基于区间值模糊推理的三Ⅰ算法的研究-基础数学专业论文.docx

曲北人学硕十学何论文摘 曲北人学硕十学何论文 摘 要 1965年，Zadeh教授建立了模糊集理论，奠定了模糊数学理论和应用的基础， 并于1973年针对FMP模型提出了著名的CRI方法。此后，王国俊教授指出了 CRl方法的若干缺陷与不足，提出了一种更合理，逻辑基础更强的模糊推理方法 ．三I方法。20世纪80年代初波兰学派提出了区间分析与模糊集方法结合使用有 更好的效果，因而区间值模糊集(以下简称IVFS)的概念被提出并被使用于模 糊推理。近年来区间值模糊推理备受人们关注，至今为止，已提出了多种模糊推 理方法。本文则主要研究了区间值模糊推理的三I方法，并且指出一般模糊推理 是在区f’lIJ值退化为点时的特殊区问值模糊推理。 本论文的结构和主要研究内容如下： 第一章介绍了模糊推理的发展、研究现状及一般蕴涵算子和≯角模的一些 性质。 第二章介绍了区间值及区间值模糊集的基本概念，并且给出了区问值上=蕴涵 算子和三角模的定义及一些性质。 第三章介绍了区间值模糊推理的三I算法及其还原性，区问值模糊推理的反 向三I算法，并且在一定条件下讨论了区间值模糊推理的j I约束算法。因此说 明了一般模糊推理是在区『刚值退化为，一_时的特殊区|’白J值模糊推理，从而把一般模 糊推理纳入于区间值模糊推理的框架之内。 关键词：区间值；模糊推理；三I算法；还原性 两北人学硕十学位论文TripJe 两北人学硕十学位论文 TripJe I Method of Interval一、，alued Fuzzy R昀SOIling Abstract The theory and application of fuzzy mathematics was based on fuzzy sets theory whjch was established by Zadeh in 1 965，and famOus CRI method for FMP was proposed by him in l 973．T．hen Wang Guo J set fbrth a new t“ple I method fbr the defect of CRI method．This new method is more reasonable and has better 109ic foundation．Polish put fonVard that the conjunction of jnten，al analysis and fuzzy set method has betterresult in the early 1 980’s，so interVal-Valued fuzzy set(IVFS)was proVided and was appljed in fUzzy reasonjng．In recent years，it has gained extensiVe attention and Various fIlzzy reasoning methods haVe been giVen．This text mainly studies the triple l method of interval-Valued fllzzy reasoning，and points out that the flJzzy reasoning is special inteⅣal—Valued fhzzy reasoning on condition that lhe interval degenerates into point． The main results，obtained in this disse九ation，may be summarjzed as follows： In the first chapter，an intmduction is first百Ven to the deVelopment，and some propenies of implication operator and triangle norm are reViewed． 1n lhe second chapter，the basis concepts of interVal-Valued fbzzy sets are giVen， and new definition of interval—valued implicatjon operator and triangle nonn is proposed，then some properties are proVed． 1n the third chapter，the triple I method and its reVersibility and t