共查询到20条相似文献,搜索用时 125 毫秒
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A short survey is given of some directions in probability theory that have developed most intensively in recent years. Separable statistics and criteria for the verification of statistical hypotheses based on them, various schemes for distributing particles among cells, and problems connected with estimating the unknown size of a finite collection are considered.Translated from Itogi Nauki i Tekhniki, Seriya Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 22, pp. 3–60, 1984. 相似文献
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Construction companies use composite indicators (CIs) to evaluate their overall project performance. However, the conventional methodology of CIs development causes indiscrimination, relative calibration, and redundancy. To address these problems, we propose a novel methodology that uses fuzzy theories. The proposed methodology includes a utility function for normalizing, a fuzzy measure for weighting, and a fuzzy integral for aggregating. We conducted a case study to assess the quality of the proposed methodology versus the alternative methodologies on 25 real projects of a construction company. The result showed that the measurement reliability of the proposed normalization method (1.96) is greater than that of the two different normalization methods (10.44 and 2.8, respectively). In addition, the measurement accuracy of the proposed aggregation method is greater than those of the four different aggregation methods. Therefore, our proposed methodology can more consistently and accurately help evaluate the overall project performance or success. 相似文献
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On the basis of fuzzy sets theory, we propose a method for structuring hierarchy for the several complex problems, and call it Fuzzy Structural Modeling (FSM) method. An important requirement for structural modeling of complex systems is that the necessary data is acquired and organized into a form such that a structural model can be developed. The main purpose of this method is to describe and illustrate a formal procedure for constructing the graphic presentation of the hierarchical arrangement given the necessary information concerning the relation of each element to each other element. The procedure permits an automatic development of the graphic structure that portrays the hierarchy. 相似文献
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Adel Hatami-Marbini Saber Saati Seyed Mojtaba Sajadi 《Central European Journal of Operations Research》2018,26(4):909-932
Two-stage data envelopment analysis (TsDEA) models evaluate the performance of a set of production systems in which each system includes two operational stages. Taking into account the internal structures is commonly found in many situations such as seller-buyer supply chain, health care provision and environmental management. Contrary to conventional DEA models as a black-box structure, TsDEA provides further insight into sources of inefficiencies and a more informative basis for performance evaluation. In addition, ignoring the qualitative and imprecise data leads to distorted evaluations, both for the subunits and the system efficiency. We present the fuzzy input and output-oriented TsDEA models to calculate the global and pure technical efficiencies of a system and sub-processes when some data are fuzzy. To this end, we propose a possibilistic programming problem and then convert it into a deterministic interval programming problem using the α-level based method. The proposed method preserves the link between two stages in the sense that the total efficiency of the system is equal to the product of the efficiencies derived from two stages. In addition to the study of technical efficiency, this research includes two further contributions to the ancillary literature; firstly, we minutely discuss the efficiency decompositions to indicate the sources of inefficiency and secondly, we present a method for ranking the efficient units in a fuzzy environment. An empirical illustration is also utilised to show the applicability of the proposed technique. 相似文献
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Arnab Kumar Laha 《International Journal of Mathematical Education in Science & Technology》2013,44(4):502-503
In this note a new proof of the divergence of the harmonic series is given based on the expected life of a parallel system with independent exponentially distributed component lifetimes. 相似文献
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Shandong University Ji''''nan China Department of Mathematics Statistics Memorial University of Newfoundland HH St. John''''s AC S Canada 《中国科学A辑(英文版)》2006,49(3):387-397
Semi-stable distributions, in classical probability theory, are characterized as limiting distributions of subsequences of normalized partial sums of independent and identically distributed random variables. We establish the noncommutative counterpart of semi-stable distributions. We study the characterization of noncommutative semi-stability through free cumulant transform and develop the free semi-stability and domain of semi-stable attraction in free probability theory. 相似文献
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For continuous random variables, we study a problem similar to that considered earlier by one of the authors for discrete random variables. Let numbers $$N > 0, E > 0, 0 \leqslant \lambda _1 \leqslant \lambda _2 \leqslant \cdots \leqslant \lambda _s $$ be given. Consider a random vector x = (x 1, …, x s), uniformly distributed on the set $$x_j \geqslant 0, j = 1, \ldots ,s; \sum\limits_{j = 1}^s {x_j = N} , \sum\limits_{j = 1}^s {\lambda _j x_j \leqslant E} .$$ We study the weak limit of x as s → ∞. 相似文献
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We continue the investigation of noncommutative cumulants. In this paper various characterizations of generalized Gaussian random variables are proved.
Supported by the European Network No. HPRN-CT-2000-00116 and the Austrian Science Fund (FWF) Project No. R2-MAT. 相似文献
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Alladi Ramakrishnan 《Journal of Mathematical Analysis and Applications》1981,83(2):408-410
A new concept called “Disparity” between two distributions is introduced, which could be useful in the study of stochastic processes. It includes the concept of “Activity” introduced earlier by the author. 相似文献
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S. D. Chatterji 《Inventiones Mathematicae》1974,25(3-4):241-251
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《International Journal of Approximate Reasoning》2014,55(6):1383-1403
Since the Age of Enlightenment, most philosophers have associated reasoning with the rules of probability and logic. This association has been enhanced over the years and now incorporates the theory of fuzzy logic as a complement to the probability theory, leading to the concept of fuzzy probability. Our insight, here, is integrating the concept of validity into the notion of fuzzy probability within an extended fuzzy logic (FLe) framework keeping with the notion of collective intelligence. In this regard, we propose a novel framework of possibility–probability–validity distribution (PPVD). The proposed distribution is applied to a real world setting of actual judicial cases to examine the role of validity measures in automated judicial decision-making within a fuzzy probabilistic framework. We compute valid fuzzy probability of conviction and acquittal based on different factors. This determines a possible overall hypothesis for the decision of a case, which is valid only to a degree. Validity is computed by aggregating validities of all the involved factors that are obtained from a factor vocabulary based on the empirical data. We then map the combined validity based on the Jaccard similarity measure into linguistic forms, so that a human can understand the results. Then PPVDs that are obtained based on the relevant factors in the given case yield the final valid fuzzy probabilities for conviction and acquittal. Finally, the judge has to make a decision; we therefore provide a numerical measure. Our approach supports the proposed hypothesis within the three-dimensional contexts of probability, possibility, and validity to improve the ability to solve problems with incomplete, unreliable, or ambiguous information to deliver a more reliable decision. 相似文献
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This paper proposes algorithms to construct fuzzy probabilities to represent or model the mixed aleatory and epistemic uncertainty in a limited-size ensemble. Specifically, we discuss the possible requirements for the fuzzy probabilities in order to model the mixed types of uncertainty, and propose algorithms to construct fuzzy probabilities for both independent and dependent datasets. The effectiveness of the proposed algorithms is demonstrated using one-dimensional and high-dimensional examples. After that, we apply the proposed uncertainty representation technique to isocontour extraction, and demonstrate its applicability using examples with both structured and unstructured meshes. 相似文献
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Incomplete information is notoriously common in planning soil and groundwater remediation. For making decisions groundwater flow and transport models are commonly used. However, uncertainty in prediction arises due to imprecise information on flow and transport parameters like saturated/unsaturated hydraulic conductivity, water retention curve parameters, precipitation and evapo-transpiration rates as well as factors governing the fate of pollutant in soil like dispersion, diffusion, degradation and chemical transformation. Different methods exist for quantifying uncertainty, e.g. first and second order Taylor’s Series and Monte-Carlo method. In this paper, a methodology based on fuzzy set theory is presented to express imprecision of input data, in terms of fuzzy number, to quantify the uncertainty in prediction. The application of the fuzzy set theory is demonstrated through pesticide (endosulfan) transport in an unsaturated layered soil profile. The governing partial differential equation along with fuzzy inputs, results in a non-linear optimization problem. The solution gives complete membership functions for flow (suction head) and pesticide concentration in soil column. 相似文献
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Based on an analytical approach to the definition of multiplicative free convolution on probability measures on the nonnegative
line ℝ+ and on the unit circle we prove analogs of limit theorems for nonidentically distributed random variables in classical Probability Theory.
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One-parameter semigroups occurring in operator-limit distributions are investigated. The topological-algebraic background of the relevant monoids is discussed and Lie semigroup theory is applied to the Urbanik Decomposability Semigroup. 相似文献
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《Bulletin des Sciences Mathématiques》2001,125(6-7):623-640
The lowest eigenvalue λ(F) of a vector bundle F over a compact Riemannian manifold M is estimated in terms of the curvature of M and of the connection Γ on F. 相似文献