约简的一致性,证明广义决策约简必为相对约简协调集且广义决策约简与广义信任约简等价,得出相对约简的核蕴含于广义决策约简的结论.最后分别给出2种信任结构下广义决策约简与相对约简相同的充分必要条件,完善不同信任结构中的约简理论.

In the inconsistent decision table, the generalized decision reduction is not fully consistent with the relative reduction. The definitions of generalized decision reduction and the relative reduction are given in both partition-based and covering-based belief structures respectively. Then, the evidence structure characteristic of the two reduction methods are intensively studied. The results show that the generalized decision reduction set is the minimal attribute set maintaining the sum of the plausibility functions of the generalized decision unchanged, while the relative reduction set is the minimal attribute set maintaining the sum of the belief functions of the generalized decision unchanged. On the basis of those, the generalized belief reduction is defined in partition-based and covering-based belief structures, respectively. The consistency among generalized decision reduction, generalized belief reduction and relative reduction are further analyzed. The results verify that the generalized decision reduction set must be a relative consistent reduction set and the generalized decision reduction is equivalent to the generalized belief reduction. It is proved that the generalized decision reduction of a given decision table must be its relative coordination set, and the core set of the relative reduction is included in the generalized decision reduction. The necessary and sufficient condition that the generalized reduction is identical with the relative reduction is given in two different belief structures respectively.