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Weighted polygonal approximation of fuzzy numbers preserving their main characteristics

FUZZY SETS AND SYSTEMS 2022年第PartA期443卷 34-51页

作者： Baez-Sanchez, A. Flores-Franulic, A. Moretti, A. C. Chalco-Cano, Y. Rojas-Medar, M. A. Fed Univ Technol Math Dept Av Sete Setembro 3165 BR-80230901 Curitiba Parana Brazil Univ Tarapaca Dept Matemat Casilla 7D Arica Chile Univ Estadual Campinas Sch Appl Sci Rua Pedro Zaccaria 1300 BR-13484350 Limeira SP Brazil

In this article we obtain an approximation of a given fuzzy number by a unique polygonal fuzzy number preserving its main characteristics such as core, support, and expected interval. For this, we consider the well-known weighted L-2 metric. We show that this weighted polygonal approximation is equivalent to a strict convex quadratic optimization problem finite dimensional with linear inequality and equality constraint. Then, we present efficient and practice solution methods illustrated with several examples. Some properties of invariance of the approximation operator are also obtained. The results presented here extend and improve the methods obtained for weighted trapezoidal approximation and piecewise linear approximation of fuzzy numbers. (C) 2021 Elsevier B.V. All rights reserved.

关键词： approximation of fuzzy numbers Polynomial fuzzy numbers Characteristics of fuzzy numbers piecewise linear approximation

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Topology-aware piecewise linearization of the AC Power Flow through Generative Modeling

Topology-aware Piecewise Linearization of the AC Power Flow ...

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North American Power Symposium (NAPS)

作者： Cho, Young-Ho Zhu, Hao Univ Texas Austin Chandra Dept Elect & Comp Engn Austin TX 78712 USA

ISBN: (纸本)9798350315097

Effective power flow modeling critically affects the ability to efficiently solve large-scale grid optimization problems, especially those with topology-related decision variables. In this work, we put forth a generative modeling approach to obtain a piecewise linear (PWL) approximation of AC power flow by training a simple neural network model from actual data samples. By using the ReLU activation, the NN models can produce a PWL mapping from the input voltage magnitudes and angles to the output power flow and injection. Our proposed generative PWL model uniquely accounts for the nonlinear and topology-related couplings of power flow models, and thus it can greatly improve the accuracy and consistency of output power variables. Most importantly, it enables to reformulate the nonlinear power flow and line status-related constraints into mixed-integer linear ones, such that one can efficiently solve grid topology optimization tasks like the AC optimal transmission switching (OTS) problem. Numerical tests using the IEEE 14- and 118-bus test systems have demonstrated the modeling accuracy of the proposed PWL approximation using a generative approach, as well as its ability in enabling competitive OTS solutions at very low computation order.

关键词： Generative modeling piecewise linear approximation nonlinear AC power flow grid topology optimization

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Exposure assessment for Cox proportional hazards cure models with interval-censored survival data

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BIOMETRICAL JOURNAL 2022年第1期64卷 91-104页

作者： Wang, Wei Cong, Ning Ye, Aijun Zhang, Hui Zhang, Bo US FDA Div Clin Evidence & Anal 2 Off Clin Evidence & Anal Off Prod Evaluat & QualCtr Devices & Radiol Hlth Silver Spring MD 20993 USA Shandong Canc Hosp & Inst Dept Surg Oncol Intervent Therapy Jinan Shandong Peoples R China Glotech Inc Rockville MD USA Northwestern Univ Dept Prevent Med Div Biostat Feinberg Sch Med Chicago IL 60611 USA Boston Childrens Hosp Dept Neurol Boston MA USA Boston Childrens Hosp ICCTR Biostat & Res Design Ctr Boston MA USA Harvard Med Sch Boston MA 02115 USA

Mixture cure models have been developed as an effective tool to analyze failure time data with a cure fraction. Used in conjunction with the logistic regression model, this model allows covariate-adjusted inference of an exposure effect on the cured probability and the hazard of failure for the uncured subjects. However, the covariate-adjusted inference for the overall exposure effect is not directly provided. In this paper, we describe a Cox proportional hazards cure model to analyze interval-censored survival data in the presence of a cured fraction and then apply a post-estimation approach by using model-predicted estimates difference to assess the overall exposure effect on the restricted mean survival time scale. For baseline hazard/survival function estimation, simple parametric models as fractional polynomials or restricted cubic splines are utilized to approximate the baseline logarithm cumulative hazard function, or, alternatively, the full likelihood is specified through a piecewise linear approximation for the cumulative baseline hazard function. Simulation studies were conducted to demonstrate the unbiasedness of both estimation methods for the overall exposure effect estimates over various baseline hazard distribution shapes. The methods are applied to analyze the interval-censored relapse time data from a smoking cessation study.

关键词： fractional polynomials interval-censored mixture cure model overall exposure effect piecewise linear approximation restricted cubic splines

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A Simultaneous Training and Input Selection Algorithm for Classification Problems Using piecewise approximations 9

A Simultaneous Training and Input Selection Algorithm for Cl...

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9th IFAC Conference on Foundations of Systems Biology in Engineering (FOSBE)

作者： Sildir, Hasan Sarrafi, Sahin Kavzoglu, Taskin Gebze Tech Univ Chem Engn TR-41400 Kocaeli Turkiye SOCAR Turkey R&D & Innovat Co TR-35800 Izmir Turkiye Gebze Tech Univ Geomat Engn TR-41400 Kocaeli Turkiye

ISBN: (纸本)9781713867890

Heart disease diagnosis using few measurements is a challenging an important task considering the increasing population. Artificial Neural Networks (ANNs) are promising mathematical architectures once the training is performed in an elegant manner to avoid theoretical challenges related to high nonlinearity, nonconvexity using few input variables to ensure generalization capability. This study shows the impact of the piecewise linear approximation of nonlinear functions in ANN architecture and training problem to benefit from the mixed integer linear problem formulation for the simultaneous input selection and training to obtain mixed integer programming based ANN (MIP-ANN). Proposed formulation is further tailored through linking constraints to remove the connections from the eliminated inputs to favor parameter identifiability. A publicly available dataset is considered as a case study of whose results are also compared to traditional ANN with all inputs (FC-ANN) and a relatively more straightforward but common input selection method (SKB-ANN). The results provide a comparable performance despite significant reduction in the input space in addition to significant computational and theoretical advantages thanks to advanced *** (c) 2022 The Authors This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0/)

关键词： piecewise linear approximation Input Selection Artificial Neural Networks Classification Mixed Integer linear Nonlinear Programming

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Modeling of Metasurfaces Using Discontinuous Galerkin Time-Domain Method Based on Generalized Sheet Transition Conditions

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2022年第8期70卷 6905-6917页

作者： Tian, Shaowen Wu, Kaiming Ren, Qiang Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China

A new discontinuous Galerkin time-domain (DGTD) method based on generalized sheet transition conditions (GSTCs) for analyzing the transient response of electromagnetic metasurfaces is presented. The discontinuities in electromagnetic fields around the vicinity of the metasurface are modeled by placing virtual edges on both sides of the metasurface. The GSTCs are incorporated in the updating equations of the standard DGTD algorithm by integrating the time-domain GSTCs formula with Galerkin' s-weighted residual method. The DGTD-GSTC formulation can also simulate a bf piecewise linear approximation of a curved metasurfaces due to the unstructured mesh. This is the first time that DGTD is applied to the simulation of GSTCs. The implementation of this new method is verified by numerical cases.

关键词： Metasurfaces Time-domain analysis Mathematical models Numerical models Method of moments Electromagnetics Finite element analysis Discontinuous Galerkin time-domain (DGTD) method electromagnetic sheet generalized sheet transition conditions (GSTCs) metasurface piecewise linear approximation spatial discontinuity

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Utility Preference Robust Optimization with Moment-Type Information Structure

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OPERATIONS RESEARCH 2024年第5期72卷 iii-vii, 1751-2261, C2-C3页

作者： Guo, Shaoyan Xu, Huifu Zhang, Sainan Dalian Univ Technol Sch Math Sci Dalian 116024 Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Peoples R China

Utility preference robust optimization (PRO) models have recently been proposed to deal with decision-making problems where the decision-maker's true utility function is unknown and the optimal decision is based on the worst-case utility function in an ambiguity set of utility functions. In this paper, we consider the case where the ambiguity set is constructed using some moment-type conditions. We propose piecewise linear approximation of the utility functions in the ambiguity set. The approximate maximin problem can be solved directly by derivative-free methods when the utility functions are nonconcave. Alternatively, we can reformulate the approximate problem as a single mixed integer linear program (MILP) and solve the MILP by existing solvers such as Gurobi. To justify the approximation scheme, we derive error bounds for the approximate ambiguity set, the optimal value and optimal solutions of the approximate maximin problem. To address the data perturbation/contamination issues arising from the construction of the ambiguity set, we derive some stability results which quantify the variation of the ambiguity set against perturbations in the elicitation data and its propagation to the optimal value and optimal solutions of the PRO model. Moreover, we extend the PRO models to allow some inconsistencies in the process of eliciting the decision-maker's preferences. Finally, we carry out numerical tests to evaluate the performances of the proposed numerical schemes and show that the computational schemes work fairly efficiently, the PRO model is resilient against small perturbations in data (with respect to both exogenous uncertainty data and preference elicitation data), and there is a potential to improve the efficiency of the preference elicitation by incorporating an optimal selection strategy.

关键词： preference robust optimization piecewise linear approximation non-concave utility functions tractability preference elicitation MILP error bounds data contamination preference inconsistency

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linear approximation of Calendar Battery Aging Costs for MILP-Based Power Dispatch Optimization

Linear Approximation of Calendar Battery Aging Costs for MIL...

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2023 IEEE PES Innovative Smart Grid Technologies Europe, ISGT EUROPE 2023

作者： Majewski, Kurt Seydenschwanz, Martin Gottschalk, Corinna Weiland, Sonja Siemens AG T DAI ORD-DE Germany Technische Universität München Munich Germany

ISBN: (纸本)9798350396782

Batteries should be operated such that benefits and associated chemical aging detriments are balanced. We present a mixed-integer linear approximation for the cost of calendar aging of batteries taking temperature and state of charge into account. An example with calendar and cyclic aging costs shows that the revenue from the operation of a battery can be increased by integrating aging costs into a model predictive control optimization. © 2023 IEEE.

关键词： battery aging battery management systems mathematical programming mixed integer linear programming piecewise linear approximation

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An Error-Bounded Space-Efficient Hybrid Learned Index with High Lookup Performance 33rd

An Error-Bounded Space-Efficient Hybrid Learned Index with H...

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33rd International Conference on Database and Expert Systems Applications (DEXA)

作者： Ding, Yuquan Zhao, Xujian Jin, Peiquan Southwest Univ Sci & Technol Mianyang Sichuan Peoples R China Univ Sci & Technol China Hefei Peoples R China

ISBN: (纸本)9783031124266;9783031124259

Learned index is a novel index structure that enhances traditional index structures like B+-tree with machine learning models. It uses a trained model to locate a key position directly without the costly rootto-leaf traversing in the conventional B+-tree. However, the performance of existing learned indices relies on the prediction accuracy of the model. Recently, to address this problem, some existing learned indices, such as PGM-index, set a threshold to ensure that the prediction error is below the threshold. However, the PGM-index introduced additional space costs because it used a bottom-up strategy to build a tree structure to maintain an error threshold at each level. In this paper, we aim to find out a better trade-off between prediction accuracy and space consumption of learned indices. In particular, we propose a new learned index called HLI (Hybrid Learned Index) that offers high prediction accuracy and searching performance with limited space costs. HLI constructs error-bounded leaf nodes to provide high prediction accuracy and searching performance. Meanwhile, it organizes inner nodes without error bounds to reduce extra space costs. Consequently, we demonstrate that HLI can deliver high searching performance with limited space overhead. We conduct experiments on various datasets to compare HLI with several existing indices, including PGM-index, RMI, and B+-tree. The results show that HLI outperforms PGM-index in lookup performance on all datasets by 1.5x on average. In addition, compared to PGM-index, HLI reduces the index size by up to 13x without decaying the lookup performance.

关键词： Learned index Hybrid index Data distribution piecewise linear approximation

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Gaussian Sum Filtering for Wiener State-Space Models with a Class of Non-Monotonic piecewise Nonlinearities ⁎

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IFAC-PapersOnLine 2024年第15期58卷 25-30页

作者： Angel L. Cedeño Rodrigo A. González Juan C. Agüero Electronics Department Universidad Técnica Federico Santa María Valparaíso Chile Department of Mechanical Engineering Eindhoven University of Technology The Netherlands

State estimation of nonlinear dynamical systems has gained significant attention due to its countless applications in control, signal processing, fault diagnosis, and power networks. The complexity posed by challenging nonlinearities like dead-zones, saturations, and linear rectification requires advanced state estimation. This paper presents a novel filtering technique designed for state-space Wiener systems encompassing these specific nonlinear behaviors. The filtering approach developed in this work introduces an explicit model for the probability function of the nonlinear output conditioned to the system state, which is derived from a Gaussian quadrature-based approximation. A Gaussian sum filtering algorithm is then used to obtain the filtering distributions and state estimates of systems with the aforementioned nonlinearities. Extensive numerical simulations are conducted to assess the accuracy of the proposed method compared to conventional techniques.

关键词： State estimation Wiener systems piecewise linear approximation Gaussian sum filtering Bayesian estimation

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Likelihood-based inference for semi-parametric transformation cure models with interval censored data

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年

作者： Pal, Suvra Barui, Sandip Univ Texas Arlington Dept Math Arlington TX USA Univ Texas Arlington Coll Sci Div Data Sci Arlington TX USA Indian Stat Inst Interdisciplinary Stat Res Unit 203 BT Rd Kolkata 700108 West Bengal India

A simple yet effective way of modeling survival data with cure fraction is by considering Box-Cox transformation cure model (BCTM) that unifies mixture and promotion time cure models. In this article, we numerically study the statistical properties of the BCTM when applied to interval censored data. Time-to-events associated with susceptible subjects are modeled through proportional hazards structure that allows for non-homogeneity across subjects, where the baseline hazard function is estimated by distribution-free piecewise linear function with varied degrees of non-parametricity. Due to missing cured statuses for right censored subjects, maximum likelihood estimates of model parameters are obtained by developing an expectation-maximization (EM) algorithm. Under the EM framework, the conditional expectation of the complete data log-likelihood function is maximized by considering all parameters (including the Box-Cox transformation parameter alpha) simultaneously, in contrast to conventional profile-likelihood technique of estimating alpha. The robustness and accuracy of the model and estimation method are established through a detailed simulation study under various parameter settings, and an analysis of real-life data obtained from a smoking cessation study.

关键词： Box-Cox transformation EM algorithm piecewise linear approximation Simultaneous-maximization Smoking cessation Unified cure models

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