摘要
提出了模糊蕴涵算子族的新概念,给出了两族蕴涵算子:L-λ-R0(λ∈[1/2,1])族算子与L-λ-G(λ∈[0,1])族算子.L-λ-R0(λ∈[1/2,1])族算子包括Lukasiewicz(简称Rlu)算子与R0算子,L-λ-G(λ∈[0,1])族算子包括Rlu算子与Gdel(RG)算子.重点讨论了L-λ-R0(λ∈[1/2,1])族算子的伴随算子及其正则性.结果表明,在蕴涵算子族L-λ-R0(λ∈[1/2,1])中,只有RLu算子与R0算子有伴随算子且具有正则性,从而说明这两种算子是较理想的蕴涵算子.最后讨论了其应用,同时提出了命题的置信区间及其可信度的新概念.
In the paper the new concept of family of fuzzy implication operators are introduced, and two new families of fuzzy implication operators are given, which are denoted by L-λ- R0（λ∈ [1/2,1]） and L-λ-G（λ∈[-0,1]）. Lukasiewicz operator Rlu and operator R0 are included in L-λ-R0（λ∈ [1/2,1]）, Lukasiewicz operator Rlu and operator Goedel （simple denoted RG）are included in L-λ-R0（λ∈ [1/2,1]）. We mainly discuss reguiarity of L-λ-R0（λ∈[1/2,1]）and the residua of L-λ-R0（λ∈ [1/2,1]）with its t-norms. The result indicates that only Lukasiewicz operator Rlu and operator R0 inL-λ-R0（λ∈ [1/2,1]）have residual t-norms and satisfy regularity. Consequently, this two operators are ideal. Finally, the applications of L-λ-R0 （λ ∈ [1/2,1]） in fuzzy reasoning are investigated. In addition, the new concept of believable interval and believable degree of proposition is presented.
出处
《计算机学报》
EI
CSCD
北大核心
2007年第3期448-453,共6页
Chinese Journal of Computers
基金
山东省自然科学基金(Y2003A01)资助.
关键词
蕴涵算子族
伴随算子
正则性
置信区间
可信度
family of implication operators
residual operators
regularity
believable interval
believe degree
