λ-弱蕴涵及其在模糊推理中的应用  

λ-Weak Implications and Its Application in Fuzzy Reasoning

作　　者：付凯 潘小东[1] 申涵寒 FU Kai;PAN Xiao-dong;SHEN Han-han(School of Mathematics,Southwest Jiaotong University,Chengdu,Sichuan 610031,China)

机构地区：[1]西南交通大学数学学院,四川成都610031

出　　处：《模糊系统与数学》2024年第1期1-15,共15页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金(61673320:61976130),四川省应用基础研究计划项目.

摘　　要：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.

关 键 词：λ-弱蕴涵 聚合函数 生成子 模糊推理三I算法 支持度理论 

分 类 号：O178[理学—数学]