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1.
Mila Stojakovi? 《Journal of Computational and Applied Mathematics》2011,235(16):4524-4531
Set valued probability and fuzzy valued probability theory is used for analyzing and modeling highly uncertain probability systems. In this paper the set valued probability and fuzzy valued probability are defined over the measurable space. They are derived from a set and fuzzy valued measure using restricted arithmetics. The range of set valued probability is the set of subsets of the unit interval and the range of fuzzy valued probability is the set of fuzzy sets of the unit interval. The expectation with respect to set valued and fuzzy valued probability is defined and some properties are discussed. Also, the fuzzy model is applied to binomial model for the price of a risky security. 相似文献
2.
We define the concept of fuzzy measure of a fuzzy event by using a general form of fuzzy integral proposed by Murofushi, called fuzzy t-conorm integral, encompassing previous definitions. Zadeh defined the probability measure of a fuzzy event, and later the possibility measure of fuzzy event. Using a duality property of fuzzy t-conorm integral, we propose a general definition of fuzzy measure of fuzzy events, which is compatible with previous definitions of Zadeh, and possesses all properties of a fuzzy measure, in particular the duality property. Using our definition, we examine the case of decomposable measures and belief functions. A comparison with previous works is provided. 相似文献
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In [4] Höhle has defined fuzzy measures on G-fuzzy sets [2] where G stands for a regular Boolean algebra. Consequently, since the unit interval is not complemented, fuzzy sets in the sense of Zadeh [8] do not fit in this framework in a straightforward manner. It is the purpose of this paper to continue the work started in [5] which deals with [0,1]-fuzzy sets and to give a natural definition of a fuzzy probability measure on a fuzzy measurable space [5]. We give necessary and sufficient conditions for such a measure to be a classical integral as in [9] in the case the space is generated. A counterexample in the general case is also presented. Finally it is shown that a fuzzy probability measure is always an integral (if the space is generated) if we replace the operations ∧ and ∨ by the t-norm To and its dual S0 (see [6]). 相似文献
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结构的失效可能度及模糊概率计算方法 总被引:2,自引:1,他引:1
依据模糊可能性理论,系统地建立含模糊变量时结构的可靠性计算模型。旨在解决模糊结构、模糊-随机结构和模糊状态假设下结构的可靠性计算问题。所建模型可给出模糊结构失效的可能度和模糊-随机结构失效概率的可能性分布。研究表明:对同时含模糊变量和随机变量的混合可靠性计算问题,把失效概率(或可靠度)作为模糊变量,能更客观地反映系统的安全状况。算例分析说明了文中方法的合理性和有效性。 相似文献
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《Journal of Mathematical Analysis and Applications》1987,122(1):265-299
Baer1-semigroups are regarded as the main abstract structures for an algebraic analysis of complex fuzzy events in generalized probability theory. This assumption is verified in the case of classical probability theory in the framework of measure and integration theory. The corresponding fuzzy language is extended to the non-commutative probability theory based on operators in Hilbert space.Starting from a quantum information system a quantum probability space is constructed, which is naturally embedded in a classical information system. In this last both exact than fuzzy quantum events are represented as classical fuzzy events. Lastly, the classical fuzzy events which correspond to exact quantum events are characterized by some minimality properties. 相似文献
7.
In this paper we study the question whether, given a fuzzy measure (as defined in [3] and [4]). there exists a classical measure such that the fuzzy measure of a measurable fuzzy set μ equals the classical measure of the area below the membership function of μ. The results are that in the case of finite additivity there is a one-to-one correspondence between classical measures and fuzzy measures, whereas in the case of countable additivity this result only holds for generated fuzzy σ-algebras. Finally, some connections of that problem with the existence of an extension of a fuzzy measure defined on an arbitrary fuzzy σ-algebra σ to the generated fuzzy σ-algebra are discussed. 相似文献
8.
针对属性信息为区间Pythagorean模糊集且属性权重和专家权重均未知的一类群决策问题, 结合信息熵理论, 提出了一种区间Pythagorean模糊VIKOR多属性群决策方法。首先定义一种新的区间Pythagorean模糊距离测度, 并讨论其性质。其次基于该距离测度定义了区间Pythagorean模糊相对距离指数, 并基于相对距离指数构建了一种熵权模型确定专家权重和属性权重。然后提出一种区间Pythagorean模糊VIKOR多属性群决策方法。最后通过企业生产方案选择案例说明了提出新方法的可行性与有效性。 相似文献
9.
基于可能度的一种直觉模糊集相似度测量方法 总被引:1,自引:0,他引:1
研究直觉模糊集的相似度测量方法. 首先给出两个直觉模糊数比较的可能度公式及其性质. 在此基础上, 定义两个直觉模糊集间的相似度测量公式, 分析用此公式进行相似度测量的优缺点, 旨为直觉模糊集在决策、模式识别和医疗诊断中的应用提供更为合理的工具. 相似文献
10.
In this paper, contributions to fuzzy probability and to differential equations with fuzzy parameters are made.After an introductory section, a review of fuzzy sets and fuzzy algebra is given in Section 2. The main new results of the investigation are contained in Section 3.In Section 3, Zadeh's definition of the probability of a ‘fuzzy event’ the average value of a fuzzy function are extended into the time domain. It is then shown that not only grades of membership, but also probabilistic processes with notions of fuzziness contained, can be defined which obey ordinary, matric, or integro-differential equations. Applications are also given in Section 3. 相似文献
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Roman Frič 《Mathematica Slovaca》2007,57(1):41-58
In probability theory, each random variable f can be viewed as channel through which the probability p of the original probability space is transported to the distribution p
f
, a probability measure on the real Borel sets. In the realm of fuzzy probability theory, fuzzy probability measures (equivalently
states) are transported via statistical maps (equivalently, fuzzy random variables, operational random variables, Markov kernels,
observables). We deal with categorical aspects of the transportation of (fuzzy) probability measures on one measurable space
into probability measures on another measurable spaces. A key role is played by D-posets (equivalently effect algebras) of fuzzy sets.
Supported by VEGA 1/2002/06. 相似文献
14.
The concept of fuzzy Galois connections is defined on fuzzy posets with Bělohlávek's fuzzy Galois connections as a special case. The properties of fuzzy Galois connections are investigated. Then the relations between fuzzy Galois connections and fuzzy closure operators, fuzzy interior operators are studied. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
犹豫模糊集的截集及其性质 总被引:1,自引:0,他引:1
谢海 《数学的实践与认识》2017,(3):251-258
通过引入犹豫模糊集的截集概念并研究截集的性质,建立了沟通犹豫模糊集合与经典集合之间的桥梁.进一步,讨论了犹豫模糊关系的截关系及其性质. 相似文献
16.
Theory of T-norms and fuzzy inference methods 总被引:3,自引:0,他引:3
In this paper, the theory of T-norm and T-conorm is reviewed and the T-norm, T-conorm and negation function are defined as a set of T-operators. Some typical T-operators and their mathematical properties are presented. Finally, the T-operators are extended to the conventional fuzzy reasoning methods which are based on the
and
operators. This extended fuzzy reasoning provides both a general and a flexible method for the design of fuzzy logic controllers and, more generally, for the modelling of any decision-making process. 相似文献
17.
In this paper a concept of fuzzy multi-valued function is introduced and other related objects are defined. Next their properties, that assume no topological structure, are presented. 相似文献
18.
提出了联盟模糊收益合理分配的一种新方法.首先,在模糊收益α截集上定义了α合理分配集,分析了该分配集与模糊收益Shapley值的关系.接着,给出了模糊收益的α合理Shapley分配函数,对其性质进行了讨论.然后,构造了模糊合理Shapley分配,证明其连续性,得到了联盟模糊收益与模糊合理Shapley分配具有包含关系的结论. 相似文献
19.
本文给出了衡量模糊连通性的三个工量:模糊连通度,模糊边连通度与模糊核度及其相关的性质。与普通图连通性的分析相比较,由于考虑了模糊性,这三个量能更好,更深入地刻划出不同的图在连通性方面的微妙差异。 相似文献