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1.
Krzysztof Piasecki 《Fuzzy Sets and Systems》1985,17(3):271-284
In this paper the probability of fuzzy events is defined as a denumerable additivity measure. This definition is based on a non-conventional approach of separativity between fuzzy subsets. The presented measure fulfils all properties analogous to the properties of classical probability in the crisp case. Further, the notion of conditional probability of fuzzy events, complete fuzzy repartition and independent fuzzy events are defined by means of the probability measure considered here. Connections between all the above notions are presented in this paper, too. Finally, the Bayes formula is proved for the fuzzy case. 相似文献
2.
Ronald R Yager 《Fuzzy Sets and Systems》1984,13(3):273-283
A representation of the probability associated with a fuzzy subset is presented. This representation, which is itself a fuzzy subset of the unit interval, is defined by the intersection of an upper and lower bound on the probability of the fuzzy event. 相似文献
3.
Herbert TOTH 《模糊系统与数学》1989,(2)
This paper presents first results on fuzzy set theory (with the emphasis on probability theoretical aspects) from an operational viewpoint, a new approach that claims to be a way out of some of the difficulties and to present a consistent framework for the set-theoretical aspects of fuzzy set theory (e.g.the complementation paradoxes vanish, and fuzzy sets become a topos under this interpretation). As a preliminary conclusion of this approach we conjecture that the concept of fuzzy set has two essentially different semantical dimensions, which have not sufficiently been separated in the traditional theory, they may be considered either as an evaluation over a universe (i.e. as a connotation) or as a collection of evaluated object (i.e.as a denotation). 相似文献
4.
Fuzzy multi-objective programming for supplier selection and risk modeling: A possibility approach 总被引:1,自引:0,他引:1
Desheng Dash Wu Yidong Zhang Dexiang Wu David L. Olson 《European Journal of Operational Research》2010,200(3):139
Selection of supply chain partners is an important decision involving multiple criteria and risk factors. This paper proposes a fuzzy multi-objective programming model to decide on supplier selection taking risk factors into consideration. We model a supply chain consisting of three levels and use simulated historical quantitative and qualitative data. We propose a possibility approach to solve the fuzzy multi-objective programming model. Possibility multi-objective programming models are obtained by applying possibility measures of fuzzy events into fuzzy multi-objective programming models. Results indicate when qualitative criteria are considered in supplier selection, the probability of a certain supplier being selected is affected. 相似文献
5.
将目标值融入到新产品开发方案选择中,考虑方案属性值达成目标值的情况,有助于企业选择更具竞争力的产品开发方案。针对属性值和目标值的混合信息表征以及属性交互的问题,提出基于目标导向决策分析和k-可加模糊测度的新产品开发方案选择方法。首先,考虑目标值和属性值表示为区间值、模糊数、语言值等混合信息的情形,将其转化为概率密度;结合属性的三种偏好,利用目标导向决策分析计算属性值达成目标值的概率。其次,基于属性交互方向和强度等信息,利用最小方差法识别k-可加模糊测度,进而利用Choquet积分算子集结各属性的目标达成概率作为产品开发方案选择的依据。最后,将方法应用于大型集成电路测试仪的开发方案选择,验证了有效性。 相似文献
6.
《European Journal of Operational Research》2005,162(3):619-629
This paper deals with stochastic programming problems where the probability distribution is not explicitly known. We suppose that the probability distribution is defined by crisp or fuzzy inequalities on the probability of the different states of nature. We formulate the problem and present a solution strategy that uses the α-cut technique in order to transform our problem into a stochastic program with linear partial information on probability distribution (SPI). The obtained SPI problem is than solved using two approaches, namely, a chance constrained approach and a recourse approach. For the recourse approach, a modified L-shaped algorithm is designed and illustrated by an example. 相似文献
7.
《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
8.
Thierry Denœux 《Fuzzy Sets and Systems》2011,183(1):72-91
A method is proposed for estimating the parameters in a parametric statistical model when the observations are fuzzy and are assumed to be related to underlying crisp realizations of a random sample. This method is based on maximizing the observed-data likelihood defined as the probability of the fuzzy data. It is shown that the EM algorithm may be used for that purpose, which makes it possible to solve a wide range of statistical problems involving fuzzy data. This approach, called the fuzzy EM (FEM) method, is illustrated using three classical problems: normal mean and variance estimation from a fuzzy sample, multiple linear regression with crisp inputs and fuzzy outputs, and univariate finite normal mixture estimation from fuzzy data. 相似文献
9.
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
10.
《European Journal of Operational Research》2005,164(3):715-729
This paper introduces how to incorporate fuzzy set theory and a fuzzy ranking measure with discrete-event simulation in order to model uncertain activity duration in simulating a real-world system, especially when insufficient or no sample data are available. Fuzzy numbers are used to describe uncertain activity durations, reflecting vagueness, imprecision and subjectivity in the estimation of them. A fuzzy ranking measure is merged with an activity scanning simulation algorithm for performing fuzzy simulation time advancement and event selection for simulation experimentation. The uses of the fuzzy activity duration and the probability distribution-modeled duration are compared through a series of simulation experiments. It is observed that the fuzzy simulation outputs are arrived at through only one cycle of fuzzy discrete-event simulation, still they contain all the statistical information that are produced through multiple cycles of simulation experiments when the probability distribution approach is adopted. 相似文献
11.
Gilles Mauris 《International Journal of Approximate Reasoning》2011,52(9):1232-1242
The paper presents a possibility theory based formulation of one-parameter estimation that unifies some usual direct probability formulations. Point and confidence interval estimation are expressed in a single theoretical formulation and incorporated into estimators of a generic form: a possibility distribution. New relationships between continuous possibility distribution and probability concepts are established. The notion of specificity ordering of a possibility distribution, corresponding to fuzzy subsets inclusion, is then used for comparing the efficiency of different estimators for the case of data points coming from a symmetric probability distribution. The usefulness of the approach is illustrated on common mean and median estimators from identical independent data sample of different size and of different common symmetric continuous probability distributions. 相似文献
12.
具有Fuzzy概率的Fuzzy可靠性问题的求解途径 总被引:5,自引:0,他引:5
本文提出了工程实践中常见的清晰事件-Fuzzy概率的Fuzzy可靠性分析问题的求解途径,首先讨论了Fuzzy数的代数运算法则,然后在此基础上将Fuzzy可靠性求解问题转换为Fuzzy数的运算问题,从而使这类Fuzzy可靠性分析问题在理论上得到解决,本文还给出了一个算例。 相似文献
13.
Pedro Terán 《International Journal of Approximate Reasoning》2011,52(9):1243-1256
This paper aims at formalizing the intuitive idea that some points are more central in a probability distribution than others. Our proposal relies on fuzzy events to define a fuzzy set of central points for a distribution (or a family of distributions, including imprecise probability models). This framework has a natural interpretation in terms of fuzzy logic and unifies many known notions from statistics, including the mean, median and mode, interquantile intervals, the Lorenz curve, the halfspace median, the zonoid and lift zonoid, the coverage function and several expectations and medians of random sets, and the Choquet integral against an infinitely alternating or infinitely monotone capacity. 相似文献
14.
《European Journal of Operational Research》2006,168(3):798-810
This paper addresses the mixed-model line balancing problem with fuzzy processing time. A fuzzy binary linear programming model is formulated for the problem. This fuzzy model is then transformed to a mixed zero–one program. Due to the complexity nature in handling fuzzy computation, new approximated fuzzy arithmetic operation is presented. A fuzzy heuristic is developed to solve this problem based on the aggregating fuzzy numbers and combined precedence constraints. The general idea of our approach is to arrange the jobs in a sequence by a varying-section exchange procedure. Then jobs are allocated into workstations based on these aggregated fuzzy times with the considerations of technological constraint and cycle time limit. Promising results are obtained by experiments. 相似文献
15.
《Fuzzy Sets and Systems》1987,24(2):231-254
This paper examines various ways to introduce subjectivity in the measures of uncertainty. In the first part, by using a simple physical remark concerning discrete entropy in Shannon sense, we derive a so-called ‘complete discrete entropy’ which provides a unified approach to discrete and continuous entropy, and applies directly to variables which involves both probability and possibility.In the second part, by using three elementary axioms, we derive a Minkowskian theory of observation which holds when the observable is a pair (syntax, semantics) and which involves a parameter which is directly related to the subjectivity of the observer. This model is then applied to the observation of uncertainty, transinformation and membership, in which case it provides a new approach to fuzzy number. 相似文献
16.
目的是对基于随机波动率模型的期权定价问题应用模糊集理论.主要思想是把波动率的概率表示转换为可能性表示,从而把关于股票价格的带随机波动率的随机过程简化为带模糊参数的随机过程.然后建立非线性偏微分方程对欧式期权进行定价. 相似文献
17.
《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
18.
19.
Input and output data, under uncertainty, must be taken into account as an essential part of data envelopment analysis (DEA) models in practice. Many researchers have dealt with this kind of problem using fuzzy approaches, DEA models with interval data or probabilistic models. This paper presents an approach to scenario-based robust optimization for conventional DEA models. To consider the uncertainty in DEA models, different scenarios are formulated with a specified probability for input and output data instead of using point estimates. The robust DEA model proposed is aimed at ranking decision-making units (DMUs) based on their sensitivity analysis within the given set of scenarios, considering both feasibility and optimality factors in the objective function. The model is based on the technique proposed by Mulvey et al. (1995) for solving stochastic optimization problems. The effect of DMUs on the product possibility set is calculated using the Monte Carlo method in order to extract weights for feasibility and optimality factors in the goal programming model. The approach proposed is illustrated and verified by a case study of an engineering company. 相似文献