The Theoretical Methods of Constructing Fuzzy Inference Relations

Wang, Xiaoning; Yuan, Xiao; Li, Hongxing

doi:10.1007/978-3-540-88914-4_21

Cited by 3 publications

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“…It is well known that the cut sets of fuzzy sets play an important role in fuzzy algebra [1,2], fuzzy optimization and decision making [3,4], fuzzy reasoning [5][6][7] [8][9][10][11][12] and so on. The cut sets on Zadeh fuzzy set [13] are described by using the neighborhood relations between fuzzy point and fuzzy set and the four kinds of cut sets on Zadeh fuzzy set are acquired in [14].…”

Section: Introductionmentioning

confidence: 99%

Interval-valued Level Cut Sets of Fuzzy Set

Yuan

Sun

2011

Fuzzy Information and Engineering

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The connections between Zadeh fuzzy set and three-valued fuzzy set are established in this paper. The concepts of interval-valued level cut sets on Zadeh fuzzy set are presented and new decomposition theorems and representation theorems of Zadeh fuzzy set are established based on new cut sets. Firstly, four interval-valued level cut sets on Zadeh fuzzy set are defined as three-valued fuzzy sets and it is shown that the interval-valued level cut sets of Zadeh fuzzy set are generalizations of normal cut sets on Zadeh fuzzy set, and have the same properties as those of normal cut sets of Zadeh fuzzy set. Secondly, the new decomposition theorems are established based on these new cut sets. It is pointed out that each kind of interval-valued level cut sets corresponds to two decomposition theorems. Thus eight decomposition theorems are obtained. Finally, the definitions of three-valued inverse order nested sets and threevalued order nested sets are presented with eight representation theorems based on new nested sets.

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