Random Output Research Articles

GPS-free synchronized pseudo-random number generators for internet-of-things

IntroductionSecuring wireless communications in internet-of-things (IoT) requires both generation and synchronization of random numbers in real-time. However, resource constraints on an IoT device limit the use of computationally intensive random number generators and the use of global positioning systems (GPS) for synchronization. In this paper, we propose a synchronized pseudo-random number generator (SPRNG) that uses a combination of a fast, low-complexity linear-feedback-shift-register (LFSR) based PRNG and a slow but secure, synchronized seed generator based on self-powered timers.MethodsA prototype synchronized self-powered timer (SSPT) array was fabricated in a standard silicon process and was used to generate dynamic random seeds for the LFSR. The SSPTs use quantum-mechanical tunneling of electrons to operate without any external power and are practically secure against tampering, snooping, and side-channel attacks (both power and electromagnetic).ResultsIn this work, we explore protocols to periodically and securely generate random bits using the self-powered timers for seeding the LFSR. We also show that the time-varying random seeds extend and break the LFSR periodic cycles, thus making it difficult for an attacker to predict the random output or the random seed. Using the National Institute of Standards and Technology (NIST) test suite we verify the randomness of the measured seeds from the fabricated ensemble of SSPTs together with the random bit sequences generated by a software-seeded LFSR.DiscussionsIn this modality, the proposed SPRNG could be used as a trusted platform module (TPM) on IoTs and used for verifying and authenticating secure transactions (e.g., software upgrades). Since the SPRNG system does not require access to GPS for synchronization, therefore it could be used in many resource-constrained and adversarial environments.

Exploring the Hysteresis Effect in SOC Estimation of Li-ion Batteries

The global energy crisis and serious environmental pollution make governments attach importance to the development of regenerating green energy. As the best battery system at present, lithium-ion battery has developed rapidly into a new generation of energy storage power. SOC estimation is an important indicator in the development of lithium-ion batteries. If SOC can be properly estimated, it will be pivotal to the investigation and exploitation of batteries, and a number of algorithms for SOC estimation have already emerged. This paper first introduces several current SOC estimation methods, and then explains the influencing factors and hysteresis effect of SOC. Then the SOC estimation value was obtained by open circuit voltage method, based on the mean value calculated by the random forest output OCV-SOC curve to reduce hysteresis effect. The effect of temperature on SOC was analysed by plotting the OCV-SOC profiles for charging and discharging at different temperatures. Finally, this paper is summarized and puts forward the improvement.

Multifidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos-Kriging

We propose novel methods for Conditional Value-at-Risk (CVaR) estimation for nonlinear systems under high-dimensional dependent random inputs. We develop a novel DD-GPCE-Kriging surrogate that merges dimensionally decomposed generalized polynomial chaos expansion and Kriging to accurately approximate nonlinear and nonsmooth random outputs. We use DD-GPCE-Kriging (1) for Monte Carlo simulation (MCS) and (2) within multifidelity importance sampling (MFIS). The MCS-based method samples from DD-GPCE-Kriging, which is efficient and accurate for high-dimensional dependent random inputs, yet introduces bias. Thus, we propose an MFIS-based method where DD-GPCE-Kriging determines the biasing density, from which we draw a few high-fidelity samples to provide an unbiased CVaR estimate. To accelerate the biasing density construction, we compute DD-GPCE-Kriging using a cheap-to-evaluate low-fidelity model. Numerical results for mathematical functions show that the MFIS-based method is more accurate than the MCS-based method when the output is nonsmooth. The scalability of the proposed methods and their applicability to complex engineering problems are demonstrated on a two-dimensional composite laminate with 28 (partly dependent) random inputs and a three-dimensional composite T-joint with 20 (partly dependent) random inputs. In the former, the proposed MFIS-based method achieves 104x speedup compared to standard MCS using the high-fidelity model, while accurately estimating CVaR with 1.15% error.

An Improved Adaptive Kalman Filter based on Auxiliary Model for State of Charge Estimation with Random Missing Outputs

In this study, an improved adaptive Kalman filter based on auxiliary model (IAKF-AM) is proposed for estimating the state of charge (SOC) with random missing outputs. Since the traditional auxiliary model (AM) method is inefficient for systems with scarce measurements, this paper provides an IAKF-AM method. Compared with the AM method, the proposed method uses the measurable data to adjust missing outputs in each interval, thus has higher estimation accuracy. In addition, a recursive least squares (RLS) algorithm is introduced, which can combine the IAKF-AM method to iteratively estimate the SOC and outputs. In the simulation part, the mean absolute errors (MAE) and the root mean squared error (RMSE) is used to evaluate the model performance under different cases. Simulation example verify the effectiveness of the proposed IAKF-AM algorithm.

Spectrum-tailored random fiber laser towards ICF laser facility

Broadband low-coherence light is considered to be an effective way to suppress laser plasma instability. Recent studies have demonstrated the ability of low-coherence laser facilities to reduce back-scattering during beam–target coupling. However, to ensure simultaneous low coherence and high energy, complex spectral modulation methods and amplification routes have to be adopted. In this work, we propose the use of a random fiber laser (RFL) as the seed source. The spectral features of this RFL can be carefully tailored to provide a good match with the gain characteristics of the laser amplification medium, thus enabling efficient amplification while maintaining low coherence. First, a theoretical model is constructed to give a comprehensive description of the output characteristics of the spectrum-tailored RFL, after which the designed RFL is experimentally realized as a seed source. Through precise pulse shaping and efficient regenerative amplification, a shaped random laser pulse output of 28 mJ is obtained, which is the first random laser system with megawatt-class peak power that is able to achieve low coherence and efficient spectrum-conformal regenerative amplification.

Last-iterate convergence analysis of stochastic momentum methods for neural networks

The stochastic momentum method is a commonly used acceleration technique for solving large-scale stochastic optimization problems. Current convergence results of stochastic momentum methods under non-convex stochastic settings mostly discuss convergence in terms of the random output and minimum output, which requires temporal and spatial statistics of historical data. On the other hand, the last-iterate convergence allows us to avoid storing or selecting past output iterates after each iteration, while maintaining rigour in convergence analysis. To this end, we address the convergence of the last iterate output (called last-iterate convergence) of the stochastic momentum methods for non-convex stochastic optimization problems, in a way which is conformal with traditional optimization theory. For generality, we prove the last-iterate convergence of the stochastic momentum methods under a unified framework, covering both stochastic heavy ball momentum and stochastic Nesterov accelerated gradient momentum, whose momentum factors can be either constant or time-varying coefficients. Finally, the last-iterate convergence of the stochastic momentum methods is verified on the benchmark MNIST and CIFAR-10 datasets. The implementation of SUM is available at: https://github.com/xudp100/SUMhttps://github.com/xudp100/SUM.

Feature alignment as a generative process.

Reversibility in artificial neural networks allows us to retrieve the input given an output. We present feature alignment, a method for approximating reversibility in arbitrary neural networks. We train a network by minimizing the distance between the output of a data point and the random output with respect to a random input. We applied the technique to the MNIST, CIFAR-10, CelebA, and STL-10 image datasets. We demonstrate that this method can roughly recover images from just their latent representation without the need of a decoder. By utilizing the formulation of variational autoencoders, we demonstrate that it is possible to produce new images that are statistically comparable to the training data. Furthermore, we demonstrate that the quality of the images can be improved by coupling a generator and a discriminator together. In addition, we show how this method, with a few minor modifications, can be used to train networks locally, which has the potential to save computational memory resources.

Food Supply Chain Sustainability Strategy for Fresh Retailer and Multi-Output Random Fresh Suppliers after COVID-19

Feeding people sustainably during the COVID-19 pandemic remains a challenge, as food productivity is declining and there is a risk of chain breakage at any time. To maintain the core function of supplying food to end consumers, a new framework must be developed to investigate the strategies for coordinating a new supply chain comprised of multiple suppliers with random output. Thus, in both decentralized and centralized systems, this paper constructs a supply chain model of a retailer procuring from multiple suppliers and characterizes each party’s optimal decisions. These results show that: (1) the optimal order quantity, profit of each part, and overall profit of the supply chain in the concentrated situation are better than those in the decentralized situation, and the transmission mechanism is slightly different from the classic newsboy model; (2) a supply chain coordination contract consisting of price discounts and compensation is designed, which can realize the coordination of a retailer and multiple suppliers with random yield in the endogenous price situation. These results imply that managers can develop sustainable food supply chains during uncertain times by ordering from these multi-suppliers with random yield. This paper adds to the literature on random yield assembly systems by taking into account that multiple suppliers have random component distributions.

Credit access and agricultural technology adoption nexus in Ethiopia: A systematic review and meta-analysis

Access to credit is a good way to overcome some of the financial obstacles associated with technology adoption by the farmers. In Ethiopia the potential effect of credit on technology adoption is controversial. To determine the overall direction of effect a meta-analysis was done using a total 42 studies. The random effect model and meta regression analysis were applied to unveil the potential effect of credit access on farmers' technology adoption in Ethiopia. The result showed that in Ethiopia farmers adopted agricultural technologies such as chemical fertilizer, high yielding varieties, livestock technologies, soil and water conservation practices, beehive technologies, poultry technologies and ICT technologies. The random effect model output showed that access to credit increases agricultural technology adoption of farmers by 1.23unit, as compared to farmers who have no access to credit. The result from the meta regression output also depicted that family size; total livestock holding and total income were the main factors that determine heterogeneity in the effect of credit access on farmers' technology adoption among farmers. It was concluded that credit is essential to improve technology adoption; however, most farmers in Ethiopia have collateral problems to have access to credit for the adoption of technologies. It was recommended that a lot of improvement is needed from the government and private financial institutions to widen credit provision for the rural communities without collateral which could boost the financial power of the farmers so as to purchase technologies from the market. • In Ethiopia farmers adopted agricultural technologies such as chemical fertilizer, high yielding varieties, livestock technologies, soil and water conservation practices, beehive technologies, poultry technologies and ICTs technologies. • access to agricultural credit is a good way to overcome some of the financial obstacles associated with technology adoption. • The random effect model output showed that access to credit increases agricultural technology adoption of farmers by 1.23unit, as compared to farmers who have no access to credit. • The result from the Meta analysis depicted that family size; total livestock holding and total income were the main factors that determine credit access effect on the farmers' technology adoption.

On New Notions of Algorithmic Dimension, Immunity, and Medvedev Degree

We prove various results connected together by the common thread of computability theory.First, we investigate a new notion of algorithmic dimension, the inescapable dimension, which lies between the effective Hausdorff and packing dimensions. We also study its generalizations, obtaining an embedding of the Turing degrees into notions of dimension.We then investigate a new notion of computability theoretic immunity that arose in the course of the previous study, that of a set of natural numbers with no co-enumerable subsets. We demonstrate how this notion of $\Pi ^0_1$ -immunity is connected to other immunity notions, and construct $\Pi ^0_1$ -immune reals throughout the high/low and Ershov hierarchies. We also study those degrees that cannot compute or cannot co-enumerate a $\Pi ^0_1$ -immune set.Finally, we discuss a recently discovered truth-table reduction for transforming a Kolmogorov–Loveland random input into a Martin-Löf random output by exploiting the fact that at least one half of such a KL-random is itself ML-random. We show that there is no better algorithm relying on this fact, in the sense that there is no positive, linear, or bounded truth-table reduction which does this. We also generalize these results to the problem of outputting randomness from infinitely many inputs, only some of which are random.Abstract prepared by David J. Webb.E-mail: dwebb@math.hawaii.eduURL: https://arxiv.org/pdf/2209.05659.pdf

Single-longitudinal-mode short-cavity Brillouin random fiber laser via frequency auto-tracking with unpumped-EDF sagnac loop

A single-longitudinal-mode high-coherence Brillouin random fiber laser (BRFL) with low-noise and narrow linewidth is proposed and experimentally demonstrated, which owns the shortest cavity structure ever reported in BRFL configuration by the combined utilization of highly nonlinear fiber (HNLF) and unpumped Er-doped-fiber sagnac loop (UESL). In this BRFL, stimulated Brillouin scattering and Rayleigh scattering are exploited to provide the resonant gain and random distributed feedback, respectively. The UESL, with a narrow bandpass width and a capability of auto-tracking the center frequency of the transmitted light, is realized by forming a dynamic fiber grating (DFG) filter with periodically modulated refractive index through the saturable absorption effect and hole-burning effect along the Er-doped fiber. The UESL can effectively act as a center-frequency-auto-tracking bandpass filter with narrow bandwidth to filter out the undesired dense random modes and simultaneously restrict the resonant modes within a very limited frequency range. It thus suppresses the modes hopping and multi-mode resonances within the Brillouin gain bandwidth so that the frequency jitter and instability of laser output are greatly alleviated. The short cavity was realized by utilizing a section of HNLF with high nonlinearity coefficient (≥10 W−1·km−1 @1550 nm), which can provide enough Brillouin gain for the BRFL when short length is employed. Compared with the currently prevalent BRFLs based on long-cavity configurations, the short-cavity structure enables a significant reduction in the number of random cavity modes so as to guarantee a high probability for the single-longitudinal-mode random lasing output. In the experiment, a stable single-longitudinal-mode lasing output with an ultra-narrow linewidth of ∼802.42 Hz is obtained from the proposed BRFL. Statistical characteristics of the mode resonances, laser noise performance and statistical analysis of the lasing output are also experimentally investigated for the proposed BRFL. In addition, broadband wavelength-tunable output is realized in the proposed BRFL.

Operational modal analysis under harmonic excitation using Ramanujan subspace projection and stochastic subspace identification

The presence of deterministic harmonic excitation, such as that induced by rotating machinery, violates the classical operational modal analysis (OMA) assumption that the system output is strictly ergodic. This paper proves that the presence of harmonic excitation has no effect on the identification of structural modes except in the case where some of the harmonic excitation frequencies are close to the structural frequencies. Therefore, the harmonic component must be removed from the mixed random and harmonic system output before further processing. This paper proposes a Ramanujan subspace projection (RSP) method for harmonic removal, which is realized by projecting the raw system output onto the complex conjugate division (CCD) of the Ramanujan subspace. The novelty of this study is that it reveals the relationship between the frequencies defined in the period and frequency domains, allowing the RSP method to directly extract the harmonic component from the specific CCD without any frequency domain analysis. In addition, an energy indicator is proposed to select the underlying CCDs with the most robust harmonic feature. Using the indicator, one only needs to project the raw system output onto a subset of the CCDs rather than all of them, thereby significantly reducing the computational effort. After removing the harmonic components from the raw output, the remainder can be fed into the covariance-driven stochastic subspace identification (Cov-SSI) method for OMA. The numerical, experimental and field test results show that the proposed RSP method is not only resistant to random noise but also capable of precisely extracting the weak harmonic component from the raw output with less computation. Furthermore, the modal parameters of the structures subjected to mixed random and harmonic excitation can be accurately identified by combining the Cov-SSI and RSP methods.

T-BFA: Targeted Bit-Flip Adversarial Weight Attack.

Traditional Deep Neural Network (DNN) security is mostly related to the well-known adversarial input example attack.Recently, another dimension of adversarial attack, namely, attack on DNN weight parameters, has been shown to be very powerful. Asa representative one, the Bit-Flip based adversarial weight Attack (BFA) injects an extremely small amount of faults into weight parameters to hijack the executing DNN function. Prior works of BFA focus on un-targeted attacks that can hack all inputs into a random output class by flipping a very small number of weight bits stored in computer memory. This paper proposes the first work oftargetedBFA based (T-BFA) adversarial weight attack on DNNs, which can intentionally mislead selected inputs to a target output class. The objective is achieved by identifying the weight bits that are highly associated with classification of a targeted output through a class-dependent weight bit searching algorithm. Our proposed T-BFA performance is successfully demonstrated on multiple DNN architectures for image classification tasks. For example, by merely flipping 27 out of 88 million weight bits of ResNet-18, our T-BFA can misclassify all the images from Hen class into Goose class (i.e., 100% attack success rate) in ImageNet dataset, while maintaining 59.35% validation accuracy.

Simultaneous hysteresis‐dynamics compensation in high‐speed, large‐range trajectory tracking: A data‐driven iterative control

AbstractIn this article, a data‐driven difference‐inversion‐based iterative control (DDD‐IIC) approach is proposed to compensate for both nonlinear hysteresis and dynamics of Hammerstein systems. Simultaneous hysteresis‐dynamics compensation is needed in control of Hammerstein systems such as smart actuators, where effects of hysteresis and dynamics coexist and become pronounced in high‐speed, large‐range output tracking. Challenges, however, arises as hysteresis modeling, as needed in many existing control methods, can be complicated and prone to uncertainties, and the hysteresis and the dynamics are coupled and tend to change due to the variations of the system conditions (e.g., the aging of smart actuators). The proposed DDD‐IIC technique aims to achieve simultaneous hysteresis‐dynamics compensation with no need for modeling hysteresis and/or dynamics, and with both precision tracking and good robustness against hysteresis/dynamics variations. The convergence of the DDD‐IIC algorithm in the presence of random output disturbance/noise is analyzed. It is shown that when the noise is negligible, exact tracking is achieved and the size of hysteresis accounted is given by the Golden ratio. The proposed DDD‐IIC method is demonstrated via experiments of high‐speed large‐range output tracking on two different types of smart actuators with symmetric and asymmetric hysteresis behavior, respectively.

A two-stage operation optimization model for isolated integrated energy systems with concentrating solar power plant considering multi-energy and multi-type demand response

The isolated integrated energy system coupled with multiple types of energy systems is one of the important ways to guarantee the quality of energy use in remote areas, but due to the lack of external main network’s support and random renewable energy output, there is a greater risk of load cutting, which puts forward higher requirements for the operation optimization of the isolated integrated energy system. Therefore, this paper first constructs a two-stage optimization model from both supply and demand side for the linkage development of resources within the isolated integrated energy system. Secondly, an evaluation index system containing economic benefits and system efficiency is constructed to quantify the comprehensive benefits of the two-stage operation optimization. Finally, a remote area in China is selected as the research background for example analysis. The results show that (1) Due to the low matching between supply and demand of the isolated integrated energy system, the unit operation optimization is only conducted from the energy supply side, and the total load shedding is about 101.402 MW. (2) Considering the load side optimization in the first stage, the demand side resources can be mobilized to improve the supply and demand matching degree. Compared with the second stage optimization in Scenario 1, the internal supply rates in Scenarios 2, 3 and 4 are increased by 0.399, 0.159 and 0.567 respectively, and the system net income is increased by 8990, 18840 and 2310 CNY respectively. Limited by factors, such as the subsidy price on the load side, the demand elasticity matrix and the energy selling price on the energy supply side, there is no negative linear relationship between the amount of load shedding and the improvement of energy supplier’s economic benefits, so it is necessary to consider actual operation scenarios and reasonably arrange operation and dispatching plans.

Research on novel var compensator based on dual-rotary phase-shifting transformers and its control strategy

With the continuous increase in the penetration of distributed power with random output, the acceleration of the urban cableization rate and the rapid development of supergrid, the active distribution network puts forward higher requirements for the performance of dynamic reactive power compensation. A topology of novel rotary VAR compensator (NRVC) is proposed by integrating the current source static synchronous compensator with the continuous regulation characteristics of dual rotary phase-shifting transformers. The NRVC compensation principle is analyzed by establishing the steady-state mathematical model of dual rotary phase-shifting transformers and NRVC. The dynamic response performance and universal applicability are improved by considering its compensation capacity constraints, applying the instantaneous reactive power theory, and constant power factor control. A dual closed-loop decoupling control strategy of power outer-loop and current inner-loop is also presented to prevent internal overcurrent. Finally, the simulation and experimental results are performed to verify the effectiveness of the proposed system and control strategy, which realized bidirectional and continuous regulation of compensated reactive power, and has manifold advantages: low cost, strong shock resistance, large heat capacity, simple control, and no harmonic pollution.

Frequency Control of a Wind-diesel-generator Hybrid System with Squirrel Search Algorithm Tuned Robust Cascade Fractional Order Controller Having Disturbance Observer Integrated

This paper proposes an optimal cascaded fractional order controller (CC-FOC) having disturbance observer (DOB) to minimize the frequency deviation of an autonomous wind-diesel-generator (WDG) system in the wake of load variation and random wind power output. The model of WDG consists of a variable-speed wind turbine (VSWT) and a diesel engine generator to match the ever-rising load demand. To regulate the frequency of the WDG system, fractional-order proportional-integral-derivative (FOPID) and tilt-integral-derivative (TID) controllers are simultaneously used as master and slave controllers, respectively, for developing the CC-FOC. An improved squirrel search algorithm (SSA) with quasi-oppositional-based learning (QOSSA) is applied to explore the optimum gains of the proposed non-integer controller. The performance of the developed controller is compared with the outputs of FOPID, TID, and PID controllers. The result demonstrates the mastery and effectiveness of the proposed controller against random load and wind power fluctuations. Finally, Kharitonov’s stability theorem is applied to ensure the robustness margin of the studied WDG plant for a wide range of system parameters variation.

Changes in coastal farming systems in a changing climate in Bangladesh

Changes in farming systems are dominated by changes in global climate and local environment, apart from the non-climatic drivers. Given the challenges in partitioning the contribution of climatic and non-climatic factors to the changes in farming systems, this paper aims to assess the types and changes of coastal farming systems, the farmer perceptions of the causes of the changes in farming systems, and the relationship between the influencing factors and perceptions. A structured interview schedule was used to collect data from 381 randomly selected coastal households during September–October 2018. The random forest classification model was applied to estimate the relative importance of the farmers’ characteristics on their perception of causes of changes in farming systems. This study reveals that the coastal farmers had mostly semi-subsistence type of mixed farming systems, which were going through dynamic changes in terms of their sizes and number of farmers. In general, the participation in rice, vegetables, and livestock farming was decreasing but increasing in fisheries, forestry, and fruit farming. Most (95.5%) of the farmers had to change at least one of the farming enterprises over the past decade (2009–2018) compared with the previous decade (1999–2008). About two-thirds of the farmers perceived that climate change had caused changes in their farming systems. Compared with the eastern coasts, the farmers in the western coasts tended to blame climate change to a higher extent for the effect on their agricultural activities. The random forest model outputs imply that the farmers who are younger in age and with less formal education, larger family, and smaller farmland should be supported with scientific knowledge on causes of changes in farming systems. This could help them more aware of climate change issues related to agriculture and increase their enthusiasm to take part in adaptive changes in farming systems.

Nonuniform Compressive Sensing via Ohmic Voltage Attenuation: A Memristive Crossbar Design Approach Leveraging Intrinsic Computation

Compressive sensing (CS) is a promising technique for transmitting signals in power-critical applications such as Internet of Things (IoT) devices. Nonuniform CS optimizes this process by adjusting sampling frequency based on the relative importance levels characterized by the signal of interest. Recent advances have yielded energy-efficient hardware implementations of CS sampling, leveraging spin-based crossbar architectures for in-memory vector-matrix multiplication and through the use of probabilistic bit (p-bit) devices to generate tunable random outputs for writing the array. Thus, a region of interest is generated via column-ordered density of on-state devices. Herein, we propose a simple design for supplying inputs to the p-bit devices, based on Ohmic voltage attenuation occurring along the word lines of the crossbar array. The technique embeds some required computations to be conducted intrinsically by the cross-points of the memristive array, thus bypassing overheads of conventional instruction execution and eliminating the need for costly hardware components, such as lookup tables (LUTs) and data converters. The design is shown to be robust for various array sizes and parasitics while generating the appropriate tuning signals within a single clock cycle duration of 1.6 ns, and at an energy overhead of 333 fJ. Compared with a standard approach using LUTs and digital to-analog converters, the design herein achieves a 583-fold reduction in energy and 23-fold reduction in transistor count.

Assessing most productive scale size with fuzzy stochastic data envelopment analysis

Classic data envelopment analysis (DEA) is a linear programming method for evaluating the relative efficiency of decision making units (DMUs) that uses multiple inputs to produce multiple outputs. In the classic DEA model inputs and outputs of DMUs are deterministic, while in the real world, are often fuzzy, random, or fuzzy-random. Many researchers have proposed different approaches to evaluate the relative efficiency with fuzzy and random data in DEA. In many studies, the most productive scale size (mpss) of decision making units has been estimated with fuzzy and random inputs and outputs. Also, the concept of fuzzy random variable is used in the DEA literature to describe events or occurrences in which fuzzy and random changes occur simultaneously. This paper has proposed the fuzzy stochastic DEA model to assess the most productive scale size of DMUs that produce multiple fuzzy random outputs using multiple fuzzy random inputs with respect to the possibility-probability constraints. For solving the fuzzy stochastic DEA model, we obtained a nonlinear deterministic equivalent for the probability constraints using chance constrained programming approaches (CCP). Then, using the possibility theory the possibilities of fuzzy events transformed to the deterministic equivalents with definite data. In the final section, the fuzzy stochastic DEA model, proposed model, has been used to evaluate the most productive scale size of sixteen Iranian hospitals with four fuzzy random inputs and two fuzzy random outputs with symmetrical triangular membership functions.