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1、河北工业大学 硕士学位论文 基于R-Fuzzy集的模糊决策 姓名：邢晓儒 申请学位级别：硕士 专业：应用数学 指导教师：米洪海 20091201 ? ? R-Fuzzy? ? R-Fuzzy? ?Zadeh Fuzzy? Fuzzy? R-Fuzzy?Fuzzy? ?Zadeh Fuzzy? R-Fuzzy?Fuzzy? ?Zadeh Fuzzy? R-Fuzzy? ? ? ? ?0,1? R? ? R-Fuzzy? ? R-Fuzzy? ? ?Zadeh Fuzzy? ? ? ? R-Fuzzy? R-Fuzzy? ? R-Fuzzy? ? R-Fuzzy? ? R-Fuzzy? i ? R
2、-Fuzzy? FUZZY DECISIONBASED ON R-FUZZY SETS ABSTRACT R-fuzzy sets is a late-model fuzzy conception recently raised by professor Li Hongxing when he studied the control problem of complex system. It is the expansion of the well- known Zadeh Fuzzy sets, and also considers Both-branch fuzzy sets as par
3、ticular case. Based on R-fuzzy sets,Empowerment fuzzy sets is raised. It is the expansion of Zadeh Fuzzy sets as well, and also considered as special style of R-fuzzy sets and Intuitionistic fuzzy sets. This paper put forth eff ort on popularizing to R-fuzzy sets from Zadeh Fuzzy sets, and made a st
4、rategic decision on the basis of factor space. On the process of being based upon decision making of feedback extension, feedback extension need to be made more meticulous. That would need a tool for ”polishing angular” T-norm. This paper took T-norm as the sally port.Through the changes of universe
5、 of dis- course, namely popularize to R from 0,1, based on the factor space and rised to R-fuzzy sets by founding on the decision of feedback extension, thereby the strategic decision of R-fuzzy sets would achieve. This paper includes the following four main parts: Part one: Genneral introduction fo
6、r the cause and developing situations of Zadeh Fuzzy sets and factor space; Part two: emphasis on factor space theory by Li Hongxing, and pull into the tool for ”polishing angular” T-norm; Part three: pulling into the concepts and related characteristics of R-fuzzy sets and Implication Operator, and
7、 providing the concepts of T-norm and studying its characteristics on the basis of R-fuzzy sets; Part four: mainly studying the fuzzy decision theory based on R-fuzzy sets. KEY WORDS: R-Fuzzy sets, factor space ,feedback extension, T-norm, fuzzy de- cision ii ? R-Fuzzy? ? X? P(X)X? F(X)X? C? X(f)? F
8、? (U,C,X(f)(fF)?C? R? RXR-Fuzzy? BF(X)X?Fuzzy? T-norm? co-T-norm? R-T-norm? co-R-T-norm? Tm-normm? co-Tm-normm? R-Tm-normm? co-R-Tm-normm? iv ? ? 1-1? ? 1965?L.A.Zadeh? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?1981?1? ?2? ? ? ? ? ? ? ? ?STIM? ? ? ? ? ? ? ? ? ? ? ? ? 1 ? R-Fuzzy? ? ? ? ? ? ? 1996? ? ? ?DFE ? ? R- Fuzzy? 1-2? ? (1)? R-Fuzzy? R-Fuzzy? (2)? R-Fuzzy? (3)? R-Fuzzy? ? ? R-Fuzzy? R-Fuzzy? 2 ? ? ?1981?1? ?2?7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20? ? 2-1? ? ?3? ? ? ?7? 1)? ? ?
