Uncertain Distribution Research Articles

Utilizing engineered extracellular vesicles as delivery vectors in the management of ischemic stroke: a special outlook on mitochondrial delivery.

Ischemic stroke is a secondary cause of mortality worldwide, imposing considerable medical and economic burdens on society. Extracellular vesicles, serving as natural nano-carriers for drug delivery, exhibit excellent biocompatibility in vivo and have significant advantages in the management of ischemic stroke. However, the uncertain distribution and rapid clearance of extracellular vesicles impede their delivery efficiency. By utilizing membrane decoration or by encapsulating therapeutic cargo within extracellular vesicles, their delivery efficacy may be greatly improved. Furthermore, previous studies have indicated that microvesicles, a subset of large-sized extracellular vesicles, can transport mitochondria to neighboring cells, thereby aiding in the restoration of mitochondrial function post-ischemic stroke. Small extracellular vesicles have also demonstrated the capability to transfer mitochondrial components, such as proteins or deoxyribonucleic acid, or their sub-components, for extracellular vesicle-based ischemic stroke therapy. In this review, we undertake a comparative analysis of the isolation techniques employed for extracellular vesicles and present an overview of the current dominant extracellular vesicle modification methodologies. Given the complex facets of treating ischemic stroke, we also delineate various extracellular vesicle modification approaches which are suited to different facets of the treatment process. Moreover, given the burgeoning interest in mitochondrial delivery, we delved into the feasibility and existing research findings on the transportation of mitochondrial fractions or intact mitochondria through small extracellular vesicles and microvesicles to offer a fresh perspective on ischemic stroke therapy.

Stochastic First-Order Algorithms for Constrained Distributionally Robust Optimization

We consider distributionally robust optimization (DRO) problems, reformulated as distributionally robust feasibility (DRF) problems, with multiple expectation constraints. We propose a generic stochastic first-order meta-algorithm, where the decision variables and uncertain distribution parameters are each updated separately by applying stochastic first-order methods. We then specialize our results to the case of using two specific versions of stochastic mirror descent (SMD): (i) a novel approximate version of SMD to update the decision variables, and (ii) the bandit mirror descent method to update the distribution parameters in the case of [Formula: see text]-divergence sets. For this specialization, we demonstrate that the total number of iterations is independent of the dimensions of the decision variables and distribution parameters. Moreover, the cost per iteration to update both sets of variables is nearly independent of the dimension of the distribution parameters, allowing for high-dimensional ambiguity sets. Furthermore, we show that the total number of iterations of our algorithm has a logarithmic dependence on the number of constraints. Experiments on logistic regression with fairness constraints, personalized parameter selection in a social network, and the multi-item newsvendor problem verify the theoretical results and show the usefulness of the algorithm, in particular when the dimension of the distribution parameters is large. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms—Continuous. Funding: This work was supported by the National Science Foundation [Grant 2112533]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2023.0167 .

Uncertain process-based data integration and residual lifetime evaluation of PCB in airborne equipment with ADT and field data

Accurately evaluating the lifespan of the Printed Circuit Board (PCB) in airborne equipment is an essential issue for aircraft design and operation in the marine atmospheric environment. This paper presents a novel evaluation method by fusing Accelerated Degradation Testing (ADT) data, degradation data, and life data of small samples based on the uncertainty degradation process. An uncertain life model of PCB in airborne equipment is constructed by employing the uncertain distribution that considers the accelerated factor of multiple environmental conditions such as temperature, humidity, and salinity. In addition, a degradation process model of PCB in airborne equipment is constructed by employing the uncertain process of fusing ADT data and field data, in which the performance characteristics of dynamic cumulative change are included. Based on minimizing the pth sample moments, an integrated method for parameter estimation of the PCB in airborne equipment is proposed by fusing the multi-source data of life, degradation, and ADT. An engineering case illustrates the effectiveness and advantage of the proposed method.

Navigating uncertain distribution problem: a new approach for resolution optimization of transportation with several objectives under uncertainty

Amidst uncertainty, decision-making in manufacturing becomes a central focus due to its complexity. This study explores complex transportation constraints and uses novel ways to guide manufacturers. The Multi-objective Stochastic Linear Fractional Transportation Problem (MOSLFTP) is a crucial tool for managing supply chains, manufacturing operations, energy distribution, emergency routes, healthcare logistics, and other related areas. It adeptly addresses uncertainty, transforming efficiency and effectiveness in several domains. Stochastic programming is the process of converting theoretical probabilities into concrete certainties. The artistic compromise programming technique acts as a proficient mediator, reconciling opposing objectives and enabling equitable decision-making. This novel approach also addresses the Multi-objective Stochastic Linear plus Linear Fractional Transportation Problem (MOSLPLFTP), which involves two interconnected issues. The effectiveness of these principles is clearly shown with the help of the LINGO® 18 optimization solver. This study uses a ranking method to compare the similar methods to solve the current problems. A meticulously designed example acts as a significant achievement, shedding light on our method in a practical setting. It serves as a distinctive instrument, leading manufacturers through the maze of uncertainty and assisting them in determining the most advantageous course of action. This journey involves subtle interactions between complexity and simplicity, uncertainty is overcome by decisiveness, and invention is predominant.

АНАЛИЗ ВЗАИМОСВЯЗИ НИКОТИНОВОЙ ЗАВИСИМОСТИ И ПАССИВНОГО КУРЕНИЯ СО СТЕПЕНЬЮ ТЯЖЕСТИ ХРОНИЧЕСКОЙ ОБСТРУКТИВНОЙ БОЛЕЗНИ ЛЕГКИХ У КУРЯЩИХ ЖЕНЩИН РЕПРОДУКТИВНОГО ВОЗРАСТА

Introduction. We studied the nicotine addiction stage and secondhand smoke interrelationships with the chronic obstructive pulmonary disease severity in smokers of reproductive age. Aim of the study was to research in the nicotine addiction and secondhand smoke impact upon the development of chronic obstructive pulmonary disease severity in smoking women of reproductive age. Materials and Methods. Using the questionnaire methodology developed, the nicotine addiction stage was analyzed in reproductive women with and without secondhand smoke (based on questionnaire survey outcomes). There were 107 smoking female patients of reproductive age divided into two groups: Those with secondhand smoke and those without it. Observational group consisted of 42 non-smoking women without any chronic diseases. Chronic obstructive pulmonary disease was diagnosed based on the clinical recommendations of the Russian Respiratory Society (2021). The data obtained during the study were analyzed followed by the comparison of the outcomes between the groups of smoking patients with secondhand and non-secondhand smoking, against the observational group. The outcomes led us to determine whether there is a statistically significant relationship between secondhand smoke and nicotine addiction stage in the development of chronic obstructive pulmonary disease. The reliability of the outcomes was assessed using the methods of parametric and nonparametric statistics. Before using all statistical research methods, we checked whether the sampling complied with the Gaussian (normal) distribution law. Variables that did not obey the normal distribution law or those with the uncertain distribution law were analyzed using a nonparametric statistical method, i. e., Pearson criterion. Results and Discussion. Average age of the smoking patients is 26.5 years. Average index of smokers was 6.59 pack-years. The smokers’ index exceeded the middle of the indicator contributing to the chronic obstructive pulmonary disease development (10 pack – years), which is typical for a young age and their smoking experience. It was found that the nicotine addiction stage correlates with the chronic obstructive pulmonary disease severity with a statistically significant reliability. Conclusions. Secondhand smoke in addition to active smoking, reduces the temporal characteristics of chronic obstructive pulmonary disease severity.

Efficient metamodel-based importance sampling coupled with single-loop estimation method for parameter global reliability sensitivity analysis

To efficiently estimate the main effects and total effects of uncertain distribution parameters on the uncertainty of failure probability, we construct single-loop estimation formulas by introducing auxiliary variables through the equal probability transformation. This approach circumvents the original nested triple-loop process. For generating samples used in the derived single-loop estimation formulas, direct Monte Carlo simulation can be employed. To reduce the number of samples in Monte Carlo simulation, the important sampling technique can be integrated into the proposed single-loop estimation formulas. Additionally, to enhance the efficiency of identifying the states (failure or safety) of all used samples, an adaptive Kriging model can be introduced. Subsequently, the adaptive Kriging model coupled with Monte Carlo simulation, and the adaptive Kriging model coupled with the importance sampling technique, are integrated into the derived single-loop formulas to concurrently and efficiently estimate the main effects and total effects of uncertain distribution parameters. The results of three case studies validate the accuracy and efficiency of the proposed method.

Joint optimization of location and allocation for spare parts depots under ($ r, Q $) inventory policy

<p>The ability to replace failed spare parts in time directly affects the supportability level of equipment systems. The selection of spare parts' depot locations, inventory mode, and allocation are often separate and independent operations. However, in these situations, the total supply cost is usually relatively high with the consideration of spare parts shortage and maintenance delays. Therefore, this article dealt with a depot location-inventory-allocation problem based on the $ (r, Q) $ inventory method and analyzed a combined network of centralized spare part depot locations, inventory, and allocation. Meanwhile, considering the convenience and speed of spare parts transportation brought about by the improvement of transportation capacity, a network is proposed to adopt a centralized storage and point-to-point allocation strategy for parts replacement, which reduces supportability costs without affecting supply efficiency. An optimization model has been developed that reduces the overall cost of support, including inventory, construction, transportation, and logistics. Three equipment support efficiency metrics were used as constraints in this model to assess the location of open depots: selection availability, fill rate, and predicted downtime. Additionally, due to the knowledge asymmetry, there are some shortage issues which always lead to extra expenditure. The model also introduces uncertain distribution to demand measurement and adopts a genetic algorithm for model solving. Ultimately, a numerical instance was developed so as to verify our results.</p>

Finite element analysis of anterior cruciate ligament reconstruction techniques: A comparison of the mechanical properties of all-inside fixation and traditional fixation.

The main purpose of this study was to explore the mechanical properties of the anterior cruciate ligament and its attachments following reconstruction with the all-inside technique after anterior cruciate ligament injury. Knee joint computed tomography data were collected from healthy volunteers, and knee joint models were created using Mimics software. A normal knee joint model, an all-inside reconstructed anterior cruciate ligament model, and a traditional reconstructed anterior cruciate ligament model were established. A tensile force of 134N and a bending moment of 5N/m were applied at the anterior aspect of the proximal tibia in these three models. The knee joint was subjected to external rotation, internal rotation, varus, valgus, flexion, and extension under this bending moment. The magnitude and distribution of stress on the ligament or graft and the magnitude and distribution of stress on the graft attachments were observed under different loading conditions. Under different external forces, the maximum stress on the ligament in the normal model fluctuated from 1.949 to 18.302MPa, with an uncertain distribution of maximum stress. The maximum stress on the graft in the all-inside reconstructed anterior cruciate ligament model fluctuated from 0.705 to 3.465MPa and was mainly distributed at the junction of the graft and the tibial footprint. In the traditional reconstructed anterior cruciate ligament model, the maximum stress on the graft fluctuated from 5.012 to 59.269MPa and was primarily distributed at the junction of the interference screw and the graft. The concentration of stress on the loop and plate in the all-inside reconstructed anterior cruciate ligament model fluctuated from 70.461 to 346.363MPa, with maximum stress distributed at the junction of the loop and the tibial surface. The maximum stress on the interference screw in the traditional reconstructed anterior cruciate ligament model fluctuated from 10.184 to 92.298MPa, with maximum stress primarily distributed at the end of the interference screw. Under different external forces, the graft used in all-inside anterior cruciate ligament reconstruction is subjected to fewer external forces than that used in traditional anterior cruciate ligament reconstruction, which may indicate a relatively stable mechanical environment. The strength of the loop and plate can theoretically tolerate daily knee joint movements of patients without injury.

Oral submucous fibrosis: Histopathogenesis

Oral submucosal fibrosis (OSMF) is a precancerous condition of the oral cavity caused by the development of inflammation and fibrosis in the submucosal tissue, causing symptoms of tension and trismus. OSMF remains a concern for healthcare providers due to its easy transmission and uncertain distribution. Over the years, many classifications based on clinical, histopathological, or functional basis have been documented in the medical literature. However, none of these classifications are universally accepted. Each distribution has advantages and disadvantages. It strives to provide and update information on the OSMF classification system to help clinicians, researchers, and researchers classify these diseases for early diagnosis, and treatment time, and reducing the number of deaths. Pathogenesis and treatment are also discussed.

Similarity-Based Remaining Useful Lifetime Prediction Method Considering Epistemic Uncertainty

Measuring the similarity between two trajectories is fundamental and essential for the similarity-based remaining useful life (RUL) prediction. Most previous methods do not adequately account for the epistemic uncertainty caused by asynchronous sampling, while others have strong assumption constraints, such as limiting the positional deviation of sampling points to a fixed threshold, which biases the results considerably. To address the issue, an uncertain ellipse model based on the uncertain theory is proposed to model the location of sampling points as an observation drawn from an uncertain distribution. Based on this, we propose a novel and effective similarity measure metric for any two degradation trajectories. Then, the Stacked Denoising Autoencoder (SDA) model is proposed for RUL prediction, in which the models can be first trained on the most similar degradation data and then fine-tuned by the target dataset. Experimental results show that the predictive performance of the new method is superior to prior methods based on edit distance on real sequence (EDR), longest common subsequence (LCSS), or dynamic time warping (DTW) and is more robust at different sampling rates.

Memory-Enhanced Twin Delayed Deep Deterministic Policy Gradient (ME-TD3)-Based Unmanned Combat Aerial Vehicle Trajectory Planning for Avoiding Radar Detection Threats in Dynamic and Unknown Environments

Unmanned combat aerial vehicle (UCAV) trajectory planning to avoid radar detection threats is a complicated optimization problem that has been widely studied. The rapid changes in Radar Cross Sections (RCSs), the unknown cruise trajectory of airborne radar, and the uncertain distribution of radars exacerbate the complexity of this problem. In this paper, we propose a novel UCAV trajectory planning method based on deep reinforcement learning (DRL) technology to overcome the adverse impacts caused by the dynamics and randomness of environments. A predictive control model is constructed to describe the dynamic characteristics of the UCAV trajectory planning problem in detail. To improve the UCAV’s predictive ability, we propose a memory-enhanced twin delayed deep deterministic policy gradient (ME-TD3) algorithm that uses an attention mechanism to effectively extract environmental patterns from historical information. The simulation results show that the proposed method can successfully train UCAVs to carry out trajectory planning tasks in dynamic and unknown environments. Furthermore, the ME-TD3 algorithm outperforms other classical DRL algorithms in UCAV trajectory planning, exhibiting superior performance and adaptability.

Probabilistic anomaly detection considering multi-level uncertainties for cable-stayed bridges

To model multi-level uncertainties within anomaly detection process for large-span bridges, a probabilistic anomaly detection method is proposed considering uncertain models in the data collection, thermal response separation, and trigger estimation. The uncertain model in the data collection is established with the measured value and measuring errors. The uncertain model in the thermal response separation is built through the linear Bayesian estimation. The uncertain distribution of the anomaly detection trigger is obtained via Bayesian estimation of generalized Pareto distribution. Subsequently, measurements from multi-sensors are used to detect anomalies in a probabilistic way. Evidential reasoning, a decision-level fusion tool, is used to derive a collective detection rate to distinguish sensor malfunctions from anomalous scenarios. Specifically, anomalous scenarios deserve a large collective detection rate, whilst sensor malfunctions are subject to a small collective detection rate and a large individual detection rate. Two cases (i.e., sensor malfunction and snow disaster) are illustrated based on measurements from a large span cable-stayed bridge. As a result, the sensor malfunction is detected with an individual detection rate of 89.20% and a collective detection rate of 2.77%. The snowstorm is detected by a collective detection rate of almost 100%.

Weekly mapping of surface water extent in the intertropical wetlands using spaceborne GNSS reflectometry

As of today, the uncertain distribution and dynamics of inundations in the tropical wetlands cause large uncertainties in the quantification of the world’s methane emissions. Long-term, global remote sensing observations currently rely on optical sensors, affected by cloud cover and vegetation, and on passive microwave imagery with a low spatial resolution. Global Navigation Satellite System Reflectometry (GNSS-R) L-band observations from space onboard the Cyclone GNSS (CYGNSS) mission can provide information about the dynamics of surface water at moderate to low spatial resolution and with a frequent revisit. In this article, we propose a methodology to compute the fraction of water contained in 0.1°pixels (∼10 km) using CYGNSS reflectivity and Above Ground Biomass (AGB) maps. We produced a 1-year time series of water fractions with a weekly time sampling for the full coverage of CYGNSS between ±38°of latitude, from August 2018 to July 2019. We evaluated the results against regional reference maps of surface water based on MODIS, JERS-1, and PALSAR, and against the Global Inundation Extent from Multi-Satellite (GIEMS) dataset. CYGNSS water fractions represent well the spatial distribution and the seasonality of inundation extent for most of the tropical wetlands, with a global RMSD of 15.0 % against GIEMS. We found a likely overestimation when the soil moisture (SM) exceeds 0.3-0.4 cm3/cm3, i.e. for saturated soils where GNSS-R reflections are coherent, as the SM was not parameterized in our retrieval model. Despite this, the results are consistent in the entire intertropical band including over densely vegetated areas. These weekly water fractions for 2018-2019 with a 0.1°pixel size are distributed to contribute to further comparisons and hydrological researches.

Robust Task Offloading and Resource Allocation in Mobile Edge Computing With Uncertain Distribution of Computation Burden

In mobile edge computing (MEC) supporting multiple mobile users (MUs), it is essential to optimize the offloading policy and communication and computation resource allocation. A main challenge is that the computation burden of a computation task may be random and even with uncertain probabilistic distribution. To address this challenge, we investigate a multiple-MU MEC system with random computation burden. For the random computation burden of an MU, only the mean and variance are known, but its distribution is unknown. Robustness is provided such that computation outage probabilities (due to uncertain distribution of computation burden) are bounded by a predefined threshold. We minimize the weighted sum of the MUs’ energy consumption. The formulated optimization problem is non-deterministic and non-convex, and thus, is hard to solve. To deal with the challenge, we transform the formulated problem into a deterministic and convex problem by applying the Chebyshev-Cantelli inequality and some mathematical manipulations. We further decompose the convex problem to a lower-level and an upper-level problem. Low-complexity algorithms are developed for the lower-level and upper-level problems. The overall complexity of our proposed method is linear with the number of MUs.

Redefining the MIS 3 climatic scenario for Neanderthals in northeastern Iberia: A multi-method approach

One of the major challenges in scientific research is to understand past climate and the mechanisms of climate change. Small vertebrates, and especially rodents, are very sensitive to shifts in climate and habitat, and their variations over time in terms of taxa and abundance can be successfully used to reconstruct past environments. The vast array of approaches to palaeoclimatic reconstruction reflects the great effort that has gone into this line of investigation. Recently, the UDA-ODA discrimination technique has been postulated as a more reliable ecologically-based methodology compared to the classical MER method.To provide biogeographical information to be analysed by the UDA-ODA discrimination technique, the distributions of four species (Sorex minutus, Chionomys nivalis, Talpa europaea and Crocidura russula) documented in levels O, N, E and D of the Abric Romaní site were processed. The results reveal a statistical difference between the climatic values for the occupied distribution areas (ODA) and those for the uncertain distribution areas (UDA). This technique was then applied to small-mammal assemblages from the above-mentioned levels of Abric Romaní, to test whether the use of the ODAs of the species improves the precision of the climatic reconstruction compared to the atlas distributions of the species used in MER procedures. Our results suggest an improvement in the discrimination analysis over the previous MER reconstructions when wider distributions for an assemblage are obtained. The coldest values obtained for level O of Abric Romaní seem to reinforce the pollen interpretation of the level as coetaneous with a cold period. For the whole MIS 3 climatic scenario for Neanderthals, a colder and wetter climate is derived from the small-mammal analysis. However, as different methods and analyses have inherent limitations, a standardization of the methods applied to the different levels and sites should be carried out in order to provide comparable results.

Prediction of Ultimate Bearing Capacity of Oil and Gas Wellbore Based on Multi-Modal Data Analysis in the Context of Machine Learning

As important research for drilling engineering, the prediction of oil and gas shaft lining conditions is changing from the traditional method based on the mechanism model to the intelligent prediction method combining the mechanism model with the data model. Therefore, this paper establishes a stacking integrated model for predicting the uniaxial compression strength (UCS) of rock based on four basic parameters that can reflect the characteristics of rock mass. At the same time, the expectation-maximation (EM) algorithm is used to optimize the hidden Markov models (HMM), and a fuzzy random model of the ultimate bearing capacity of oil and gas shaft lining is established. The uncertain distribution of main parameters of rock mass is analyzed, and the corresponding fuzzy random distribution law is obtained. The experimental results show that the stacking integration algorithm is of great help to improve the prediction effect of rock mass compressive strength. The EM-HMM model has the advantages of small error, high efficiency, and fast convergence after two fuzzy random processes. Using this algorithm is helpful to analyze the stress state and parameter response mechanism of the shaft lining, dynamically generate optimized parameters, and provide technical support for reducing the incidence of complex drilling accidents, shortening the well construction period and lowering the drilling cost.

Optimal Planning of Wind -based DG Units in Uncertain Distribution Network

This paper presents the Zebra Optimization Algorithm (ZOA), a novel bio-inspired metaheuristic algorithm for optimizing the allocation of distributed generation (DG) units based on wind turbine (WT) technology in distribution networks (DN). The algorithm is based on the foraging and defense strategies of zebras in the wild. ZOA seeks to reduce total energy losses and improve the distribution network's daily voltage profile. The proposed method was applied to a typical IEEE 33-node distribution network, and the simulation results were compared to those obtained by other recently developed optimization algorithms. The comparison report affirmed the efficiency of the Zebra Optimization Algorithm method, demonstrating its ability to outperform existing optimization algorithms.

Optimal Planning of Photovoltaic-based DG Units in Uncertain Distribution Network

This paper introduces a novel bio-inspired metaheuristic algorithm called the Zebra Optimization Algorithm (ZOA) for optimizing the allocation of distributed generation (DG) units based on photovoltaic (PV) technology in distribution networks (DN). The algorithm is inspired by the foraging behavior and defense strategies of zebras in nature. ZOA aims to minimize total energy losses and improve the daily voltage profile in the distribution network. The proposed approach was applied to the typical IEEE 33 node distribution network, and the simulation results were compared with those obtained by other optimization algorithms developed in recent literature. The effectiveness of the Zebra Optimization Algorithm method was confirmed by the comparison report, demonstrating its ability to outperform existing optimization algorithms.

Modal Regression-Based Graph Representation for Noise Robust Face Hallucination.

Manifold learning-based face hallucination technologies have been widely developed during the past decades. However, the conventional learning methods always become ineffective in noise environment due to the least-square regression, which usually generates distorted representations for noisy inputs they employed for error modeling. To solve this problem, in this article, we propose a modal regression-based graph representation (MRGR) model for noisy face hallucination. In MRGR, the modal regression-based function is incorporated into graph learning framework to improve the resolution of noisy face images. Specifically, the modal regression-induced metric is used instead of the least-square metric to regularize the encoding errors, which admits the MRGR to robust against noise with uncertain distribution. Moreover, a graph representation is learned from feature space to exploit the inherent typological structure of patch manifold for data representation, resulting in more accurate reconstruction coefficients. Besides, for noisy color face hallucination, the MRGR is extended into quaternion (MRGR-Q) space, where the abundant correlations among different color channels can be well preserved. Experimental results on both the grayscale and color face images demonstrate the superiority of MRGR and MRGR-Q compared with several state-of-the-art methods.

A Distributionally Robust Fuzzy Optimization Method for Single-Period Inventory Management Problems

This paper investigates single-period inventory management problems with uncertain market demand, where the exact possibility distribution of demand is unavailable. In this condition, it is important to order a reliable quantity which can immunize against distribution uncertainty. To model this type of single-period inventory management problem, this paper characterizes the uncertain demand by generalized interval-valued possibility distributions. We present a novel concept about an uncertain distribution set to describe distribution perturbation characterization. First, we introduce a lambda selection of the interval-valued fuzzy variable, and the uncertain distribution set is a collection of all generalized possibility distributions of lambda selection variables. According to the uncertain distribution set, a new distributionally robust fuzzy optimization method is developed for single-period inventory management problems. Under mild assumptions, the robust counterpart of the proposed fuzzy single-period inventory management model is formulated, which is an optimization program with certain linear objectives and infinitely many integral constraints. We discuss the computational issue of integral constraints and reformulate equivalently the robust counterpart as three deterministic inventory submodels under generalized interval-valued trapezoidal possibility distributions. According to the characteristics of three submodels, a domain decomposition method is designed to find the robust optimal solution that can immunize against uncertainty in our single-period inventory management problem. Finally, some computational results demonstrate the efficiency of the proposed distributionally robust fuzzy optimization method.