Interval Input Data Research Articles

A Mathematical Programming Model to Determine Objective Weights for the Interval Extension of TOPSIS

Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method has been extended in previous literature to consider the situation with interval input data. However, the weights associated with criteria are still subjectively assigned by decision makers. This paper develops a mathematical programming model to determine objective weights for the implementation of interval extension of TOPSIS. Our method not only takes into account the optimization of interval-valued Multiple Criteria Decision Making (MCDM) problems, but also determines the weights only based upon the data set itself. An illustrative example is performed to compare our results with that of existing literature.

DC power flow analysis incorporating interval input data and network parameters through the optimizing-scenarios method

DC power flow analysis is based on a linear approximation model for AC power flow equations, and represents an efficient approach for acquiring the bus angles and active transmission power of a power grid. However, the input data and network parameters of the power grid are uncertain due to numerous internal and external factors. Therefore, the DC power flow model should be considered as an uncertain problem, which makes deterministic DC power flow analysis methods unworkable. The present work overcomes this problem by regarding uncertain input data and network parameters as interval values, respectively, and establishes the interval DC power flow (IDCPF) models considering interval input data only (denoted as IDCPF01), and IDCPF model including both interval input data and network parameters (denoted as IDCPF02). Analyses based on the IDCPF models seek to obtain conservative ranges of bus angles and active transmission power flow, which can be employed by dispatchers to develop strategies for ensuring the operational security of the power system. The optimizing-scenarios method (OSM) is employed here to solve the IDCPF models. In addition, it is proven that the lower (or upper) bounds of the bus angles of the IDCPF01 model are simultaneously obtained when the injected power is set as its lower (or upper) interval bounds. This fact greatly improves the efficiency of the OSM for solving the IDCPF models. The results obtained by the proposed method are compared with those obtained by Monte Carlo simulation, the AA-based method, and the interval AC power flow method. The overall simulation results demonstrate the effectiveness and robustness of the proposed method.

A system of recurrent neural networks for modularising, parameterising and dynamic analysis of cell signalling networks

In this paper, we show how to extend our previously proposed novel continuous time Recurrent Neural Networks (RNN) approach that retains the advantage of continuous dynamics offered by Ordinary Differential Equations (ODE) while enabling parameter estimation through adaptation, to larger signalling networks using a modular approach. Specifically, the signalling network is decomposed into several sub-models based on important temporal events in the network. Each sub-model is represented by the proposed RNN and trained using data generated from the corresponding ODE model. Trained sub-models are assembled into a whole system RNN which is then subjected to systems dynamics and sensitivity analyses. The concept is illustrated by application to G1/S transition in cell cycle using Iwamoto et al. (2008) ODE model. We decomposed the G1/S network into 3 sub-models: (i) E2F transcription factor release; (ii) E2F and CycE positive feedback loop for elevating cyclin levels; and (iii) E2F and CycA negative feedback to degrade E2F. The trained sub-models accurately represented system dynamics and parameters were in good agreement with the ODE model. The whole system RNN however revealed couple of parameters contributing to compounding errors due to feedback and required refinement to sub-model 2. These related to the reversible reaction between CycE/CDK2 and p27, its inhibitor. The revised whole system RNN model very accurately matched dynamics of the ODE system. Local sensitivity analysis of the whole system model further revealed the most dominant influence of the above two parameters in perturbing G1/S transition, giving support to a recent hypothesis that the release of inhibitor p27 from Cyc/CDK complex triggers cell cycle stage transition. To make the model useful in a practical setting, we modified each RNN sub-model with a time relay switch to facilitate larger interval input data (≈20min) (original model used data for 30s or less) and retrained them that produced parameters and protein concentrations similar to the original RNN system. Results thus demonstrated the reliability of the proposed RNN method for modelling relatively large networks by modularisation for practical settings. Advantages of the method are its ability to represent accurate continuous system dynamics and ease of: parameter estimation through training with data from a practical setting, model analysis (40% faster than ODE), fine tuning parameters when more data are available, sub-model extension when new elements and/or interactions come to light and model expansion with addition of sub-models.

Interval twin support vector regression algorithm for interval input-output data

It is necessary to use interval data to define terms or describe extreme behaviors because of the existence of uncertainty in many real-world problems. In this paper, a novel efficient interval twin support vector regression (ITSVR) is proposed to handle such interval data. This ITSVR employs two nonparallel functions to identify the upper and lower sides of the interval output data, respectively, in which the Hausdorff distance is incorporated into the Gaussian kernel as the interval kernel for interval input data. Compared with other support vector regression (SVR)-based interval regression methods, such as the interval support vector interval regression networks (ISVIRN), this ITSVR algorithm is more efficient since only two smaller-sized QPPs are solved, respectively. The experimental results on several artificial datasets and three stock index datasets show the validity of ITSVR.

The development of an interval grey regression model for limited time series forecasting

The grey model GM(1, 1) is a popular forecasting method in management and engineering applications. In order to obtain more validity and reliable forecasting values, fuzzy grey regression model is proposed by hybridizing fuzzy set into grey model GM(1, 1) for solving crisp-input and fuzzy-input limited time series. In the present study, we continue to investigate and derive the interval grey regression model with a minimum regression interval by necessity analysis in which the predicted interval is possibly to be belonged to the collected interval data with certain membership degree. In the illustrative example we did not have as much information as the research institutes of Display search, iSuppli, and PIPA, but we succeeded at forecasting LCD TV demand by using the interval grey regression model with limited and interval-input data.

Computational Experience with Rigorous Error Bounds for the Netlib Linear Programming Library

The Netlib library of linear programming problems is a well known suite containing many real world applications. Recently it was shown by Ordóñez and Freund that 71% of these problems are ill-conditioned. Hence, numerical difficulties may occur. Here, we present rigorous results for this library that are computed by a verification method using interval arithmetic. In addition to the original input data of these problems we also consider interval input data. The computed rigorous bounds and the performance of the algorithms are related to the distance to the next ill-posed linear programming problem.

L-CLASS ENUMERATION ALGORITHMS FOR ONE INTERVAL PRODUCTION PLANNING PROBLEM

A discrete production planning problem with interval input data is considered. An approach for solving this problem based on using its relaxation set is suggested. Some L-class enumeration algorithms for the problem are described. Results of computational experiments are presented.

Scientific Computing with Automatic Result Verification.

Automatic Result Verification.- I. Numerical Methods with Result Verification.- A Method for Producing Verified Results for Two-point Boundary Value Problems.- A Kind of Difference Method for Enclosing Solutions of Ordinary Linear Boundary Value Problems.- A Self-validating Method for Solving Linear Programming Problems with Interval Input Data.- Enclosing the Solutions of Linear Equations by Interval Iterative Processes.- Errorbounds for Quadratic Systems of Nonlinear Equations Using the Precise Scalar Product.- Inclusion of Eigenvalues of General Eigenvalue Problems of Matrices.- Verified Inclusion for Eigenvalues of Certain Difference and Differential Equations.- II. Applications in the Technical Sciences.- VIB - Verified Inclusions of Critical Bending Vibrations.- Stability Test for Periodic Differential Equations on Digital Computers with Applications.- The Periodic Solutions of the Oregonator and Verification of Results.- On Arithmetical Problems of Geometric Algorithms in the Plane.- III. Improving the Tools.- Precise Evaluation of Polynomials in Several Variables.- Evaluation of Arithmetic Expressions with Guaranteed High Accuracy.- Standard Functions for Real and Complex Point and Interval Arguments with Dynamic Accuracy.- Inverse Standard Functions for Real and Complex Point and Interval Arguments with Dynamic Accuracy.- Inclusion Algorithms with Functions as Data.- FORTRAN-SC. A Study of a FORTRAN Extension for Engineering/Scientific Computation with Access to ACRITH.

On the solution of interval linear systems

In the literature efficient algorithms have been described for calculating guaranteed inclusions for the solution of a number of standard numerical problems [3,4,8,11,12,13]. The inclusions are given by means of a set containing the solution. In [12,13] this set is calculated using an affine iteration which is stopped when a nonempty and compact set is mapped into itself. For exactly given input data (point data) it has been shown that this iteration stops if and only if the iteration matrix is convergent (cf. [13]). In this paper we give a necessary and sufficient stopping criterion for the above mentioned iteration for interval input data and interval operations. Stopping is equivalent to the fact that the algorithm presented in [12] for solving interval linear systems computes an inclusion of the solution. An algorithm given by Neumaier is discussed and an algorithm is proposed combining the advantages of our algorithm and a modification of Neumaier's. The combined algorithm yields tight bounds for input intervals of small and large diameter. Using a paper by Jansson [6,7] we give a quite different geometrical interpretation of inclusion methods. It can be shown that our inclusion methods are optimal in a specified geometrical sense. For another class of sets, for standard simplices, we give some interesting examples.

Interval linear systems with symmetric matrices, skew-symmetric matrices and dependencies in the right hand side

The methods of Interval Arithmetic permit to calculate guaranteed a posteriori bounds for the solution set of problems with interval input data. At present, these methods assume that all input data vary independently between their given lower and upper bounds. This paper shows for special interval linear systems how to handle the case where dependencies of the input data occur.