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The fuzzy safety index (FSI) is put forward in this article under the assumption that the fuzzy inputs are independently and identically distributed. Then, the failure possibility-based constraints in original possibility-based design optimization (PBDO) are equivalently converted to the FSI-based constraints, and the fuzzy safety index approach (FSIA) is presented for solving PBDO. Based on the definition of FSI and the relationship between FSI and the fuzzy most possible failure point (F-MPP), the analytical expression is derived for the local sensitivity of FSI (LS-FSI) with respect to the design parameters, and it is used to provide the exact gradient for FSIA. An efficient iterative method is proposed for solving the FSI, which can estimate LS-FSI as a by-product of analysing the FSI without any additional computational cost. Finally, five numerical examples are demonstrated to show the feasibility of the derived analytical expression of LS-FSI and the proposed FSIA for PBDO. [ABSTRACT FROM AUTHOR]

The construction supply chain is presently the focus of considerable interest among numerous project-related businesses. Strong project management is essential for the effective completion of a project, since restricted budgets and time constraints are considered for each project. The research uses multi-objective linear programming to create a mathematical model of the building supply chain. The primary aims of the present investigation are to limit the expenses associated with logistics and to diminish the release of greenhouse gases caused by transportation. Given the reality of managing several projects concurrently, the model provided comprises a network of projects. Following the completion of each project, an inspection is arranged to assess its level of success. Estimating the costs of a project relies on several variables. In reality, there are always uncertainties highlighted in several studies about the uncertainty of cost and time parameters. This research incorporates many characteristics concurrently to simulate real-world settings and address the issue of uncertainty. The expression of uncertainty for all costs, activity length, inspection, supplier capacity, and resource demand are represented by triangular fuzzy numbers. Ultimately, the precision of the model's performance has been verified using a numerical illustration.

This article addresses a cooperative game-oriented optimal constraint-following problem for fuzzy mechanical systems. The state of the concerned system is affected by possibly (fast) time-varying uncertainty. The fuzzy set theory is adopted to describe such uncertainty. The task is to drive the system to obey a set of prescribed constraints optimally. Since the control objective may be changing along with the system uncertainty, a time-varying β-measure is defined to gauge the constraint-following error; based on which, an adaptive robust control scheme with two tunable parameters is then proposed to render it to be uniform boundedness and uniform ultimate boundedness. For the seeking of the optimal design parameters, two cost functions, each of which is dominated by one tunable parameter, are developed with the fuzzy information, and thereout a two-player cooperative game is formulated. Finally, the optimal design problem is successfully solved: with the existence, uniqueness, and analytical expression of the Pareto optimality.

Most textile manufacturing companies in the world heavily rely on manual labor, particularly in the fabric inspection section, especially for cotton fabric. Establishing smart manufacturing systems like industrial automation in the textile industry for cotton fabric inspection is important for error-free inspection. The proposed make-to-order (MTO) inventory model focuses on the strategic development of a supply chain network under fuzzy uncertainty. The distinctiveness of this research lies in integrating a methodology that involves human and machine interaction, along with allocating resources to investment in smart manufacturing. This article presents a case study of the Jagatjit Cotton Textiles (JCT) manufacturing company in Punjab, India, as an example to validate the model and check the performance of SMT in the fabric inspection process in cotton TC mills. This paper contributes by developing four distinct textile supply chain models with industrial automation under triangular and trapezoidal fuzzy demand. A numerical analysis is conducted to verify the effectiveness of installing automated fabric inspection machines in the cotton plant. This article proposes an iterative solution algorithm (KDPMG) to obtain the global optimum for the proposed model. A comparative study of the proposed algorithm, KDPMG, and the genetic algorithm (GA) is presented in this study to verify the credibility of the obtained results. It is observed that KDPMG provides more appropriate solutions to the problem compared to the GA. Moreover, the computational time of KDPMG is significantly less than that of the GA. The rigorous analysis reveals that maximum profit can be achieved under trapezoidal fuzzy demand with fully automated fabric inspection technology. Using a triangular fuzzy demand pattern, the model with fully automated smart manufacturing achieves an 8.62% higher profit compared to a traditional system. Similarly, in the case of a trapezoidal fuzzy demand pattern, the adoption of automation in cotton plants can achieve an 8.69% higher profit. Hence, the implementation of smart manufacturing systems in the mending section of the cotton textile industry proves to be more profitable compared to the traditional inspection process. [ABSTRACT FROM AUTHOR]

Equivalent constraint method (ECM) is an efficient method for safety life analysis under target time-dependent failure possibility (TDFP) constraint. However, the efficiency of existing ECM still needs to be improved for problems with complex performance functions. In this paper, an efficient method based on equivalent constraint and sequential Kriging model with fuzzy simulation (EC-SK-FS) is proposed to improve the efficiency of solving safety life. In EC-SK-FS, the TDFP constraint is first equivalently transformed into performance function constraint with respect to target TDFP, which can avoid performance function evaluations under unnecessary membership level. Second, based on the EC of the lower bound of extremum performance function being equal to zero, the traditional dichotomy method is embedded to search for the safety life. For each possible life searched by dichotomy, the Kriging model of time-dependent performance function is sequentially trained in the corresponding candidate sample pool (CSP) for estimating the lower bound of extremum performance function, in which a new stopping criterion is established to improve the efficiency of training Kriging model. The new stopping criterion only requires at least one failure sample point accurately identified by the current Kriging model, which reduces the computational cost while ensuring the accuracy of estimating the lower bound of extremum performance function. In addition, the strategy of reducing CSP is adopted to further improve the efficiency of the proposed method. Compared with the existing ECM, the results of examples fully prove that the proposed EC-SK-FS method is more efficient under acceptable accuracy. [ABSTRACT FROM AUTHOR]

To complete a successful energy project, all aspects and criteria which can influence the project should be considered. Classic time-cost trade-off (TCT) is used when the completion time of project is not acceptable for customers or top managers. This paper proposes a new cost-risk-quality-social consideration trade-off (CRQST) model for energy projects in a time-constrained problem for achieving specified due date under uncertainty. Moreover, a new comprehensive definition of risk criterion is proposed, and a novel approach for the quality criterion of project based on the dependence of the quality of activities with each other is presented. The internal and external environment of the energy project are considered simultaneously and a new criterion in TCT problem, called social consideration criterion, is introduced. A developed fuzzy augmented ε-constraint method is introduced for the presented multi-objective model to generate Pareto-optimal solutions. To depict the accuracy of results, the proposed model is solved by goal attainment method, and the results of two methods are compared. As a case study, a real oil and gas project is presented, and results show that the proposed method enables managers to effectively handle construction projects in real-world uncertain environments.

Organ transplantation is a crucial task in the healthcare supply chain, which organizes the supply and demand for various vital organs. In this regard, dealing with uncertainty is one of the main challengings in designing an organ transplant supply chain. To address this gap, in the present research, a mathematical formulation and solution method is proposed to optimize the organ transplants supply chain under shipment time uncertainty. A possibilistic programming model and simulation-based solution method are developed for organ transplant center location, allocation, and distribution. The proposed mathematical model optimizes the overall cost by considering the fuzzy uncertainty of organ demands and transportation time. Moreover, a novel simulation-based optimization is applied using the credibility theory to deal with the uncertainty in the optimization of this mathematical model. In addition, the proposed model and solution method are evaluated by implementing different test problems. The numerical results demonstrate that the optimal credibility level is between 0.2 and 0.6 in all tested cases. Moreover, the patient's satisfaction rate is higher than the viability rate in the designed organ supply chain. [ABSTRACT FROM AUTHOR]

In this study, a novel distributed Kalman filter based on a possibilistic framework was proposed to mitigate fuzzy noisein nonlinear multiagent systems. To describe fuzzy uncertainty, noises were modeled as fuzzy random variables with trapezoidal probability distributions instead of Gaussian distributions. A fuzzy information fusion (FIF) algorithm was proposed to fuse fuzzy state estimations from neighboring nodes. The nonlinear problem was solved by using local linearization. A distributed extended fuzzy information filter was designed by combining the FIF algorithm and local linearization in distributed sensor networks. The stability of this filter was analyzed. Finally, a target tracking simulation was performed to detail the effectiveness of the proposed filter algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a two-stage model is designed for arranging and locating vehicle routes with simultaneous pickup and delivery. The model developed in the first stage optimizes the arrangement of products in packages and thus optimizes packages' length, width, and height for delivery to customers. In the second stage, the goal is to provide customers with vehicle in simultaneous pickup and delivery. In this part of the model, the location of distribution centers is potentially considered, and the demand and cost parameters are considered uncertain. To solve the problem, precise methods and meta-heuristic algorithms of PSO for the first stage and multi-objective meta-heuristic algorithms NSGA II and MOALO for the set have been used. The results of examining the efficiency of the algorithms in the second stage show the high efficiency of the MOALO algorithm with a valuable weight of 0.8388. Therefore, to implement the model in the real problem (Golrang Broadcasting Company), the MOLAO algorithm has been used, the management results include obtaining 15 efficient answers.

Building energy retrofits can reduce emissions and increase cost savings. Some retrofits that can deliver higher emissions savings are not popular due to a lack of economic justifications. Financial incentives can be used to change buyer perception around such retrofits. This study proposes a framework to identify the best-performing retrofit strategies for a given building cluster and the optimal incentive amounts to promote the chosen strategies, accounting for uncertainties, stakeholder priorities, and budget constraints. The proposed framework was demonstrated using a case study complemented with policy insights. Life cycle cost savings and capital cost significantly impact retrofit purchase decisions. Case study results showed that retrofitting houses heated with electricity can produce significant cost savings. However, adopting energy-conscious behaviours in houses heated with natural gas and injecting renewable natural gas into the gas supply can produce two times more emissions savings achieved by any retrofit strategy applied to an electrically heated house. This indicates the need for adopting performance-based incentives over the prescriptive approach to reward occupant efforts in addition to asset performance. Despite potential life cycle cost savings, incentives must be complemented with low-interest loans to promote retrofit strategies carrying higher capital costs. [ABSTRACT FROM AUTHOR]

In hub-and-spoke systems, hub location and allocation decisions depend on some parameters, such as transportation demand. When demand is time-dependent, a function can be estimated that reflects demand changes over time. In real-world conditions, due to the lack of knowledge and the nature of transportation demand, the coefficients of this function cannot be determined precisely. In this case, these coefficients are considered as uncertain parameters. In this paper, we propose a multi-objective mixed-integer nonlinear programming model for a sustainable multi-period hub location problem when demand changes are based on a linear function of time, and the coefficients of this function are fuzzy parameters. In the proposed model, it is possible to increase the capacity of hubs and hub links and transfer the capacity between hubs through modules. Also, the model determines the best timing for implementing the decisions. The objectives include minimizing system costs, minimizing emissions, and maximizing job opportunities related to sustainability aspects. We linearize the model and present a crisp counterpart formulation. Then, the computational results and sensitivity analysis are presented. Results show that the cost of designing the hub network with economic and social considerations is higher than the cost of designing the network with economic and environmental considerations. Ignoring the uncertainty in the problem can lead to non-optimal solutions. Also, the impact of increasing the number of hubs on reducing emissions after a threshold is marginal. We also introduce some valid inequalities to strengthen the formulation. The results indicate the acceptable performance of valid inequalities. [ABSTRACT FROM AUTHOR]

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 λ -cut of FuIMF variables are considered as interval-boundary intervals. Second, the λ -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. [ABSTRACT FROM AUTHOR]

• An improved adaptive Kriging method is proposed for possibility-based design optimization. • The enhanced expected improvement learning function is adopted to improve the efficiency of Kriging model. • Active possibility constraint is identified to improve efficiency of possibility-based design optimization. • The proposed method is applied to an aeroengine turbine disk. Possibility-based design optimization (PBDO) can provide theoretical basis for the structural optimal design of fuzzy uncertainty model in engineering, so as to obtain the optimal design variables. The genetic algorithm (GA) based on adaptive Kriging method for PBDO requires high precision in the whole design space, while the region far from the limit state surface (LSS) of the constraint function has little effect on PBDO, thus greatly affects the computational efficiency. In order to improve the efficiency of PBDO, an improved adaptive Kriging method combined with active possibility constraint (I-AK-AC) is proposed in this paper. In I-AK-AC, the enhanced expected improvement learning function is first put forward to promote the convergence efficiency of Kriging model by reducing the accuracy of the region far from the LSS of the constraint function. Whereafter, the active possibility constraint is identified, and only the boundaries of active possibility constraint need to be approximated precisely by Kriging model. By these ways, the convergence speed of Kriging model is further ameliorated without affecting the computational accuracy, and the efficiency of PBDO is significantly improved. Three test examples and an engineering application of aeroengine turbine disk illustrate the validity and accuracy of the proposed I-AK-AC. [ABSTRACT FROM AUTHOR]

Evaluating the quality of the performances of higher education centers is very important due to their important and effective role. Evaluating the quality of the performance of higher education centers leads to identifying strengths and weaknesses, as well as opportunities and factors hindering development, and the possibility of an appropriate planning for improving the situation are also provided. In order to continuously modify and improve the university system, it seems necessary to establish an appropriate performance evaluation mechanism through which the improvement of the entire university system can be considered in addition to improving and enhancing the scientific quality, and at the same time, which has arisen from the text of the university system and conforms to the characteristics of this system. In this research, considering the uncertain decision-making environment, a new evaluation model called Fuzzy Improved Input Efficiency Profiling - Common Weights Based on the Optimal Solution (FIIEP - CWBOS) has been proposed, which improves the performance of the classic input efficiency profile model. The results of this study showed that the proposed model has the necessary validity and optimal performance compared to other models presented so far. [ABSTRACT FROM AUTHOR]

For the uncertain structural system with fuzzy uncertainties as well as random ones, a new approach is proposed to assess the reliability of the mixed uncertain structure, which the membership levels of the different fuzzy input variables are treated as random variables with independent and uniform distributions. The possible combination of the membership levels of the different fuzzy variables was considered, which contains more available information. By analyzing the relationship between the proposed approach and traditional approaches, the rationality and advancement of the proposed approach are verified. In order to improve the computation efficiency of the proposed approach, a highly efficient kriging-based solution is established in this paper. Furthermore, two practical engineering examples are used to demonstrate the feasibility of the proposed approach and the efficiency of the proposed solution. [ABSTRACT FROM AUTHOR]

In this paper, a two-stage model is designed for arranging and locating vehicle routes with simultaneous pickup and delivery. The model developed in the first stage optimizes the arrangement of products in packages and thus optimizes packages' length, width, and height for delivery to customers. In the second stage, the goal is to provide customers with vehicle in simultaneous pickup and delivery. In this part of the model, the location of distribution centers is potentially considered, and the demand and cost parameters are considered uncertain. To solve the problem, precise methods and meta-heuristic algorithms of PSO for the first stage and multi-objective meta-heuristic algorithms NSGA II and MOALO for the set have been used. The results of examining the efficiency of the algorithms in the second stage show the high efficiency of the MOALO algorithm with a valuable weight of 0.8388. Therefore, to implement the model in the real problem (Golrang Broadcasting Company), the MOLAO algorithm has been used, the management results include obtaining 15 efficient answers. [ABSTRACT FROM AUTHOR]

In group decision-making (GDM) problems, the elicitation of preferences from decision makers (DMs) and consensus reaching process are two critical issues to be resolved. Many kinds of preference relations have been proposed in the recent two decades. In this paper, we propose a novel pairwise comparison structure called fuzzy-uncertainty-based distributed preference relation (FUDPR), which could not only indicate the intensity of preferred, non-preferred, indifferent and uncertain information of one alternative against another simultaneously, but also has the ability to represent local ignorance expressed by DMs. The FUDPR introduces the set of consecutive evaluation grades into the distributed preference relation (DPR) where only discrete single evaluation grades and global ignorance can be modeled in the preference relation. The missing values in FUDPR are estimated by the defined score function. Two kinds of consensus reaching process (CRP) are then proposed, namely soft and hard consensus mechanism, respectively, which are suitable for different decision-making situations. Both of them consider the individual dissimilarity, trust relations and self-confidence in the designed feedback mechanism. Comparative analysis is performed between the proposed method and other state-of-the-art pairwise comparison GDM models. An illustrative example of life cycle sustainability assessment (LCSA) is proposed to demonstrate the rationality and effectiveness of the proposed method in supporting real-world GDM problems. [ABSTRACT FROM AUTHOR]

As a major concern of chief managers in each organization, project portfolio selection has a special place in their responsibilities. To assist managers in making decisions, applicable optimization models play an essential role in such processes. In this regard, this paper provides a stochastic optimization model for a project portfolio selection problem under different scenarios. Providing the novelty in the model along with making it closer to reality, the interdependency between revenue and cost of projects is considered. Due to the inherent uncertainty of parameters, the revenue and cost of each project, as well as contributed capital, follow triangular fuzzy parameters. Contrary to the previous model, the appreciation of assets is considered in the proposed model as the other novelty of the proposed model. To tackle the uncertainty of parameters, a robust possibilistic approach is used, which has been first-ever devised in such problems. Being both optimistic and pessimistic approaches available for decision-makers, a new measure is introduced to make the model inclusive. Moreover, by considering the confidence level as both parameter and decision variables, the robust possibilistic programming approach is adopted to solve the proposed model. Using the new proposed measure, the optimal average value of robust model are obtained under different confidence level. Finally, solving the optimization model, the results are provided by implementing the realization for uncertain parameters, and regarding the obtained results, discussions are made to provide some insights to the managers. [ABSTRACT FROM AUTHOR]

Information of the real world is often imperfect and partially reliable. Thus, processing the uncertain information is of great importance. Z-number, proposed by Zadeh, is an effective tool to describe the real-world information, which contains both fuzziness and reliability of information. In most decision-making problems, information is usually provided by experts. However, opinions among experts may be conflicting. How to deal with the opinions of multiple experts from an objective point of view, especially when there is a conflict among the opinions of multiple experts, is still an open issue. Therefore, in this paper, an improved model in fusing multi-source information based on Z-numbers and power ordered weighted average (POWA) operator is proposed, considering both the decision makers' attitude characteristics and the support degree among evidence. The soft likelihood function based on Z-numbers is included in the improved model. A case study in medical diagnosis and some other examples of scenario simulation are used to illustrate the validity and superiority of the proposed model. [ABSTRACT FROM AUTHOR]

Time‐dependent failure possibility (TDFP) can measure the structural safety level for a time interval of interest under fuzzy uncertainty, but its calculational cost is unaffordable by using fuzzy simulation (FS) due to a required large size of FS candidate sampling pool (CSP). Although time‐dependent adaptive Kriging model (T‐AK) combined with FS (T‐AK‐FS) was presented to reduce the number of calling performance function, a large FS CSP still makes training T‐AK time‐consuming. To improve its efficiency, an adaptive truncated FS (ATFS) with T‐AK (T‐AK‐ATFS) is proposed by CSP size reduction approach. By T‐AK‐ATFS, the largest safety hypercube in fuzzy standard space is adaptively searched, in which the samples are in safety states and can be removed from the FS CSP. Moreover, T‐AK is adaptively trained to search the largest safety hypercube and estimate TDFP simultaneously. In adaptively searching process, the FS CSP is divided into several sub‐CSPs, on which training T‐AK is more time‐saving. Overall, strategies of T‐AK‐ATFS include proposing ATFS to reduce the FS CSP, adaptively searching the largest safety hypercube, estimating the TDFP with the same T‐AK and training T‐AK in the sub‐CSPs sequentially. Verified by examples, these strategies make T‐AK‐ATFS more efficient than existing FS and T‐AK‐FS. [ABSTRACT FROM AUTHOR]

The problem which is actually being addressed in this study includes two parts: One is on establishing time-dependent reliability-based design optimization (tRBDO) formulation under fuzzy and interval uncertainties to obtain the optimal design parameter solution for the time-dependent structure. The other is on presenting a serial single-loop optimization (SSLO) strategy to estimate the optimal design parameter. For addressing the optimal design parameter of the time-dependent structure involving fuzzy and interval uncertainties, a novel tRBDO model with the constraint of time-dependent failure possibility (TDFP) based on the possibility theory of the safety measure is proposed. For evaluating the optimal design parameter, the established SSLO method converts the original triple-loop optimization which is TDFP-index-based approach into a sequence of deterministic optimization, interval value corresponding to the worst case scenario, the estimation of time instant, and the minimum most probable point. Iterative searching step is not needed to find the minimum most probable point at each iteration step in the proposed SSLO strategy; therefore, the computational time is extremely reduced. Several examples are given to demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

The system failure possibility of multi-mode structural system (referred to as system) under fuzzy uncertainty is the joint membership function of input vector at the system fuzzy design point, and it can reasonably measure the safety degree of the system. The system fuzzy simulation (S-FS) can be combined with adaptive Kriging model (AK-S-FS) to solve the system failure possibility. In the current AK-S-FS method, the system fuzzy design point is searched in the maximum value region of the fuzzy input vector corresponding to the 0 membership level, and its computational efficiency still needs to be improved. Thus, a hierarchical system fuzzy simulation combined with adaptive Kriging model (AK-HS-FS) method is proposed to improve the efficiency of searching the system fuzzy design point in this paper. The efficiency of the proposed AK-HS-FS method comes from the innovative strategies of three aspects. The first is the strategy of the hierarchical system fuzzy simulation (HS-FS). Compared with the S-FS with the system fuzzy design point searched roughly in the maximum possible value region, the strategy of the HS-FS is to exploratively expand the search region by transferring from a larger membership level to a smaller one. The overall search region of the system fuzzy design point can be reduced without losing the search accuracy in the HS-FS. The second is the strategy of the hierarchical training. Compared with training the system Kriging model in the combined candidate sample pool (CSP) of all layers, it is more time-saving to train the system Kriging model layer by layer in the hierarchical CSP. The third is the strategy of iteratively reducing the CSP. According to the properties of the system fuzzy design point and the probability properties of the Kriging prediction, the required time of training the system Kriging model can be further reduced by iteratively reducing the CSP, and the reduction of the CSP can ensure the accuracy without introducing any computational cost and complexity. The results of case studies fully verify that the AK-HS-FS is much more efficient than the AK-S-FS under satisfying the computational accuracy. [ABSTRACT FROM AUTHOR]

The prioritization of the failure risks of the components in an existing product is critical for product redesign decision-making considering various uncertainties. Two issues need to be addressed in the failure risk prioritization process. One is the evaluation of the failure risk considering each failure mode for each component. Currently, many failure mode effects and analysis (FMEA) methods based on fuzzy logic seldom deal with the randomness in failure mode occurrence during the product operation stage. Therefore, in this research, the information axiom is extended to calculate the information contents of risk indices considering these two types of uncertainty. The second issue is the evaluation of the degree of failure risk for each of the components. The weighted sum of information content considering all failure modes is used to assess the risk of components based on a fuzzy logarithmic least squares method (FLLSM). Additionally, a case study to prioritize the failure risks of various components in a crawler crane is implemented to demonstrate the effectiveness of the developed approach. [ABSTRACT FROM AUTHOR]

When there exists fuzzy uncertainty in experimentally determined information, viscoelastic constitutive parameters to be identified are treated as fuzzy variables, and a two-stage strategy cooperating with particle swarm method is presented to identify membership functions of fuzzy parameters. At each stage, inverse fuzzy problem is formulated as a series of α-level strategy-based inverse interval problems, which are described by optimization problems and are solved utilizing particle swarm method. Forward interval analysis required in inverse interval analysis is conducted by solving two optimization problems via modified coordinate search algorithm. To alleviate heavy computational burden, dimension-adaptive sparse grid (DSG) surrogate is embedded in optimization process. The surrogate is constructed on a solid platform of high fidelity deterministic solutions, which is provided by scaled boundary finite element method and temporally piecewise adaptive algorithm. Eventually, membership functions of fuzzy parameters can be obtained by fuzzy decomposition theorem with interval bounds acquired at each of α-sublevels. Parallelization is realized for construction of DSG surrogate and implementation of particle swarm method for a further computation reduction. Numerical examples are provided to illustrate effectiveness of proposed approach, where regional inhomogeneity and impact of measurement points selection on identification results are explored. [ABSTRACT FROM AUTHOR]

Failure possibility (FP) is widely used to measure safety degree of structure in the presence of fuzzy uncertainty, but how to quantify the effect of fuzzy distribution parameter on FP is seldom investigated. For searching the important parameter to FP and guiding the FP-based design optimization, the local sensitivity of FP (LS-FP) is firstly defined by the partial derivative of FP with respect to the fuzzy distribution parameter in this paper. Then, the analytical solution is derived for the LS-FP in special cases; a universal algorithm is proposed to solve LS-FP by use of the fuzzy simulation. The proposed universal algorithm includes three creative steps. The first is explicitly expressing FP as the joint membership function of the fuzzy inputs at the fuzzy most possible failure point (F-MPP) by use of the fuzzy simulation, on which LS-FP can be equivalently transformed as the partial derivative of F-MPP with respect to the fuzzy distribution parameter. The second is using the characteristic of F-MPP to derive the analytical solution of the partial derivative of F-MPP. The third is establishing an efficient method to estimate F-MPP for completing LS-FP, where new learning function and stopping criterion are proposed to improve the computational efficiency. The proposed algorithm has no limitation on the nonlinearity of performance function and can be applied in any fuzzy membership distribution form of the fuzzy input. Several examples are used to validate the wide applicability, the accuracy, and the efficiency of the proposed algorithm to solve LS-FP. [ABSTRACT FROM AUTHOR]

Failure credibility is popular in measuring safety degree of structure under fuzzy uncertainty, but the heavy computational cost is still a challenge in estimating the failure credibility. To alleviate this issue, an iterative method combining adaptive Kriging and fuzzy simulation (AK-FS) has been developed by Ling et al. However, for the problem with complex performance function, a large candidate sampling pool is needed in the AK-FS, which makes the training process of the Kriging model fairly time consuming. In order to improve the estimation efficiency of failure credibility through reducing the size of candidate sampling pool in AK-FS, an efficient sample reduction strategy based on adaptive Kriging (SR-AK) is proposed in this paper. In the SR-AK, the estimation of failure credibility is transformed into searching two active points in candidate sampling pool. After updating the Kriging model in each circle, current active points can be easily identified. Then, according to the properties of the active points and the prediction characteristics of Kriging model, the samples in current candidate sampling pool can be divided into two sets, i.e., the samples affect the estimation of active points and the samples have no effect on it. Obviously, the samples in the latter set can be deleted from current candidate sampling pool to reduce its size. By using this sample reduction strategy, the process for training Kriging model is accelerated circle by circle, which is very helpful to save the analysis time and improve the computational efficiency in estimating failure credibility. Four examples are employed to demonstrate the performance of the proposed SR-AK in fuzzy safety degree analysis. [ABSTRACT FROM AUTHOR]

• Time-variant creep coefficient and shrinkage strain model is developed. • Corrosion is considered. • Epistemic uncertainty is considered to incorporate vagueness of variables. • To evaluate TDFP and TDR, a single-loop optimization method is applied. • Fuzzy reliability estimated by the area ratio of failure domain to the total area of MF. • Real-time data from Addis Ababa is used for the case-study. • The proposed methodology prevents the exploitation of the probability theory. Time-dependent reliability (TDR) is the possibility that a structure or system under consideration can perform the intended function under specified service conditions over a given time instant under fuzzy uncertainty. This paper is mainly concerned to identify fuzzy variables, generate the membership function of the input variables and output quantities, analyze timedependent performance level, estimate the possibility safety index, and evaluate the TDR of the structures. To evaluate TDR by a possibilistic approach, the fuzzy uncertainty that is characterized by membership function is considered. The type of uncertainty defines the method of reliability analysis, i.e., aleatory uncertainty possesses a probabilistic approach, whereas epistemic uncertainty leads to a possibilistic approach. The TDR analysis of the structures subjected to sustained load and corrosion based on probability theory is well developed. On the contrary, the TDR of structures subjected to combined effects sustained load, corrosion, creep, and shrinkage based on possibility theory lack research. Thus, this paper is significant to evaluate the TDR of structures subjected to the aforementioned effects based on possibility theory. However, it requires a rigorous procedure, a single-loop optimization method (SLOM) is employed to evaluate the TDR of structures involving epistemic uncertainty. To enhance the validation of the proposed approach, several examples are thoroughly carried out. [ABSTRACT FROM AUTHOR]

Time-dependent failure possibility (TDFP) can reasonably measure the safety degree of time-dependent structure under fuzzy uncertainty, but there lacks design optimization under the constraint of TDFP for the trade-off of the performance and the safety. Thus, a time-dependent failure possibility-based design optimization (T-PBDO) under fuzzy uncertainty is established, and a time-dependent performance measure approach (T-PMA) for solving T-PBDO is proposed in this paper. In the proposed T-PMA, the TDFP constraint is equivalently transformed into the performance function constraint corresponding to the required target TDFP. The minimum performance target point (MPTP) and its corresponding time instant in the performance function constraint with respect to the target TDFP are determined by the single-loop optimization method of inverse TDFP analysis. This strategy completed by the inverse TDFP analysis with respect to the target TDFP can avoid analysis of the performance function under the unnecessary membership level, and then lead to improve the numerical stability and computational efficiency of solving the T-PBDO model. A numerical and three engineering case studies are introduced to verify the effectiveness of the proposed method. The results show that the proposed T-PMA is accurate, and its efficiency is higher than that of the direct optimization method. [ABSTRACT FROM AUTHOR]

In the present study, for the first time, a new framework is used by combining metaheuristic algorithms, decomposition and machine learning for flood frequency analysis under climate-change conditions and application of HadCM3 (A2 and B2 scenarios), CGCM3 (A2 and A1B scenarios) and CanESM2 (RCP2.6, RCP4.5 and RCP8.5 scenarios) in global climate models (GCM). In the proposed framework, Multivariate Adaptive Regression Splines (MARS) and M5 Model tree are used for classification of precipitation (wet and dry days), whale optimization algorithm (WOA) is considered for training least square support vector machine (LSSVM), wavelet transform (WT) is used for decomposition of precipitation and temperature, LSSVM-WOA, LSSVM, K nearest neighbor (KNN) and artificial neural network (ANN) are performed for downscaling precipitation and temperature, and discharge is simulated under present period (1972–2000), near future (2020–2040) and far future (2070–2100). Log normal distribution is used for flood frequency analysis. Furthermore, analysis of variance (ANOVA) and fuzzy method are employed for uncertainty analysis. Karun3 Basin, in southwest of Iran, is considered as a case study. Results indicated that MARS performed better than M5 model tree. In downscaling, ANN and LSSVM_WOA slightly outperformed other machine learning algorithms. Results of simulating the discharge showed superiority of LSSVM_WOA_WT algorithm (Nash-Sutcliffe efficiency (NSE) = 0.911). Results of flood frequency analysis revealed that 200-year discharge decreases for all scenarios, except CanESM2 RCP2.6 scenario, in the near future. In the near and far future periods, it is obvious from ANOVA uncertainty analysis that hydrological models are one of the most important sources of uncertainty. Based on the fuzzy uncertainty analysis, HadCM3 model has lower uncertainty in higher return periods (up to 60% lower than other models in 1000-year return period). [ABSTRACT FROM AUTHOR]

• A novel fuzzy analysis approach for free vibration of FGM semi-rigid structures is developed. • A new Timishenko beam element is established to account for the connection flexibility. • An efficient response surface-based optimization solution is introduced to estimate the fuzzy natural frequency. • The method can estimate accurately the fuzzy natural frequency with affordable computational cost. • Connection uncertainties significantly enlarge the fuzziness of the natural frequencies. This study contributes a practical approach for the fuzzy free vibration quantification of functionally graded semi-rigid frame structures. A new Timoshenko beam element is formulated to include the connection rigidity for the analysis purpose. The finite element formulation is general to present different semi-rigid conditions, whereas hinged and rigid connections are special cases. Furthermore, an efficient response-surface-based fuzzy analysis is established based on the α–cut strategy and first-order Taylor's approximation to predict the fuzzy natural frequencies of the structures. Highlighted point is that various input uncertainties, such as the material characteristics, the member dimensions, and the connection rigidities, can be incorporated in the analysis by the presented fuzzy methodology. Computational efficiency and correctness of the proposed method are shown, and the effect of the uncertainties, especially of the connection rigidities, on the natural frequency of semi-rigid FGM structures is explored via solving some numerical examples. [ABSTRACT FROM AUTHOR]

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The time-dependent failure credibility (TDFC) can reasonably measure the safety level of the time-dependent structure under the fuzzy uncertainty, but the direct optimization algorithm to estimate the TDFC requires large computational cost and even results in locally optimal solutions. Therefore, an efficient method is proposed for estimating the TDFC by combining the fuzzy simulation and the single-loop Kriging model. In the proposed method, fuzzy inverse transformation theorem is firstly used to transform the estimation of the TDFC into a sample classification problem, in which the candidate sample pool generated by fuzzy simulation (FS) is classified into the failure group and the safety one. For improving the efficiency of the classification, a Kriging model is adaptively trained by an elaborate U-learning function in the candidate sample pool. After the candidate sample is divided into the failure group and the safety one by the convergent Kriging model, the TDFC can be estimated as a byproduct easily. The innovation of the proposed method includes two aspects: establishing the idea of the fuzzy simulation combined with the single-loop Kriging model to estimate TDFC efficiently and robustly, and designing an elaborate U-learning function to improve the efficiency of training the single-loop Kriging model. The presented examples validate the efficiency of the proposed method under the acceptable precision. [ABSTRACT FROM AUTHOR]

Time-dependent failure credibility (TDFC) in a given service time of interest can reasonably quantify the safety of the structure with fuzzy inputs. However, the estimation of TDFC requires high computational cost because it involves multi-layer optimization, especially for problems with the implicit performance functions in engineering. In order to improve the efficiency of estimating TDFC under satisfied precision, this paper proposes an efficient dichotomy searching algorithm (DSA) combined with double-loop adaptive Kriging (D-AK) model (shorten as D-AK-DSA). In the proposed D-AK-DSA, a double-loop adaptive Kriging model is constructed to provide the directions for the dichotomy searching TDFC. In the inner loop, the AK model is constructed to surrogate the relation of the performance function and time variable at the given fuzzy input realization so as to obtain the minimum performance function with respect to the time for the outer loop, and in the outer loop, the AK model is constructed to identify the sign of the upper/lower boundary of the minimum performance function with the fuzzy inputs at a given membership interval so as to provide the dichotomy searching direction for TDFC. By the proposed dichotomy searching strategy, accurately solving the values of the upper/lower boundaries in evaluating TDFC is innovatively replaced by identifying the signs of them, which greatly reduces the difficulty of constructing the outer AK model. At the same time, the proposed method enhances the convergence of the outer AK surrogate model by establishing a reasonably improved learning function. Three examples verify the accuracy and efficiency of the proposed D-AK-DSA method. [ABSTRACT FROM AUTHOR]

Failure credibility is popular in measuring safety degree of structure under fuzzy uncertainty due to its excellent property of self-duality. Existing methods for estimating failure credibility can be mainly divided into two categories, i.e., the simulation-based methods and the optimization-based methods. The simulation-based methods are universal and robust, but time-consuming in dealing with high-dimensional problems. The optimization-based methods are efficient and flexible, but the precision of the failure credibility estimate will be impacted by the local optimum solution resulted from some optimization techniques. Thus, in order to overcome the disadvantages of existing methods, an efficient method by combining genetic algorithm and active learning Kriging (AK-GA) is proposed to estimate failure credibility in this paper. Firstly, by use of the fuzzy simulation, the estimation of failure credibility is transformed into finding for the failure/safety sample that processes the maximum joint membership function (MF) from the fuzzy simulation pool, which makes the credibility estimation less difficult to be computed. Secondly, the genetic algorithm is used to find the failure/safety sample with maximum joint MF. Thirdly, to drastically improve the computational efficiency of the proposed method, active learning Kriging is embedded to accurately and efficiently distinguish the failure and safety sample in computing the fitness function of genetic algorithm. Four mathematical and engineering test examples are used to demonstrate the accuracy and efficiency of the proposed AK-GA for estimating failure credibility. [ABSTRACT FROM AUTHOR]

Climate warming has triggered a series of external uneconomic problems that have had a tremendous impact on human production and life. At the same time, the current intelligent models for low-carbon economic research have some drawbacks. Therefore, in order to explore a more scientific low-carbon development model, based on the analysis of low-carbon development at home and abroad, this study combines particle swarm optimization and neural network to analyze China's carbon productivity through multidimensional analysis, determine multiple factors and select more important data as factor analysis objects.In this paper, the authors analyze the neural network model for new energy industry economy based on particle swarm optimization. The result shows that the particle swarm algorithm has a very fast convergence rate and can avoid falling into local minimum values in the later stage and finally achieve higher solution precision. The development of new energy industry is an important strategy and means for implementing sustainable development and adjusting the industrial structure. This article, from the perspective of industrial economics, uses genetic neural networks and fuzzy uncertainty to explore how to effectively combine the capital market with the development of new energy industries. Bring into play the role of the capital market in supporting the development of new energy industries. [ABSTRACT FROM AUTHOR]