λ-弱蕴涵及其在模糊推理中的应用

λ-Weak Implications and Its Application in Fuzzy Reasoning

针对现有模糊蕴涵算子对于变元取值差异不敏感的问题,本文引入了一种新的蕴涵算子:λ-弱蕴涵.首先.给出了λ-弱蕴涵的两种合成方式;其次,给出了三类λ-弱蕴涵族弱蕴涵族、f-生成弱蕴涵族和生成λ-弱蕴涵族,并讨论了每类λ-弱蕴涵的左单位元性质,交换性、有序性以及关于模糊否定的换置位对称性等代数性质;最后,将λ-弱蕴涵应用于全蕴涵三I算法,针对一类特定的λ-弱蘊涵算子,建立了α-ЗIλ算法并分析算法的还原性.

In this paper,a new implication operator:λ-weak implication is introduced to solve the problem that the existing fuzzy implication operators are not sensitive to the diference of argument values.First,two ways of synthesizing λ-weak implication are given.Secondly,three types of λ-weak implication families are presented,i.e,(F,N)-α-weak implication family,f-generated-λ-weak implication family and g-generated-λ-weak implication family,and the algebraic properties of these implication families,such as left neutrality property,exchange principe,ordering property and the contrapositive symmetry with respect to fuzzy negation are discussed.Finally,the λ-weak implication is applied to the full implication reasoning algorithm,and the algorithm is es-tablished based on a special type of λ-weak implication operators and the reducibility of the algorithm is analyzed.