Non-statistical Uncertainty Research Articles

Otimização sob incerteza de sistemas de produção: interação lavoura-pecuária, com enfase em bovinocultura de leite

Na modelagem de sistema de produção agropecuária, a possibilidade de combinar livremente as pastagens para a composição do sistema de alimentação dificulta a avaliação em termos probabilísticos da bovinocultura de leite. Neste trabalho, propõe-se um modelo de otimização que, utilizando uma abordagem não probabilista da incerteza, permite contornar este problema. A aplicação do modelo para a análise de uma unidade de produção agropecuária indicou que uma diminuição das culturas de grãos comerciais com a constituição de reservas de pastagens pode se constituir em uma estratégia interessante para minimizar as perdas econômicas em caso de queda de rendimento físico das forrageiras. Além disto, pelo fato de dispensar pressupostos estatísticos e basear-se em cenários que representam condições técnicas e econômicas que puderam ser facilmente discutidas com o agricultor, concluiu-se que a abordagem utilizada neste trabalho pode se constituir em um procedimento útil no planejamento de sistemas de produção sob incerteza.

Estimation of non-statistical uncertainty in precision measurement using grey system theory

A new uncertainty assessment method is proposed to characterize non-statistical uncertainties in precision measurement. The proposed method is based on grey system theory to address the problem involved in uncertainty assessment where the sampling size is small and the distribution of the data is unknown. The advantage of the proposed approach is that the requirements of the statistics based methods are removed. In the proposed method, an accumulated true size vector and an accumulated measurement data vector are established to reduce the effects of the errors in the measurement and in the numerical calculation. The uncertainty assessment is based on the l∞ norm of the difference between the accumulation of the sorted measurement data vector and that of the true size vector. A number of computational and experimental tests were carried out. The results demonstrated the effectiveness and consistency of the proposed method in non-statistical uncertainty assessment, compared with the existing methods.

Improvement of the fine-structure constant obtained from the electron g-2

At present the most precise value of the fine-structure constant is /spl alpha/(a/sub e/) obtained from the anomalous magnetic moment of the electron, or the electron g-2. Further improvement in the theoretical calculation of /spl alpha/(a/sub e/) requires reduction of both statistical and nonstatistical uncertainties in the Monte-Carlo evaluation of the /spl alpha//sup 4/ term. This paper analyzes some inconsistency of earlier results and identifies its source as a deviation of nonstatistical nature caused by round-off errors. This information enables us to greatly improve the statistical basis of the electron g-2 value to very high statistics while minimizing the uncertainty of the nonstatistical type. This work will lead to a value of /spl alpha/(a/sub e/) with a relative uncertainty of less than 10/sup -9/ when new measurements become available.

Estimation of non-statistical uncertainty using fuzzy-set theory

A novel method using a fuzzy practicable interval to characterize non-statistical uncertainty in dynamic measurement is proposed. The method permits the uncertainty being estimated under the conditions that the number of measurements is very small and the probability distribution unknown. The feasibility of the method is validated by computer-simulation experiments.

Fuzzy engineering economic analysis [of electric utilities

This paper presents an approach for including nonstatistical uncertainties in engineering economic analysis, particularly utility economic analysis, by modeling uncertain variables with fuzzy numbers. In this case, the mathematical operations are defined by the extension principle and the results obtained are also in a form of fuzzy numbers. This approach can be seen as an extension of a previously proposed one that uses interval numbers and interval analysis for including such uncertainties. However, this paper considers also the dependence which may exist between the fuzzy variables and shows the impact this dependence may have on the results. In this context, a way of modeling partial correlation between the variables of the same kind is proposed.

A survey of recent advances in fuzzy logic in telecommunications networks and new challenges

The use of fuzzy logic in telecommunication systems and networks is recent and limited. Fundamentally, Zadeh's fuzzy set theory provides a robust mathematical framework for dealing with real-world imprecision and nonstatistical uncertainty. Given that the present day complex networks are dynamic, that there is great uncertainty associated with the input traffic and other environmental parameters, that they are subject to unexpected overloads, failures and perturbations, and that they defy accurate analytical modeling, fuzzy logic appears to be a promising approach to address many important aspects of networks. This paper reviews the current research efforts in fuzzy logic-based approaches to queuing, buffer management, distributed access control, load management, routing, call acceptance, policing, congestion mitigation, bandwidth allocation, channel assignment, network management, and quantitative performance evaluation in networks. The review underscores the future potential and promise of fuzzy logic in networks. The paper then presents a list of key research efforts in the areas of fuzzy logic-based algorithms and new hardware and software architectures that are necessary both to address new challenges in networking and to help realize the full potential of fuzzy logic in networks.

A Review of Probabilistic, Fuzzy, and Neural Models for Pattern Recognition

Fuzzy sets were introduced by Zadeh in 1965 to represent and manipulate data and information that possess nonstatistical uncertainty. Computational neural networks were first discussed by McCulloug...

A Review of Probabilistic, Fuzzy, and Neural Models for Pattern Recognition

Fuzzy sets were introduced by Zadeh in 1965 to represent and manipulate data and information that possess nonstatistical uncertainty. Computational neural networks were first discussed by McCullough and Pitts in 1943 as a means of imitating the power of biologic systems for data and information processing. Probabilistic models for data analysis, are, of course, several hundred years old. This article discusses the basic ideas of and some synergisms between probabilistic, fuzzy, and computational neural networks models as they apply to pattern recognition. We also provide a brief discussion of the relationship of both approaches to statistical pattern recognition methodologies.

Generating fuzzy measures

Fuzzy measure and integration theory was introduced by Sugeno [ 131 in order to deal with events affected by nonstatistical uncertainty. Further developments were concerned both with the analytical treatment of the concept of fuzzy measure-and its links with the classical measure theory (see, e.g., [3-5, 8, 9, 11, 14])-and the determination of a unique framework into which fuzziness and randomness can be set (see [7]). The main feature of the fuzzy measure in comparison with the classical one is the loss of additivity conditions, while continuity and monotonicity axioms are assumed. Our present aim is to exhibit some constructive examples of fuzzy measures, in terms of compositions of o-additive measures and suitable real valued functions. Furthermore we show some properties that are peculiar to the related class of the fuzzy measures above.

COMPUTER AIDED OPTIMUM STRUCTURAL DESIGN UNDER UNCERTAINTY

Abstract This paper is concerned with the incorporation of different forms of imprecision and uncertainty into the formulation and solution of optimum structural design problems. The statistical uncertainties inherent in material properties and structural loadings are modelled by a first-order second-moment reliability approach. Resulting constraint boundaries are then treated as “soft” boundary regions in which the non-statistical uncertainties, and quality aspects of design and construction are handled by fuzzy set operations.

Toward a general theory of fuzzy variables

A general framework for a theory is presented that encompasses both statistical uncertainty, which falls within the province of probability theory, and nonstatistical uncertainty, which relates to the concept of a fuzzy set and possibility theory [L. A. Zadeh, J. Fuzzy Sets 1 (1978), 3–28]. The concept of a fuzzy integral is used to define the expected value of a random variable. Properties of the fuzzy expectation are stated and a mean-value theorem for the fuzzy integral is proved. Comparisons between the fuzzy and the Lebesgue integral are presented. After a new concept of dependence is formulated, various convergence concepts are defined and their relationships are studied by using a Chebyshev-like inequality for the fuzzy integral. The possibility of using this theory in Bayesian estimation with fuzzy prior information is explored.

Fatigue Under Wide Band Random Stresses Using the Rain-Flow Method

A fatigue design procedure is proposed for the structural elements subjected to a stress process, modeled as stationary wide-band gaussian. This procedure, restricted to high cycle fatigue design, uses available constant amplitude material fatigue data and a modified, probability based, Palmgren-Miner (PM) rule. Statistical uncertainty in fatigue behavior and nonstatistical uncertainty in the PM rule are implicitly accounted for by treating the PM index at failure as a random variable. The rain flow method of counting stress cycles is used. The fatigue design algorithm requires only that the RMS and irregularity factor of the stress process be specified in addition to the constant amplitude S-N curve for the material.

Determination of the Pion-Nucleon Coupling Constant fromn−pScattering Angular Distribution

S>By the use of a method recently proposed by Chew, the pion-nucleon coupling constant is determined from differential cross sections for neutron- proton scattering. Data at 90 and 400 Mev were used. Details of the extrapolation procedure are discussed and the statistical methods used in interpreting the results are explained. The resulting value of the coupling constant is between 0.06 and 0.07, depending on the range and energy of the data included in the analysis. The discrepancy between this value and the usually quoted 0.08 should not be taken seriously, however, because several nonstatistical uncertainties could not be taken into account. The origin of these uncertainties is discussed. (auth)