模糊推理中一级泛蕴涵的信息约束研究

Information Measure Requirement of 1-Level Universal Implication Operators Based on Linear Specificity Measure in Fuzzy Reasoning

基于线性特征测度的定义,本文详细讨论了在模糊推理中一级泛蕴涵满足信息有界性原则的条件,并得出结论:如果命题真值具有正的测量误差,则当命题间是相斥相关,且其广义相关系数h∈[0.5,((n+1)-(n^2-n+1)~1/2)/2]以及命题间是相克相关(h∈[0,0.5])时,一级泛蕴涵算子满足信息有界性原则;如果命题真值具有负的测量误差,则当命题间是相克相关,且其广义相关系数h∈[0,((n+1)-(n^2-n+1)^(1/2))/2]时,一级泛蕴涵算子满足信息有界性原则。这一结论对于在实际控制应用中,如何给定命题间的广义相关系数h值具有重要的指导意义。

This paper discusses comprehensively if the l-level universal implication operators satisfy the information boundedness principle based on linear specificity measure in fuzzy reasoning. And some important conclusions are proposed ： if there is positive measure errors , 1-level Universal implication operators satisfy the information boundedness principle only if fuzzy propositions are rejecting or restraining correlative; if there is negative ones, the operators satisfy the principle only if they are restraining correlative. This conclusion has important directive meaning for how to give the value of the general correlative coefficient h in practical control application.