双枝模糊集(Ⅲ)

提出双枝模糊集Ｓ的理论,本课题是［Ⅰ,Ⅱ］研究的继续．在单枝模糊集理论（Ｌ．Ａ．ＺａｄｅｈＦｕｚｚｙＳｅｔＴｈｅｏｒｙ）研究中,由于引进λ－截集Ｓλ的概念,便产生了单枝模糊集的并－普通分解定理［３］,交－普通分解定理［４］．［Ⅰ,Ⅱ］提出了双枝模糊集Ｓ,由于引进了λ－截集Ｓλ的概念,便产生了双枝模糊集Ｓ的并－普通分解定理,交－普通分解定理．人们自然提出这样的问题：双枝模糊集可以分解成若干个普通集Ｓλ;双枝模糊集Ｓ是否能分解成若干个模糊集Ｓα？本文的研究说明：双枝模糊集Ｓ可以分解成若干个模糊集Ｓα．（一个单枝模糊集Ａ也可以分解成若干个模糊集Ａα,但是在单枝模糊集理论中没有被人们去研究．）本文给出Ｓ的α－嵌入集Ｓα的概念,提出Ｓ的α－嵌入定理,Ｓ的α－嵌入模糊分解定理．     

双枝模糊集(Ⅱ)

提出双枝模糊集Ｓ的理论,是（Ｉ）研究的继续．提出双枝模糊集Ｓ的并－普通分解定理,交－普通分解定理．这些结论建立了双枝模糊集Ｓ与普通集Ｓλ之间的关系,这些结论为建立双枝模糊推理,双枝模糊控制作了理论准备．结论指出：（１）双枝模糊集Ｓ同时存在并－普通分解形式：Ｓ＝∪λ∈［－１,１］λＳλ和交－普通分解形式：Ｓ＝∩λ∈［－１,１］λＳλ;这两种分解形式是建立双枝模糊推理理论,双枝模糊控制理论的理论基础．（２）单枝模糊集Ａ（Ｌ．Ａ．ＺａｄｅｈＦｕｚｚｙＳｅｔＡ）的并－普通分解定理,交－普通分解定理是双枝模糊集Ｓ的并－普通分解定理,交－普通分解定理的特例．     

含模糊变量结构的可靠性分析方法

针对基本变量具有随机和模糊不确定性的结构,在模糊随机失效概率计算的通用数字模拟方法基础上,推导模糊随机失效概率数字模拟解的方差和变异系数的计算公式.由于正态型模糊隶属函数情况下的模糊随机失效概率可以转化为随机失效概率的计算,对于工程中常用的对称三角型隶属函数,探讨两种对称三角型隶属函数等价为正态型隶属函数的近似方法,其一是"3σ规则"法,其二是"最大最小"法.理论分析和算例结果表明,"最大最小"法能使得等价正态隶属函数较好地在函数形状上替代对称三角型隶属函数,因此"最大最小"法更适用于对称三角型隶属函数情况下模糊随机失效概率的近似估计.     

基于子集抽样的模糊失效概率分析新方法

针对结构失效和安全状态具有模糊性的失效概率分析问题,提出一种基于子集抽样的新方法.所提方法首先将模糊失效域离散为功能函数变化较小的若干子集,然后利用马尔可夫链Monte Carlo法求得各子集上不考虑状态模糊性的随机失效概率,最后利用各子集中功能函数对模糊失效域的隶属度与相应随机失效概率乘积的和,求得模糊失效概率.文中用简单算例和工程算例比较所提方法与Monte Carlo法的效率和精度,结果表明,文中方法在保证计算精度的条件下,具有更高的计算效率.     

Parameter determination for a generalized fuzzy model

This paper underlines a way to evolve a generalized fuzzy model (GFM), using the interpolation of CRI and TS models in their consequent parts of fuzzy rules. The GFM possesses the index of fuzziness of CRI model and the local model of the TS model. The parameters of the GFM are estimated by a two-step process. The consequent part of fuzzy rules is reformulated to suit the LSE framework for estimating the associated parameters. By assuming Generalized Gaussian membership function for the premise parts, Gradient descent technique is used to update its parameters. The performance of two classes of GFM has been tested on two systems and it is shown that class II GFM is the best out of all the fuzzy models tested.     

汽车主动安全性的模糊优化设计

将安全极限状态设计、汽车系统动力学分析、主动安全性评价与模糊运算相结合，给出汽车安全性的模糊优化设计新方法，为汽车主动安全性优化设计提供了理论指导。     

On the absence of strict boundaries—Vagueness, haziness, and fuzziness in philosophy, science, and medicine

This contribution deals with developments in the history of philosophy, logic, and mathematics during the time before and up to the beginning of fuzzy logic. Even though the term “fuzzy” was introduced by Lotfi A. Zadeh in 1964/1965, it should be noted that older concepts of “vagueness” and “haziness” had previously been discussed in philosophy, logic, mathematics, applied sciences, and medicine. This paper delineates some specific paths through the history of the use of these “loose concepts”. Vagueness was avidly discussed in the fields of logic and philosophy during the first decades of the 20th century—particularly in Vienna, at Cambridge and in Warsaw and Lvov. An interesting sequel to these developments can be seen in the work of the Polish physician and medical philosopher Ludwik Fleck.Haziness and fuzziness were concepts of interest in mathematics and engineering during the second half of the 1900s. The logico-philosophical history presented here covers the work of Bertrand Russell, Max Black, and others. The mathematical–technical history deals with the theories founded by Karl Menger and Lotfi Zadeh. Menger's concepts of probabilistic metrics, hazy sets (ensembles flous) and micro-geometry as well as Zadeh's theory of fuzzy sets paved the way for the establishment of soft computing methods using vague concepts that connote the nonexistence of sharp boundaries.     

Towards a formal taxonomy of hybrid uncertainty representations

In this paper we present some ideas about how to formally relate various uncertainty representations together in a taxonomic structure, capturing both syntactic and semantic generalization. Fuzziness and nonspecificity are presumed as primitive concepts of uncertainty, and transitive and intransitive methods operating with nonspecificity and fuzziness are introduced to generate a base class of hybrid uncertainty representational forms. Additive, maximal, and interval constraints then complete the characterization of the most important hybrid forms.     

起重机可靠性指标的综合评定

采用模糊物元分析方法,对起重机的多项可靠性进行物元关联变换和不同评定等级贴近度的计算定量确定不同生产厂和不同生产批最的起重机可靠性综合评价值,最终得到起重机可靠性的综合整体水平排序和质量分等结果。     

工程模糊随机结构失效模式的确定方法

根据模糊数学中的有关定义,提出在考虑模糊因素影响时,利用λ-截集法将模糊随机结构的极限状态方程转化为普通的随机集上的极限状态方程,然后用响应面方法确定结构失效模式的新方法,计算与分析表明,该方法的求解范围比一般的随机有限元方法广,而且几乎可以不加限制地与其他算法例如有限元、边界元、有限差分法等相结合。因而具有较好的应用价值。