GENERALIZED FUZZY FILTERS OF BL-ALGEBRAS

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered.In fact,this is a generalization of quasi-coincidence of a fuzzy point With a fuzzy set.By using this new idea,the notion of interval valued(∈,∈∨q)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras,is defined,and related properties are investigated.In particular,the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.     

半群的模糊内理想

Abstract The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is a generalization of the quasi-coincidence of a fuzzy point in a fuzzy set. With this new concept, the interval valued （∈, ∈ Vq）-fuzzy interior ideal in semigroups is introduced. In fact, this kind of new fuzzy interior ideals is a generalization of fuzzy interior ideals in semigroups. In this paper, this kind of fuzzy interior ideals and related properties will be investigated. Moreover, the concept of a fuzzy subgroup with threshold is extended to the concept of an interval valued fuzzy interior ideal with threshold in semigroups.     

Minimizing maximum risk for fair network connection with interval data

In this paper we introduce a minimax model for network connection problems with interval parameters. We consider how to connect given nodes in a network with a path or a spanning tree under a given budget, where each link is associated with an interval and can be established at a cost of any value in the interval. The quality of an individual link （or the risk of link failure, etc.） depends on its construction cost and associated interval. To achieve fairness of the network connection, our model aims at the minimization of the maximum risk over all links used. We propose two algorithms that find optimal paths and spanning trees in polynomial time, respectively. The polynomial solvability indicates salient difference between our minimax model and the model of robust deviation criterion for network connection with interval data, which gives rise to NP-hard optimization problems.     

具有随机区间收益的效用优化分析(英文)

This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor’s subjective view toward random interval wealth. Some techniques are proposed to transfer a complex programming involving interval numbers into a simple non-linear programming. Under the existence of the optimal strategy, relations between the optimal strategy and assets’ prices are discussed. Some properties of the maximal utility function with respect to the endowment are given.     

A Prediction Model for Skin Wound Suture Forces With Uncertain Material Parameters北大核心CSCD

To evaluate the forces required for the suture of skin wounds quickly and effectively, the nonlinear finite element method was used to calculate the suture forces for skin wounds with different sizes and material parameters. With the calculated results as samples, the prediction model for skin wound suture forces was constructed by means of the EBF neural network model. Given the uncertain skin material parameters influencing the reliability of numerical results, the Monte-Carlo method was used to analyze the uncertainty propagation of skin material parameters. Finally, the prediction analysis and measuring experiment of wound suture forces were carried out with pig skin specimens to verify the reliability of the method. The results showed that, the suture force increases first and then decreases according to the suture point sequence, and the peak force occurs before the center of the wound. For a 40 mm×10 mm wound, the peak suture force is about 1.7 N, and that for a 40 mm×14 mm wound is about 2.5 N. Influenced by the uncertainty of material parameters, the prediction results of suture forces fluctuate by as much as ±0.6 N. The proposed theoretical prediction model provides an effective solution to the problem of parameter uncertainty propagation for biological soft tissue materials such as skins, and makes an important mechanical reference for robotic surgical suture. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Non-gaussian Test Models for Prediction and State Estimation with Model Errors

Turbulent dynamical systems involve dynamics with both a large dimensional phase space and a large number of positive Lyapunov exponents. Such systems are ubiquitous in applications in contemporary science and engineering where the statistical ensemble prediction and the real time filtering/state estimation are needed despite the underlying complexity of the system. Statistically exactly solvable test models have a crucial role to provide firm mathematical underpinning or new algorithms for vastly more complex scientific phenomena. Here, a class of statistically exactly solvable non-Gaussian test models is introduced, where a generalized Feynman-Kac formulation reduces the exact behavior of conditional statistical moments to the solution to inhomogeneous Fokker-Planck equations modified by linear lower order coupling and source terms. This procedure is applied to a test model with hidden instabilities and is combined with information theory to address two important issues in the contemporary statistical prediction of turbulent dynamical systems: the coarse-grained ensemble prediction in a perfect model and the improving long range forecasting in imperfect models. The models discussed here should be useful for many other applications and algorithms for the real time prediction and the state estimation.     

APPROXIMATE COMMON DIVISORS OF POLYNOMIALS AND DEGREE REDUCTION FOR RATIONAL CURVES

This paper deals with how to perturb a given set of polynomials so as to include a common linear factor. An algorithm is derived for determining such a set of perturbation polyrlomials which are subject to certain constrains at the endpoints of a prescribed parametric interval and minimized in a certain sense. This result can be combined with subdivision technique to obtain a continuous piecewise approximation to a rational curve.     

Operator Jensen＇s Inequality on C＊-algebras

A real continuous function which is defined on an interval is said to beA-convex if it is convex on the set of self-adjoint elements,with spectra in the interval,in all matrix algebras of the unital C-algebra A.We give a general formation of Jensen’s inequality for A-convex functions.     

DENSITY OF MARKOV SYSTEMS AND ZEROS OF CHEBYSHEV POLYNOMIALS

We raise and partly answer the question: whether there exists a Markov system with respectto which the zeros of the Chebyshev polynomials are dense, but the maximum length of a zerofree interval of the nth Chebyshev polynomial does not tends to zero. We also draw the conclu-tion that a Markov system, under an additional assumption, is dense if and only if the maxi-mum length of a zero free interval of the nth associated Chebyshev polynomial tends to zero.     

Interval Valued Intuitionistic （S, T）-fuzzy Hv-submodules

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an Hv-module with respect to a t-norm T and an s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated. In particular, the connections between interval valued intuitionistic （S, T）-fuzzy Hv-submodules and interval valued intuitionistic （S, T）-fuzzy submodules are discussed.     

基于标准区间灰数的发展带离散DDGM预测模型

由于区间灰数运算体系尚不完善,灰数间的代数运算将导致结果灰度增加,难以有效构建基于"区间灰数"的灰色发展带预测模型.对此,通过将区间灰数进行标准化处理,分解成基于实数形式的"白部"和"灰部"两个部分;然后分别对"白部"和"灰部"建立发展带预测模型,再推导并还原得到区间灰数的发展带预测模型;最后,将模型用于摆动幅度大且整体趋势增长的区间灰数在未来时刻的预测,预测效果验证了所提出模型的有效性.     

The asymptotic efficiency of improved prediction intervals

We consider the Barndorff-Nielsen and Cox (1994, p. 319) method of modifying an estimative prediction interval to obtain an improved prediction interval with better conditional coverage properties. The parameter estimator, on which this improved interval is based, is assumed to have the same asymptotic distribution as the conditional maximum likelihood estimator. This improved interval depends strongly on the asymptotic conditional bias of this estimator, which can be very sensitive to small changes in this estimator. We show, however, that the asymptotic efficiency of this improved prediction interval does not depend on this bias.     

Admissibility of prediction intervals

Admissibility of prediction intervals is considered in a specified family. It is shown that the best invariant prediction interval is strongly admissible in a location family and in a scale family. Though the similar result has not been obtained for a location and scale family, the best invariant prediction interval for a normal distribution is shown to be weakly admissible.     

一类相关性指标优化IOWHA区间预测模型的比较研究——以民航客运量为例

单点值预测有其局限性,因为客观世界许多影响因素都呈现出动态的范围区间.运用变权系数区间组合思想,引入相关性指标,将相关性指标与IOWHA结合,研究相关性指标优化IOWHA区间组合算法的可行性,建立基于区间中点和区间半径的相关性指标优化IOWHA区间组合预测模型,基于偏好系数把多目标最优化问题转化为单目标最优化问题.实例演算得出基于相关系数、向量夹角余弦和灰色关联度优化的IOWHA区间模型能有效地提高预测精度,证实了相关性指标优化IOWHA区间组合模型的有效性与合理性.     

Prediction interval for disease mapping using hierarchical likelihood

In disease mapping, the Bayesian approach is widely used for forming the prediction interval of relative risks. In this paper we propose a hierarchical-likelihood interval for disease mapping, which accounts for the inflation of standard error estimates caused by uncertainty in the estimation of the fixed parameters. Comparison is made with the Bayesian prediction intervals derived from penalized quasi-likelihood and fully Bayesian methods. Through simulation studies, we show that prediction intervals for random effects using hierarchical likelihood maintains the required level.     

Predicting a cyclic Poisson process

We construct and investigate a (1−α)-upper prediction bound for a future observation of a cyclic Poisson process using past data. A normal based confidence interval for our upper prediction bound is established. A comparison of the new prediction bound with a simpler nonparametric prediction bound is also given.     

Do forecasts expressed as prediction intervals improve production planning decisions?

A number of studies have shown that providing point forecasts to decision makers can lead to improved production planning decisions. However, point forecasts do not convey information about the level of uncertainty that is associated with forecasts. In theory, the provision of prediction intervals, in addition to point forecasts, should therefore lead to further enhancements in decision quality. To test whether this is the case in practice, participants in an experiment were asked to decide on the production levels that were needed to meet the following week’s demand for a series of products. Either underproduction cost twice as much per unit as overproduction or vice versa. The participants were supplied with either a point forecast, a 50% prediction interval, or a 95% prediction interval for the following week’s demand. The prediction intervals did not improve the quality of the decisions and also reduced the propensity of the decision makers to respond appropriately to the asymmetry in the loss function. A simple heuristic is suggested to allow people to make more effective use of prediction intervals. It is found that applying this heuristic to 85% prediction intervals would lead to nearly optimal decisions.     

Multi-variable grey model based on dynamic background algorithm for forecasting the interval sequence

The multi-variable grey model based on dynamic background algorithm improves the forecasting performance of the multi-variable grey model on the precise number sequence. In order to make this model suitable for the interval sequence, the matrix form of the multi-variable grey model based on dynamic background algorithm is proposed in the paper. In the modeling process, the interval is treated as a two-dimensional column vector, the parameters of the multi-variable grey model are replaced by matrices, and the dynamic background algorithm for interval sequences is proposed. The analysis results of the matrix algorithm for the dynamic background value and the prediction formula show that the new model is essentially a way to predict one of the two bounds of an interval by combining them, reflecting the integrity and interaction between the lower and upper bounds. The interval predictions of industrial electricity consumption of Zhejiang Province, China national electricity consumption and consumer price index show that the new model can well predict the minimum and maximum values of the interval sequence and has better prediction performance compared with the method of predicting each boundary sequence separately.     

Shorter nonparametric prediction intervals for an order statistic from a future sample

Standard nonparametric prediction intervals for a future order statistic are obtained by taking the interval between two order statistics of the initial sample. We obtain improved prediction intervals by taking the shortest of two or more standard intervals.     

Short-term prediction method of wind speed series based on fractal interpolation

In order to improve the prediction performance of the wind speed series, the rescaled range analysis is used to analyze the fractal characteristics of the wind speed series. An improved fractal interpolation prediction method is proposed to predict the wind speed series whose Hurst exponents are close to 1. An optimization function which is composed of the interpolation error and the constraint items of the vertical scaling factors in the fractal interpolation iterated function system is designed. The chaos optimization algorithm is used to optimize the function to resolve the optimal vertical scaling factors. According to the self-similarity characteristic and the scale invariance, the fractal extrapolate interpolation prediction can be performed by extending the fractal characteristic from internal interval to external interval. Simulation results show that the fractal interpolation prediction method can get better prediction result than others for the wind speed series with the fractal characteristic, and the prediction performance of the proposed method can be improved further because the fractal characteristic of its iterated function system is similar to that of the predicted wind speed series.