Fuzzy Uncertainty Research Articles

Robust Pricing for a Dual-Channel Green Supply Chain Under Fuzzy Demand Ambiguity

The pricing decision is a fundamental problem in a two-echelon dual-channel supply chain, and it is a challenging issue to get the optimal pricing strategy due to high demand ambiguity. Although this problem has been studied by many researchers, the market demand is usually assumed to be deterministic or described as a fuzzy variable with exact distribution information in most of the existing literature. In this article, the uncertain demand is assumed to possess fuzzy uncertainty instead of stochastic nature. In the case that the demand distribution information is partially available, this article proposes a new uncertainty distribution set to depict the demand distribution uncertainty based on the type-2 fuzzy theory. Then, a novel robust pricing game modeling framework is developed for the dual-channel green supply chain with the demand distribution varying in the proposed uncertainty distribution set. Finally, a new method is proposed for obtaining the robust equilibrium decisions of supply chain members. Numerical analysis and comparisons are conducted to demonstrate the impacts of the demand ambiguity on the manufacturer’s equilibrium channel choice strategy. We also demonstrate that our solution results are robust in the setting that the prices of the green products are not equal in the retail and the direct channels.

Risk uncertainty analysis in shield tunnel projects

Subway shield tunnels usually pass through the complex geological environment of a city. There are many uncertain factors in shield tunnel construction risk, undoubtedly increasing the difficulty of construction safety control. Risk evaluation prior to project construction is necessary for the implementation of tunnel projects and reduces risk levels during construction. However, tunnel risks are uncertain and are characterized by random and fuzzy uncertainty. To account for these two uncertainties in the quantitative transformation of risk qualitative concepts and to improve the evaluation accuracy, in this study a new risk evaluation method based on a two-dimensional cloud model (TDCM) is proposed for shield tunnel projects. First, the risk evaluation criteria are quantified with the harmfulness and the probability of risk as the evaluation dimensions of the two-dimensional cloud, and the conversion relationship between the risk level and the quantitative domain is improved. A risk evaluation index system based on construction accidents and risk types for shield tunnel projects is established. Then, the Delphi method is used to evaluate the probability and harmfulness of the risk, the index weight and numerical characteristics of the two-dimensional cloud model are determined, and a shaped two-dimensional comprehensive cloud of thousands of cloud droplets is generated by a positive cloud generator. Finally, the domain is defined as the overlap between the comprehensive evaluation cloud and the standard cloud at different risk levels, and the contribution of comprehensive evaluation cloud drops to the comprehensive evaluation cloud in each domain is analysed. The risk level of the project is predicted based on the principle of maximum membership degree. The risk evaluation method proposed in this study is applied to two subway shield sections, and the risk level of these projects is accurately predicted. The TDCM evaluation method is compared with the one-dimensional cloud model (ODCM) evaluation method and the fuzzy comprehensive evaluation method (FCEM), and the advantages and applicability of the TDCM evaluation method are discussed.

Two-stage distributionally robust optimization model of integrated energy system group considering energy sharing and carbon transfer

Due to the small scale and few functions of the single integrated energy system, the absorption capacity of wind turbine and photovoltaic is limited, the ability to cope with uncertainties is weak, and the space for optimal allocation of resources is limited. To solve the coordination problem of robustness, economy, environmental protection and efficiency, this paper forms an integrated energy system group (IESG) by means of energy sharing and carbon transfer, and innovatively proposes a two-stage distributionally robust optimization model (TSDRO) based on kernel density estimation (KDE) and Wasserstein metric. Firstly, the structure of IESG with carbon capture, utilization, and storage-power-to-gas (CCUS-P2G) system is introduced. Then, the nonparametric KDE method is applied to fit the probability density functions of the forecast power error of wind turbine and photovoltaic. Wasserstein metric is used to characterize the fuzzy uncertainty set of distributions. The cumulative distribution function of KDE is taken as the center, and the obtained distance is taken as the radius to form the Wasserstein ball of probability distribution. Based on affinely adjustable policy, a correlation model of real-time variables with respect to day-ahead variables is established. Finally, according to the dual theory and convex optimization theory, the TSDRO model is reformulated into a solvable model. The simulation results show that: (1) energy sharing and carbon transfer can improve the ability of IESG to cope with uncertainty and expand the boundary of resource optimal allocation, and the minimum expected operating cost under the worst distribution is $ 40,259.94. (2) CCUS-P2G system strengthens the synergistic relationship between electricity and carbon and reduces the carbon emission of the system by 128.2 t. (3) After testing, the results obtained by nonparametric KDE are closer to the true distribution and more objective. (4) The TSDRO model is data-driven and has the advantages of high solving efficiency and low decision-making conservatism. The solution time of the TSDRO model is 73.03 % less than that of the stochastic optimization model, and the operation cost is 1.69 % less than that of the robust optimization model, which achieves the balance of economy, robustness and environmental protection of IESG.

Trustworthy Breast Ultrasound Image Semantic Segmentation Based on Fuzzy Uncertainty Reduction.

Medical image semantic segmentation is essential in computer-aided diagnosis systems. It can separate tissues and lesions in the image and provide valuable information to radiologists and doctors. The breast ultrasound (BUS) images have advantages: no radiation, low cost, portable, etc. However, there are two unfavorable characteristics: (1) the dataset size is often small due to the difficulty in obtaining the ground truths, and (2) BUS images are usually in poor quality. Trustworthy BUS image segmentation is urgent in breast cancer computer-aided diagnosis systems, especially for fully understanding the BUS images and segmenting the breast anatomy, which supports breast cancer risk assessment. The main challenge for this task is uncertainty in both pixels and channels of the BUS images. In this paper, we propose a Spatial and Channel-wise Fuzzy Uncertainty Reduction Network (SCFURNet) for BUS image semantic segmentation. The proposed architecture can reduce the uncertainty in the original segmentation frameworks. We apply the proposed method to four datasets: (1) a five-category BUS image dataset with 325 images, and (2) three BUS image datasets with only tumor category (1830 images in total). The proposed approach compares state-of-the-art methods such as U-Net with VGG-16, ResNet-50/ResNet-101, Deeplab, FCN-8s, PSPNet, U-Net with information extension, attention U-Net, and U-Net with the self-attention mechanism. It achieves 2.03%, 1.84%, and 2.88% improvements in the Jaccard index on three public BUS datasets, and 6.72% improvement in the tumor category and 4.32% improvement in the overall performance on the five-category dataset compared with that of the original U-shape network with ResNet-101 since it can handle the uncertainty effectively and efficiently.

IDENTIFICATION OF ENTRANT’S ABILITIES ON THE BASIS OF SUGENO-TYPE FUZZY INFERENCE SYSTEMS

In the conditions of effective training in aviation for dispatchers and pilots, it requires the use of infocommunication systems capable of working under conditions of fuzzy uncertainty in real time. The functioning of such systems is based on fuzzy inference systems. However, the development and implementation of these systems requires the creation of fuzzy knowledge bases. Therefore, special attention in this study is paid to the creation of a system of fuzzy inferences and the formation of a fuzzy knowledge base of this system. The result is a lozenge-type fuzzy inference system. The fuzzy knowledge base of the system contains the rules according to which, based on the results of test computer game problems of varying complexity, a conclusion is formed about the applicant’s ability to acquire knowledge and skills in a certain specialty.When developing the rules, both the results of passing different levels of professionally oriented computer test games were taken into account, and the interest of dispatchers and pilots was taken into account. Therefore, the proposed fuzzy rules of the knowledge base of the fuzzy inference system make it possible to assess not only the ability of the controller or pilot to solve certain problems. This dependence of the input dataset on time allows the implementation of a fuzzy inference system of the Sugeno type, using clear input data in the formation of inferences.

Managing water-energy-carbon nexus in integrated regional water network planning through graph theory-based bi-level programming

The water-energy-carbon nexus (WECN) has raised the attentions in the past years due to the shortages of water and energy resources, climate change and their close connection. It is critical to study WECN in water network systems due to their energy- and carbon-intensive characteristics. In optimization of WECN in water network planning, decision makers with conflictive objectives may have different decision-making power levels. In this study, an integrated Graph Theory-Based Bi-Level Water Network Planning Model, named GraBiL is developed, which represents a methodological contribution to the challenge of quantitative interrelationships of WECN and hierarchical decision-making problem in regional-scale water network planning. The GraBiL model has improved upon the existing bi-level programming and graph theory-based method for solving spatial layout optimization in two-level decision-making problem. Two-level conflictive objectives including minimizing total system cost and maximizing energy saving are considered. Fuzzy uncertainties associated with water loads are quantified. The impacts of carbon emission control on total system economic costs, energy consumption and the optimal water network planning are effectively addressed. The results from a hypothetical case study indicate that enhanced overall satisfaction for meeting the two-level objectives can be achieved with the proposed GraBiL model. Optimal water network planning schemes including spatial layout under four representative carbon emission control scenarios are compared. The proposed model has provided insight into quantitative interrelationships of WECN, hierarchical decision-making, optimization of water network spatial layout and quantification of fuzzy uncertainty associated with water loads in regional-scale water network planning.

Uncertainty Propagation Analysis of Fuzzy Uncertain Structures Involving Imprecise Membership Functions

Uncertain structures may exhibit fuzzy uncertainty involving imprecise membership function (FuIMF). In this study, the uncertain parameters in FuIMF case are characterized as fuzzy variables, whereas the key parameters of their membership functions are treated as interval variables rather than exact values. Two ideas are put forward to handle FuIMF variables. First, the interval-boundary interval method (IBIM) is derived to conduct uncertainty propagation analysis, in which the [Formula: see text]-cut of FuIMF variables are considered as interval-boundary intervals. Second, the [Formula: see text]-cut of FuIMF variables are presented by the conservative and radical approximations, and the conservative and radical approximations method I (CRAM I) is proposed to conduct uncertainty propagation analysis. To further promote the computational efficiency, the conservative and radical approximations method II (CRAM II) is developed. Afterwards, a reference method based on Monte Carlo simulation is presented to verify the proposed methods. Finally, the effectiveness of proposed methods is demonstrated by numerical examples.

A fuzzy-interval nonlinear programming for boosters under uncertainty

Abstract In this paper, an integration of a fuzzy-interval credibility-constrained (FIC) model expressed by fuzzy interval sets (FIS) and interval nonlinear programming (INP), termed an FIC-INP model, was proposed and applied to two cases. After formulating the FIC-INP model, upper and lower disinfection booster costs can be obtained for two cases under various combinations of credibility levels of upper and lower limits. The results indicated that the upper and lower booster costs increased with the credibility levels of the lower limits. The upper as well as the lower booster costs increased with the booster numbers. For credibility levels of lower limit constraints ranging from 0.6 to 0.9, the upper and lower booster costs increased under enlarging/widening trapezoidal distributions, and the intervals of booster costs increased with interval uncertainty. For a lower limit constraint credibility level of 0.5, the upper and lower booster costs decreased under shrinking/narrowing trapezoidal distributions, and the booster cost intervals increased under larger interval trapezoidal distributions. The degrees of effect of the interval uncertainty are higher than the fuzzy uncertainty. The results obtained can provide more information for managers to make booster schemes under fuzzy and interval uncertainties.

A new qualitative and quantitative analytical approach for risk management in energy project time-cost trade-off problem under interval type-2 fuzzy uncertainty: A case study in the gas industry

This paper proposes a novel risk management approach to develop a Time-Cost Trade-off (TCT) mathematical model under fuzzy uncertainty. In this paper, firstly, a Linear Assignment Method (LAM) is proposed to rank the activities of a project according to their encountering risks when the activities are crashed. Secondly, activities are grouped into different classes in accordance with their risk level so as to concentrate on high-risk activities. Then, a new fuzzy TCT mathematical model considering the risk criterion is presented. In the next step, a quantitative analysis of risks is proposed by Primavera Risk Analysis. Ultimately, risk response strategies are presented, and the results are meticulously scrutinized. Due to more precision in considering uncertainty and advantages of interval type-2 fuzzy set (IT2FS), this fuzzy set is applied throughout the whole methodology. An actual project of a company in the gas industry is adopted to examine the method efficiency.

Sequential optimization method based on the adaptive Kriging model for the possibility-based design optimization

The possibility-based design optimization (PBDO) model under the fuzzy uncertainty can provide the optimal design parameters by taking a trade-off between the performance and security. In order to efficiently solve the PBDO model with implicit failure possibility constraints in engineering, a Sequential Optimization Method based on the Adaptive Kriging model (AK-SOM) is proposed in this paper. The AK-SOM firstly constructs the Kriging model of the performance function corresponding to each failure possibility constraint. The optimized design parameters of the PBDO based on the current Kriging model (It is called the current K-PBDO) can be obtained without any additional model evaluations. Then, the effective possibility constraints in the current K-PBDO can be identified by the effective constraint criterion proposed in this paper, and only the Kriging models of the effective constraints are updated. The sequential optimization process continues until both the relative error stopping criterion and the U-function stopping criterion are satisfied simultaneously. The effectiveness and superiority of the AK-SOM are verified by five examples, and the obtained experimental results indicate that the proposed AK-SOM has no restrictions on the expression of the performance function, and it can effectively improve the efficiency of solving the PBDO model while ensuring the accuracy. Additionally, the proposed method is employed in the PBDO of a GH4169 aero-engine turbine disk, and the optimal scheme of PBDO shows that the failure possibility of the disk is reduced and the maximum stress in the dangerous part is also greatly reduced.

Cooperative R&D investment decisions: A fuzzy real option approach

We study the optimal firms' strategies in an R&D oligopoly environment for different types of cooperative agreements under fuzzy uncertainty about the effects of cooperation. We address the problem as an R&D fuzzy bargaining game, in which the firms' fuzzy payoffs are computed using the real exchange option methodology that takes into account the managerial flexibility embedded in the R&D opportunities. The main novelty of our contribution is the parametric description both of the intensity of the collaboration for each dimension involved in the agreement and of its fuzzy impact on the firms' payoffs. Interestingly, we show that the degree of imprecise knowledge has a significant impact on the strategic alliances adopted by firms.

Global Reliability Sensitivity of the Structure Under Fuzzy Uncertainty and Its Estimations

Global reliability sensitivity (GRS) index under fuzzy uncertainty is defined as the mean of the absolute difference between unconditional failure credibility and conditional failure credibility, which is important to quantify the effect of fuzzy inputs on failure credibility of the structure. The solution of this index requires nested analysis of conditional failure credibility and fuzzy mean, which introduces a large amount of computation. To efficiently estimate the GRS under fuzzy uncertainty, a method combining fuzzy simulation (FS) with fuzzy first-order and second moment (FS–FFOSM) method as well as a fuzzy sequential optimization and reliability assessment (FSORA) method are proposed. Compared with the direct double-loop FS method, in which both the conditional failure credibility and the fuzzy mean are estimated by FS, the proposed FS–FFOSM uses a more efficient FFOSM method to estimate the conditional failure credibility in the inner loop, which improves the computational efficiency of estimating GRS under fuzzy uncertainty. To further improve the computational efficiency, this paper also transforms the estimation of GRS into the solution of the optimization model under the constraint of failure credibility and establishes the FSORA method to solve the optimization model. The FSORA method uses a series of cycles of deterministic optimization and inverse design point analysis corresponding to the required fuzzy reliability index by GRS to reduce the iterations, and then the computational efficiency is further improved. Several examples illustrate the computational efficiency and accuracy of the proposed methods.

Sustainable multi-channel supply chain design: an intuitive fuzzy game theory approach to deal with uncertain business environment

AbstractBy introducing the concept of sustainable development, managers and policymakers in many industries have been encouraged to consider environmental and social issues in addition to economic objectives in their planning. Following this concept, sustainable supply chain management has become the main concern of many studies. Among all the strategies to achieve sustainability targets in a supply chain, cooperating with third-party logistics companies has attracted lots of attention. By providing more sustainable and efficient transportation services, 3PLs can help all types of regular, closed-loop, and circular SCs achieve more profit, while they are still sustainable, at least in distribution and collection/recycling stages. This study investigates the sustainable multi-channel SC design problem in the presence of the government and 3PLs. To bring the present study closer to the real-world situation, the problem is modeled using an intuitionistic fuzzy uncertainty approach. Considering the government as the leader of the SC in two centralized and decentralized decision structures, game theory has been applied to model the game between players and obtain optimal decision values. For the first time in the literature, public awareness toward green activities of the players, emission reduction, uncertainty, and delivery time have been considered in this study. The results show the presence of a 3PL will reduce the delivery time and the amount of pollution. Also, the findings confirm that governments can control the players' activities and encourage them to apply green strategies using financial tools.

Fabric Selection Based on Sine Trigonometric Aggregation Operators Under Pythagorean Fuzzy Uncertainty

ABSTRACT In the textile industry, selecting the optimal fabric is crucial in the design and production process. The multiple-criteria decision-making (MCDM) technique has been applied to address fabric selection problems. Because the sine trigonometry function maintains the periodicity and symmetry of the origin in nature, it satisfies the preferences of experts over multiple parameters. Considering the advantages of the sine trigonometry function, we introduce sine trigonometry Pythagorean fuzzy sets (ST-PFSs) and weighted averaging (ST-PFWA) and geometric (ST-PFWG) aggregation operators (AOs). Additionally, we propose a novel method based on ST-PFWA and ST-PFWG AOs to solve two different types of fabric selection MCDM problems. The first problem is provided by Pythagorean fuzzy numbers (PFNs), and we apply the proposed method to address the issue and conduct a comparative analysis with other PFS AOs. The second problem is offered with crisp values, and we apply a PFS linguistic term transform system to convert the values into PFNs. Then, we apply ST-PFWA and ST-PFWG AOs to settle the problem and perform a comparative analysis among different PFS linguistic terms. The complete ranking results illustrate that our proposed methodology is more efficient and reliable than previous approaches and can be used in other textile fields.

Multi-Shift Single-Vehicle Routing Problem Under Fuzzy Uncertainty During the COVID-19 Pandemic

Background: This work studies the single vehicle routing problem (VRP) with multishift and fuzzy uncertainty. In this case, a company perpetually exploits a vehicle to accomplish demand over a scheduling period of several work shifts. In our problem, a crew performs maintenance jobs at different locations. The working team operates in different shifts with a maximum duration but recurrently returns to the depot by the end of the shift to avoid overtime. Methods: The objective is to minimize the number of shifts and the completion time (makespan). In addition, we analyze the influence of uncertainty in driving and processing times on the overtime avoidance constraint in shift duration. We develop an Artificial Immune Heuristic to determine optimal solutions considering both makespan and overtime avoidance. We implement a Pareto-based framework to evaluate the impact of uncertainty. Results: We present several numerical case studies to examine the problem. In particular, we analyze different case study scenarios inferred from the environmental changes in travel and processing times observed in the Apulia region (SE Italy) during the COVID-19 lockdown periods that occurred in spring (started on March 9, 2020) and autumn (after November 6, 2020) of the year 2020. Conclusion: The work program was revised as soon as the Italian COVID-19 restrictions were implemented in the spring and autumn of 2020 due to the changing environment. Our approach allowed for the rapid release of new robust maintenance programs. Results show significant improvements with the presented approach.

Fuzzy analytic hierarchy process‐based risk priority number for risk assessments of commissioning process of a ring gantry LINAC

We propose a fuzzy analytic hierarchy process (AHP)-based risk priority number (RPN) method in failure modes and effects analysis (FMEA) to overcome the shortcomings of traditional RPN-based FMEA. Our research group has previously published the FMEA to mitigate the failure modes (FMs) for the commissioning process of a ring gantry LINAC. However, inter-relationships among FMs were observed in high ranked FMs due to a heavy reliance on imaging system. Fuzzy AHP was applied to determine relative weights of risk impacts based on inter-relationships among FMs. Since the time sequence dependency is a major factor for risk factors, a hierarchical structure of AHP was used to reflect the directional impacts such as causal influence and feedback loop. Two fuzzy weighted RPNs, called (RPNW and FRPNW , were calculated depending on the input values of severity (S), occurrence (O), and probability of not being detected (D) from the evaluators. The RPNW used numerical values, whereas the fuzzy values were used for FRPNW . Both RPNs were calculated by multiplying the weighted O, S, and D using the fuzzy AHP method. The differences between the two fuzzy RPN rankings are due to inherent fuzzy uncertainty and deviations in O, S, and D values submitted by the evaluators. Considering all results of traditional and fuzzy-based FMEA, the two most highly ranked FMs were identified: errors in determining the non-isocentric SSD and SSD from MV images because of the unique features of the ring gantry LINAC. This study has demonstrated the feasibility of the use of a fuzzy AHP-based RPN to perform comprehensive analysis and prioritization of FMs. The risk analysis using fuzzy AHP can be improved and/or refined based on the department's specific workflow and clinical preferences taking various priority weighting approaches into account.

Optimizing water allocation in an inter-basin water diversion project with equity-efficiency tradeoff: A bi-level multiobjective programming model under uncertainty

Achieving optimal water allocation in an inter-basin water diversion project is a challenge that involves multilevel stakeholders, and the uncertainty and disequilibrium of water allocation further intensify competition among different stakeholders. This study proposes a bi-level multiobjective programming model for water allocation in inter-basin water diversions that considers equilibrium sustainability. The model integrates interval parameter programming, fuzzy credibility-constrained programming, bi-level multiobjective programming, and the Gini coefficient into a general framework. The model not only balances the stakeholders at different levels to ensure water allocation equity but also comprehensively considers the fuzzy uncertainty of parameters and constraints to obtain the interrelationship among water diversion, water allocation satisfaction, and efficiency objectives. The developed model was applied to allocate water for the Hanjiang-to-Weihe Water Diversion Project in Shaanxi Province, China. The results showed that 1) the model derived a feasible tradeoff between upper basin manager and lower regional managers under different water diversion scenarios; 2) water allocations and objectives at each level are sensitive to changes in the credibility of water diversion; 3) the new model improves the equity of water allocation and ensures the efficient allocation to various stakeholders at each level based on a comparison of the proposed model with a model that does not consider equilibrium. The proposed model can help decision makers choose the optimal scheme based on their acceptable risk level to achieve a more efficient and sustainable water allocation for inter-basin water diversions.

Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment

In this manuscript, a new hybrid technique viz Sawi transform-based homotopy perturbation method is implemented to solve one-dimensional shallow water wave equations. In general, the quantities involved with such equations are commonly assumed to be crisp, but the parameters involved in the actual scenario may be imprecise/uncertain. Therefore, fuzzy uncertainty is introduced as an initial condition. The main focus of this study is to find the approximate solution of one-dimensional shallow water wave equations with crisp, as well as fuzzy, uncertain initial conditions. First, by taking the initial condition as crisp, the approximate series solutions are obtained. Then these solutions are compared graphically with existing solutions, showing the reliability of the present method. Further, by considering uncertain initial conditions in terms of Gaussian fuzzy number, the governing equation leads to fuzzy shallow water wave equations. Finally, the solutions obtained by the proposed method are presented in the form of Gaussian fuzzy number plots.

An optimization model for construction project scheduling by considering CO2 emissions with multi-mode resource constraints under interval-valued fuzzy uncertainty

An optimization model for construction project scheduling by considering CO2 emissions with multi-mode resource constraints under interval-valued fuzzy uncertainty

Dynamic Bayesian Network for Predicting Tunnel-Collapse Risk in the Case of Incomplete Data

Collapse is one of the most dangerous aspects of drilling–blasting construction in highway tunnels. To accurately control tunnel-collapse risk, a multistate dynamic Bayesian network (DBN) evaluation method for highway tunnel collapse based on parameter learning was proposed. First, by analyzing the risk mechanism of tunnel construction, the initial BN model was established based on the causal relationship between risk factors and construction risk in hydrogeological conditions, construction technology, and construction management. Next, the construction process was discretized into finite time slices. In consideration of the fuzzy uncertainty of nodes, node polymorphism was introduced to construct a multistate DBN. Then, 50 typical tunnel-collapse cases were taken as sample data, and the conditional probability distribution of initial BN was derived using parameter learning based on the expectation-maximization (EM) algorithm. Using DBN reasoning and sensitivity analysis, the dynamic risk probability and the dominant factors of tunnel collapse were predicted. Finally, the DBN model was fed back with the measured cumulative values and velocity of the crown settlement, which updated the dynamic risk probability assessment results. In analyzing the collapse probability of Jinzhupa tunnel passing through the angular unconformity contact zone as an example, the results demonstrated that dynamic risk assessment results combined with monitoring data could better reflect the reality of construction contingencies, providing real-time risk management guidance.