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Siegfried Weber 《Fuzzy Sets and Systems》1984,13(3):247-271
The measures presented in this paper are defined by using Weber's concept of decomposable measures m of crisp sets, having in particular the Archimedean decomposable operations in view (Section 2). Measures of fuzzy sets are introduced as integrals with respect to m. For the Archimedean cases, Weber's integral will be used as alternative to Sugeno's and Choquet's concepts (Section 3). What ‘fuzziness’ means will be described by functions of fuzziness F (another name: entropy N-functions) with respect to a negation. In addition to the types of functions of fuzziness which are induced by concave functions, we discuss also the ones which are induced by fuzzy connectives (Section 4). Now, using m for measuring the ‘importance of items’ and F for the ‘fuzziness’ of the possible values of a fuzzy set ?, m?(F ° ?) serves us as a measure of the fuzziness ? of ?. The concepts of De Luca and Termini, Capocelli and De Luca, Kaufmann, Knopfmacher, Loo, Gottwald, Dombi and, under the restriction to the Archimedean cases, also the concepts of Trillas and Riera and Yager turn out to be special cases (Section 5). 相似文献
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J. Dombi 《Fuzzy Sets and Systems》1982,8(2):149-163
In this paper we examine operators which can be derived from the general solution of functional equations on associativity. We define the characteristics of those functions f(x) which are necessary for the production of operators. We shall show, that with the help of the negation operator for every such function f(x) a function g(x) can be given, from which a disjunctive operator can be derived, and for the three operators the DeMorgan identity is fulfilled. For the fulfillment of the DeMorgan identity the necessary and sufficient conditions are given.We shall also show that an fλ(x) can be constructed for every f(x), so that for the derived kλ(x,y) and dλ(x,y) limλ→∞kλ(x,y) and limλ→∞dλ(x,y) = max(x,y).As Yager's operator is not reducible, for every λ there exists an α, for which, in case x < α and y<α, kλ(x,y) = 0.We shall give an f(x) which has the characteristics of Yager's operator, and which is strictly monotone.Finally we shall show, that with the help of all those f(x), which are necessary when constructing a k(x,y), an F(x) can be constructed which has the properties of the measures of fuzziness introduced by A. De Luca and S. Termini. Some classical fuzziness measures are obtained as special cases of our system. 相似文献
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概率统计是大学数学的基础课程之一,我们通过具体的例子分析了概率统计课程教学应该重视的几个问题,并提出了解决问题的建议.这对概率统计课程的教学有一定的借鉴意义. 相似文献
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For nilpotent quantum groups [as introduced by Franz et al.
(7)], we show that (in sharp contrast to the classical case) the symmetrization
of a probability distribution and the first moments of together determine uniquely the original distribution . 相似文献
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浅谈概率论与数理统计的教学 总被引:6,自引:0,他引:6
概率论与数理统计跟其它的数学分支课程相比,有其特殊的思维模式.本文主要从激发学生学习兴趣、平行概念类比教学、锻炼概率思维,N重视“辨误”数学四个方面阐述了如何搞好概率统计课的教学. 相似文献
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Philippe Smets 《Fuzzy Sets and Systems》1982,7(2):153-164
Axioms are proposed that could justify the natural definition of the probability of a fuzzy event initially given by Zadeh. They are based (1) on the postulate that the sum of the conditional probability of a fuzzy event and of its complement given any fuzzy event adds to one or (2) on soft independence for orthogonal sets with independent constitutive elements. A general postulate is also required concerning the complement of a fuzzy set. The classical definition of the operator representing the complement can also be deduced. 相似文献
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Xicheng Zhang 《随机分析与应用》2013,31(6):1129-1150
Abstract This article is devoted to the study of the probability measure solutions to the spatially homogeneous Boltzmann equations. First, we provide a measure theoretical treatment to the Boltzmann collision operator. Then, the existence results both for the cutoff kernels and the non cutoff ones are established in the sense of measure-valued solutions. We also give a partial uniqueness result and some estimates for pth order moment (p > 2). 相似文献
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Probability dominance in random outcomes 总被引:2,自引:0,他引:2
An intuitively appealing probability dominance relation for random outcomes is defined and investigated. Its properties, strengths, and weaknesses relative to stochastic dominance and meanvariance dominance are studied. It is shown that the proposed probability dominance complements existing solution concepts and strengthens one's confidence in decision making under uncertainty. Fundamental characteristics of nondominated random payoffs and methods for identifying them, for both general and specific classes, are reported. Application pitfalls and possible extensions are also discussed. 相似文献
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We prove that the functor of Radon probability measures transforms any open map between completely metrizable spaces into a soft map. This result is applied to establish some properties of Milyutin maps between completely metrizable spaces. 相似文献
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IstvanSzalkai和DanVelleman讨论了与抛掷非均匀硬币的概率有关的一类模拟问题,提出一个尚未解决的无理概率的模拟问题:若q和r是(0,1)内的代数数,是否存在数p∈(0,1),使得p可同时模拟q和r?本文对这一问题进行了讨论,得到了相应的结果. 相似文献
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利用势为3的非均匀概率空间的无穷乘积在三值标准序列逻辑系统中引入了公式的概率真度概念,证明了全体公式的概率真度值之集在[0,1]中没有孤立点;利用概率真度定义了概率相似度和伪距离,进而建立了概率逻辑度量空间,证明了该空间中没有孤立点,为三值命题的近似推理理论提供了一种可能的框架. 相似文献
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In this paper, we propose an efficient technique for linearizing facility location problems with site-dependent failure probabilities, focusing on the unreliable p-median problem. Our approach is based on the use of a specialized flow network, which we refer to as a probability chain, to evaluate compound probability terms. The resulting linear model is compact in size. The method can be employed in a straightforward way to linearize similarly structured problems, such as the maximum expected covering problem. We further discuss how probability chains can be extended to problems with co-location and other, more general problem classes. Additional lower bounds as well as valid inequalities for use within a branch and cut algorithm are introduced to significantly speed up overall solution time. Computational results are presented for several test problems showing the efficiency of our linear model in comparison to existing problem formulations. 相似文献
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保险市场中存在激烈的竞争,针对这种情形提出竞争型的n元风险模型,定义了两种破产时间,利用经典风险模型已有结论和条件期望的性质,得到相应的有限时间破产概率和最终破产概率表达式,以及每个保险公司有限时间破产概率和最终破产概率. 相似文献
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本文在Black-Scholes金融市场设置下,基于概率准则,研究连续时间金融市场最优动态资产组合的选择问题,导出了最优解的显式表达式,对结论给出了金融学解释,所得结果可以方便地应用于投资决策与管理实践中。 相似文献