Uncertain Problem Research Articles

Stochastic filtering under model ambiguity

In this paper, we study a non-linear filtering problem in the presence of signal model uncertainty. The model ambiguity is characterized by a class of probability measures from which the true one is taken. After interchanging the order of extremum problems by using the min-max theorem, we find that the uncertain filtering problem can be converted to a weighted conditional mean-field optimal control problem. Further, we characterize the ambiguity filter and prove its unique existence.

A Multi-Objective Genetic Programming Algorithm With α Dominance and Archive for Uncertain Capacitated Arc Routing Problem

The uncertain capacitated arc routing problem is an important combinatorial optimization problem with many applications in the real world. Genetic programming hyper heuristic has been successfully used to automatically evolve routing policies, which can make real-time routing decisions for uncertain capacitated arc routing problems. It is desired to evolve routing policies that are both effective and small/simple to be easily understood. The effectiveness and size are two potentially conflicting objectives. A further challenge is the objective selection bias issue, i.e., it is much more likely to obtain small but ineffective routing policies than the effective ones that are typically large. In this paper, we propose a new multi-objective genetic programming algorithm to evolve effective and small routing policies. The new algorithm employs the α dominance strategy with a newly proposed α adaptation scheme to address the objective selection bias issue. In addition, it contains a new archive strategy to prevent the loss of promising individuals due to the rotation of training instances. The experimental results showed that the newly proposed algorithm can evolve significantly better routing policies than the current state-of-the-art algorithms for uncertain capacitated arc routing problem in terms of both effectiveness and size. We have also analysed the evolved routing policies to show better interpretability.

Max-type reliability in uncertain post-disaster networks through the lens of sensitivity and stability analysis

The functionality of infrastructures, particularly in densely populated areas, is greatly impacted by natural disasters, resulting in uncertain networks. Thus, it is important for crisis management professionals and computer-based systems for transportation networks (such as expert systems) to utilize trustworthy data and robust computational methodologies when addressing convoluted decision-making predicaments concerning the design of transportation networks and optimal routes. This study aims to evaluate the vulnerability of paths in post-disaster transportation networks, with the aim of facilitating rescue operations and ensuring the safe delivery of supplies to affected regions. To investigate the problem of links' tolerances in uncertain networks and the resiliency and reliability of paths, an uncertainty theory-based model that employs minmax optimization with a bottleneck objective function is used. The model addresses the uncertain maximum reliable paths problem, which takes into account uncertain risk variables associated with links. Rather than using conventional methods for calculating the deterministic tolerances of a single element in combinatorial optimization, this study introduces a generalization of stability analysis based on tolerances while the perturbations in a group of links are involved. The analysis defines set tolerances that specify the minimum and maximum values that a designated group of links could simultaneously fluctuate while maintaining the optimality of the max-type reliable paths. The study shows that set tolerances can be considered as well-defined and proposes computational methods to calculate or bound such quantities - which were previously unresearched and difficult to measure. The model and methods are demonstrated to be both theoretically and numerically efficient by applying them to four subnetworks from our case study. In conclusion, this study provides a comprehensive approach to addressing uncertainty in reliability problems in networks, with potential applications in various fields.

Free Vibration Analysis of Arches with Interval-Uncertain Parameters

The dynamic characteristics of a structure serve as a crucial foundation for structural assessment, fault diagnosis, and ensuring structural safety. Therefore, it is imperative to investigate the impacts of uncertain parameters on the dynamic performance of structures. The dynamic characteristics of arches with uncertain parameters are analyzed in this paper. The uncertain parameters are regarded as non-probabilistic uncertainties and represented as interval variables. A model of an arch considering interval-uncertain parameters is built, and kinematic equations are established. The natural frequencies are obtained using the differential quadrature (DQ) method, and the relationships between natural frequency, radius, and central angle are also analyzed. On this basis, the Chebyshev polynomial surrogate (CPS) model is employed to solve the uncertain dynamic problem, and the natural frequencies are seen to be the objective functions of the CPS model. The accuracy verification of the model is achieved by comparison with the Monte Carlo simulation (MCS). Simulations are carried out considering different uncertainties, and the results show that the bounds of natural frequencies are influenced not only by the types of uncertain parameters, but also by their combinations.

Research on multi-granularity sequential three-way decisions based on the fuzzy T-equivalence relation

The fuzzy decision-theoretic rough set (FDTRS) is a data processing method based on the fuzzy theory designed to handle decision problems with uncertainty and fuzziness. It simplifies the complexity of decision-making and provides decision strategies by integrating multiple sources of information. This approach makes the decision process more scientific and rational. The mainstream FDTRS model breaks the over restrictive limits of classical decision-theoretic rough sets, computes the fuzzy similarity relation between two objects utilizing the Gaussian kernel function, which is another major breakthrough and innovation in the field of decision-theoretic rough sets. However, this model suffers from the problems of insufficient decision information, single perspective and high decision-making cost when dealing with dynamic, complex and uncertain problems. Emerging in recent years, sequential three-way decisions not only provides a flexible mechanism to implement the idea of progressive computation, but also deals with dynamic, complex and uncertain problems. To this end, this paper proposes a sequential three-way decision model based on the fuzzy T-equivalence relation (FTE-based sequential three-way decision model) from the perspective of sequential three-way decisions, and gives relevant definitions and examples to effectively solve the problem of insufficient information. Then in order to solve the single-view problem, we extend the sequential three-way decisions to the case of multi-granularity, and propose FTE-based multi-granularity sequential three-way decisions in four aggregation strategies with the corresponding properties and algorithms. In addition, the rationality of models are tentatively analyzed through specific examples. Finally, six sets of UCI standard datasets are used to validate the proposed models, which demonstrate their good performance. These models contribute to the field of fuzzy decision-theoretic rough sets and sequential three-way decisions.

Prediction of Production Capability for Subcontractors in Automotive Rubber Part Supply Chain Using Neuro-Fuzzy System

The paper proposes prediction production capability for automotive rubber part supply chain subcontractors in order to remain competitive in the global market. Rubber parts are used widely in automotive, motorcycles, trucks and other types of vehicles which are mostly small sizes but huge quantities to support original equipment manufacturer (OEM) brands with specific parts. The rubber part manufacturing process is complex and uncertain with compression molding and rubber curing conditions. Therefore, good conditions can predict to obtain high production capability for customer commissioning and delivery on schedule. The Neuro-fuzzy system is adopted and developed to deal with the uncertain capability under multi-criteria decision making. The methodology development can be used in the actual situation of the rubber part manufacturing supply chain environment and can predict uncertain problems that might occur in the subcontractor factories. The prediction of the production capability of the rubber part supply chain might be more effective on the real-time monitoring control system and can be tracked location part progressive for further planning both successful or has to be rescheduled. The platform was applied to audit and test in the actual industrial supply chain in Thailand. The methodology development was originally created for the particular supply chain in rubber automotive parts that can replace the existing manual approach to obtain a more efficient process of monthly performance evaluation.

On Mond–Weir-Type Robust Duality for a Class of Uncertain Fractional Optimization Problems

This article is focused on the investigation of Mond–Weir-type robust duality for a class of semi-infinite multi-objective fractional optimization with uncertainty in the constraint functions. We first establish a Mond–Weir-type robust dual problem for this fractional optimization problem. Then, by combining a new robust-type subdifferential constraint qualification condition and a generalized convex-inclusion assumption, we present robust ε-quasi-weak and strong duality properties between this uncertain fractional optimization and its uncertain Mond–Weir-type robust dual problem. Moreover, we also investigate robust ε-quasi converse-like duality properties between them.

A multiscale bidirectional fuzzy-driven learning network for remote sensing image segmentation

ABSTRACT Semantic segmentation is a fundamental but meaningful task in the remote sensing image understanding community. Great progress has been made in optical sensor photography technology, which poses an opportunity and a challenge for remote sensing image segmentation task. But, in fact, a longstanding and intractable problem is that many hard pixels in special position, i.e. the prevalent intra-class noise and a poor boundary delineation, is difficult to classify due to their inherent uncertainty. In this paper, we comprehensively consider the characteristics of deep learning and introduce traditional pattern recognition methods to drive structure learning, which can leverage the corresponding fuzzy logic model to alleviate the aforementioned problem in remote sensing images. Specifically, this paper designs a multiscale bidirectional fuzzy-driven learning network (MBFNet), which takes advantage of both deep learning and fuzzy logic to effectively alleviate the inherent uncertainty of these hard pixels. The structure of convolutional neural networks driven by fuzzy systems also provides a new modelling paradigm for solving the uncertain problem in remote sensing images. Meanwhile, multiscale techniques and bidirectional fusion are introduced to enhance feature aggregation and avoid the potential adverse effects of fuzzy systems, respectively. Experimental results on two datasets demonstrate qualitatively and quantitatively that the proposed MBFNet is competitive.

Neutrosophic hyperbolic programming strategy for uncertain multi-objective transportation problem

This paper suggests a neutrosophic hyperbolic programming approach based on the hyperbolic membership function to get an efficient solution for an uncertain multi-objective transportation problem where the uncertain normal distribution presents uncertainty. This technique provides flexibility to the decision-maker to select various confidence levels according to his/her own choice and analyze the satisfaction percentage of the obtained optimal compromise solution along with its truth, indeterminacy, and falsity values. In this approach, the parameters are changed from uncertain to crisp by using the inverse measure theorem, and the neutrosophic non-linear hyperbolic membership functions are used to convert the whole model into a non-linear programming problem in a neutrosophic environment. The advantages of our recommended method in real-world applications are effectively illustrated by a numerical illustration. This illustration also makes it easier to compare the results attained using our suggested strategy to those obtained using the methodologies put forward by Uddin et al. (2021) and Miah et al. (2022). Also, MATLAB software (version R2019a,64bit(win64)) is used to develop the code for the solution of this non-linear uncertain multi-objective transportation problem.

Data-driven distributionally robust support vector machine method for multiple criteria sorting problem with uncertainty

The multiple criteria sorting decision is a critical area of research in decision science. However, accurately capturing the decision maker’s cognition for each criterion using precise values poses significant challenges. To address this issue, our study investigates an uncertain multiple criteria sorting problem with indeterminate values for each criterion, which closely aligns with real-life decision-making processes. We adopt stochastic programming (SP) and distributionally robust optimization (DRO) to deal with the associated uncertainties. We formulate the preference learning process as a binary classification problem, where a piecewise-linear function is employed to measure the preference. Specifically, we develop a distributionally robust support vector machine model that incorporates the Wasserstein metric. By leveraging duality theory, the resulting DRO-based model can be transformed into a tractable convex problem. Then, we introduce an incremental projected subgradient algorithm to solve the tractable model, which can effectively utilize the separable structure. Finally, the efficiency of the proposed method is demonstrated through numerical experiments. The comparative evolution of the marginal value functions exhibits a similar tendency, highlighting the advantage and robustness of our approach.

Multiple-factor optimistic value based model and parameter estimation for uncertain portfolio optimization

In the traditional portfolio models, the return rates of risky assets are usually defined as random variables or fuzzy variables. However, when some events such as financial crises or wars occur that can cause instability in financial markets, the results of these assumptions are not always satisfactory. Therefore, some scholars try to use uncertain variables to express the return rates. In this paper, a two-factor uncertain portfolio problem under optimistic value criteria is studied, where we use the optimistic value instead of expected value to describe the investment return and study the impact of economic circumstance factor and corporation’s specificity factor on the return rates. Firstly, a two-factor optimistic value-variance-entropy model with background risk is constructed, in which the total investment return consists of the risky asset return and the background asset return. Then, considering the investors with two kinds of risk preferences, a three-step method is applied to convert the bi-objective optimization model. Moreover, a moment estimation method is used to process the expert-estimated data on the return rates. Finally, a numerical simulation is presented for showing the applicability of our models and solution method.

Intuitionistic uncertain linguistic prioritized aggregation operators and their application to multi-criteria decision making

The intuitionistic uncertain linguistic information aggregation problems considering different priority levels of criteria are investigated. Firstly, we extended the prioritized averaging (PA) operator to intuitionistic uncertain linguistic environment, defined two new prioritized aggregation operators called the intuitionistic uncertain linguistic prioritized weighted average (IULPWA) operator and the intuitionistic uncertain linguistic prioritized weighted geometric (IULPWG) operator, and established various desirable properties of the proposed operators. Secondly, we developed a multi-criteria decision making (MCDM) approach based on the IULPWA operator (or the IULPWG operator) to deal with the MCDM problems in which the criterion values take the form of intuitionistic uncertain linguistic numbers (IULNs) and the criteria are in different priority levels. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed method, and a comparison analysis is conducted to make clear the differences among the IULPWA operator, the IULPWG operator, the intuitionistic uncertain linguistic number weighted averaging (IULNWA) operator and the intuitionistic uncertain linguistic weighted geometric average (IULWGA) operator.

A Spatial Network-Based Assessment of Individual Exposure to COVID-19

This study seeks to examine the possible impacts of sociodemographic factors, individual mobility patterns, and daily activities on individual exposure to COVID-19 risk when assessed by different risk measures. Taking Hong Kong as the study area, we first model the risk of COVID-19 using a density-based approach and a network-based approach and reveal the differences in the spatial distributions of COVID-19 transmission risk they obtained. Then, using two-day individual Global Positioning System trajectory data and travel diaries collected from individuals in two communities, we measure individual exposure to COVID-19 transmission risk based on their mobility patterns and reveal the disparities in COVID-19 risk exposure among residents of different demographic groups and neighborhoods when conducting different activities. This study reveals the differences in the spatial patterns of COVID-19 transmission risk when the risk is conceptualized by density and network. It demonstrates the power of a spatial network approach in enhancing our understanding of individual exposure to infectious diseases. This study also advances the existing literature by exploring COVID-19 risk exposure, considering individual daily mobility and addressing the uncertain geographic context problem in analyzing individual COVID-19 risk exposure.

On optimality for fuzzy optimization problems with granular differentiable fuzzy objective functions

In recent years, there has been a growing interest in optimization problems with uncertainty. Fuzzy optimization is one of the approaches for investigation of such real-world extremum problems that contain uncertain data and, therefore, that are not well defined. Nonetheless, there is not enough discussion on the optimality conditions for optimal solutions (with regard to distinct fuzzy numbers) in (nonconvex) granular differentiable fuzzy optimization problems and methods for solving such uncertain extremum problems. Although the convexity notion is a very important property of optimization models, there are many real-world extremum problems and processes with uncertainty that cannot be modeled as convex fuzzy optimization problems. In this work, therefore, a new notion of granular differentiable generalized convexity is defined. Namely, the definition of granular differentiable F-convexity is introduced for fuzzy optimization problems and some properties of this concept are analyzed. Further, both the Fritz John necessary optimality conditions and, under the Guignard constraint qualification, the Karush-Kuhn-Tucker necessary optimality conditions are established for an optimal solution (with respect to distinct fuzzy numbers) in a fuzzy extremum problem with granular differentiable fuzzy-valued objective function and both inequality and equality constraints. As main applications of the introduced concept of granular differentiable F-convexity, the sufficiency of the derived Karush-Kuhn-Tucker necessary optimality conditions are proved and a new approach based on the so-called modified F-objective function method is proposed for solving the investigated fuzzy extremum problem.

Optimized Selection of Motorcycle Battery Swapping Stations Under Flexible Demand by Using Distance Function And Gis Technique

Our research proposes an approach to finding a suitable location for a motorcycle Battery Swapping Station (BSS) that considers multiple objectives. We developed a model based on Euclidean distance with K-NN, the AHP function, a desired number of stations, and GIS-based road infrastructure data. This model also considers the maximum coverage area and satisfies the number of stations and geographical features. Additionally, we consider the average driving distance of the battery swapping station location. To facilitate analysis, square grids form cells representing road type, environmental characteristics, places, and population density. Our proposed framework provides decision-makers with a multi-objective and visually optimized motorcycle BSS location, allowing for a more flexible selection of exact BSS locations shown on a map. Our demonstration can be used to resolve the uncertain problem related to finding a place for a motorcycle battery swapping station location. to finding a place for a motorcycle battery swapping station location.

Uncertain 4D-transportation problem with maximum profit and minimum carbon emission

Uncertain 4D-transportation problem with maximum profit and minimum carbon emission

Varying Built Environment Contexts and Trip Chain Decisions: A Multinomial-Choice Gradient Boosting Decision Trees Analysis

Understanding daily trip chain decisions is important for facilitating sustainable travel behavior and reducing traffic congestion. However, the relationships between varying built environment contexts across activity locations and trip chain choices remain unclear. This study adopts a multinomial-choice gradient boosting decision trees (MC-GBDT) model to compare the relative importance of socioeconomic variables with built environment variables. Additionally, it investigates the nonlinear and threshold effects between residential areas and primary activity areas. In the 2017 Beijing household activity survey, socioeconomic variables account for only about 21% of the relative importance in predicting the trip chain choices, whereas built environment variables constitute 78%, including 46% attribute to the primary activity area and 32% to the residential area. Moreover, several built environment variables have distinctive nonlinear and threshold effects, including local access to daily facilities, road density, and transit accessibility measures. Street design features and access to public transit have greater impacts on trip chain decisions in both residential and primary activity areas. These findings echo the uncertain geographic context problem (UGCoP) and imply that traditional built environment-trip chain research might underestimate the impact of built environment contexts at primary activity locations.

Adaboost-based SVDD for anomaly detection with dictionary learning

Anomaly detection aims to identify unusual behavior or discriminate abnormal samples by referring to the normal samples of data. Most exiting anomaly detection approaches train the model using only the normal data due to the scarcity of anomalies. However, the negative data or anomalies do occur in many practical applications. In this paper, we propose a novel anomaly detection method called AdaDL-SVDD for addressing uncertain data problem. In this method, both normal and anomalous samples are utilized to generate sparse representations with dictionary learning in the training phase. Meanwhile, we incorporate Support Vector Data Description (SVDD) into framework to construct a minimum hypersphere for anomaly detection over the test data. Additionally, the AdaBoost method is considered to construct a strong classifier via combining the weak classifiers. In the end, the experimental results demonstrate that the proposed AdaDL-SVDD method achieves superior performance over the UCI datasets with uncertainty and noise.

Probabilistic-based seismic fragility assessment of earthquake-induced site liquefaction

As a very complex and uncertain problem, seismic liquefaction is affected by many factors, such as earthquake intensity, site conditions, soil properties, etc. During the past half a century, the state-of-the-art in analysis and evaluation of earthquake-induced soil liquefaction and its consequences as well as the state-of-the-practice in improving seismic stability to resist liquefaction have been made much progress. However, the fragility analysis and assessment for seismic liquefaction of sites have not been paid enough attention to. In this paper, the concept of seismic liquefaction fragility for building sites is proposed. The soil resistance to liquefaction and liquefaction possibility are expressed as a fragility function of ground motion intensity, which can be used to describe minor, moderate and severe liquefaction potential under different ground motion intensity. Combined with the existing research results of seismic liquefaction evaluation, the analysis method of liquefaction fragility is given. Taking a specific site as an example for liquefaction fragility analysis, it is found that taking the calculated exceedance probability of different liquefaction levels as the observation value, the liquefaction fragility function follows both lognormal distribution and log-logistic distribution. With the increase of liquefaction level, the median value of liquefaction fragility function increases, while the site liquefaction fragility curve moves to the right, which shows that the ability of the site to resist more severe liquefaction is increasing. When convolved with the analysis results of liquefaction triggering and hazard, the liquefaction fragility function can be a much efficient tool for seismic liquefaction risk analysis of specific sites.

Higher-order optimality conditions of robust Benson proper efficient solutions in uncertain vector optimization problems

Higher-order optimality conditions of robust Benson proper efficient solutions in uncertain vector optimization problems