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1、复合模糊命题中基于弱逻辑的拟三角模算子研究第3O卷第6期2007年6月计算机CHINESEJOURNALOFCOMPUTERSVo1.3ONo.6June2007复合模糊命题中基于弱逻辑的拟三角模算子研究李爱平吴泉源(国防科学技术大学计算机学院长沙410073)摘要修正了,范数的概念,指出了符合弱逻辑关系的算子实际上是一种拟三角模算子中的Uninorm算子,接着给出了严格弱逻辑关系的拟三角模算子概念,在提出概念时,考虑了多维,基于单一数值和基于区间值以及加权的情况,并证明了符合弱逻辑关系的连续拟三角模算子是不存在的;给出了弱逻辑拟三角模算子的具体形式,给出了具体的四类弱逻辑关系的
2、拟三角模算子,讨论了它们的性质,并进行了比较;定义了评价算子的边缘性测度和敏感性测度,对各算子进行了对比和评价.结果表明,文中给出的弱逻辑拟三角模算子可以在不同应用背景下,有效地处理不同类型的复合模糊命题真值运算,也可以在其它的模糊系统中有效处理多个模糊子集之间的聚集运算.关键词复合模糊命题;拟三角模算子;弱逻辑关系;边缘性测度;敏感性测度中图法分类号TP18AStudyoftheGeneralizedTriangularNormBasedonWeakLogicinCompoundFuzzyPropositionLIAi～PingWUQuan—Yuan(SchoolofCompu
3、terScience?NationaliversityofDelenseTechnology.Changsha410073)AbstractDuringthedevelopmentoffuzzyexpertsystemandfuzzycontrolsystems,weshoulddealwiththeaggregationatomicpropositionsincompoundfuzzypropositions.Besidesthecorn—monrelationshipoftheatomicproposition,whichisconjunction,disjunctionan
4、dweightedaver—ageoperator,thereisanimportantweaklogicoperator.Firstly,theauthorsamendthedefinition0ffnormsinthepaperappearedbyAnShi—Hu:pointouttheweaklogicoperatorisageneralizedtriangularnorm,givethedefinitionofweaklogicgeneralizedtriangularnormoperatorandstrictweaklogicgeneralizedtriangularn
5、ormoperator,includingbothnumericalvalueandintervalofnumerica1values,multi-dimensionformoperatorarealsodiscussed.Theweightsassociatedwiththeatomicpropositionarealsoconsideredintheforms.Thenaproofofcontinuousgeneralizedtriangularnormoperatorthatassociatedwithweaklogicdoesnotexistisprovided.Seco
6、ndly,thedetailformgeneralizedtriangularnormoperatorbasedonweaklogicisgiven,fourtypesofgen—eralizedtriangularnormoperatorbasedonweaklogicarebroughtforward.Characteristicsoftheoperatorsarediscussed.Thirdly,tWOmeasuresassociatedwiththeoperatorsaredefined,oneiSmargina1measureandtheotheriSsensitiv
7、emeasure.Basedonthemeasure,therelationshipsofthoseoperatorsandclassicaloperatorsareevaluatedandcompared.Theresuitshowsthattheop—eratorsofferanewmethodtOaggregationoffuzzyatomicpropositions(multi?fuzzyinputsinfuzz—?Ycontro1systems)infuzzyenvir
