Search Results (17)

To address the economic and reliability challenges of high-penetration renewable energy integration in electricity-heat-hydrogen integrated energy systems and support the dual-carbon strategy, this paper proposes an optimal dispatch method integrating Information Gap Decision Theory (IGDT) and Fuzzy Chance-Constrained Programming (FCCP). An IES model coupling multiple energy components was constructed to exploit multi-energy complementarity. A stepped carbon trading mechanism was introduced to quantify emission costs. For interval uncertainties in renewable generation, IGDT-based robust and opportunistic dispatch models were established; for fuzzy load uncertainties, FCCP transformed them into deterministic equivalents, forming a dual-layer “IGDT-FCCP” uncertainty handling framework. Simulation using CPLEX demonstrated that the proposed model dynamically adjusts uncertainty tolerance and confidence levels, effectively balancing economy, robustness, and low-carbon performance under complex uncertainties: reducing total costs by 12.7%, cutting carbon emissions by 28.1%, and lowering renewable curtailment to 1.8%. This study provides an advanced decision-making paradigm for low-carbon resilient IES. Full article

The rapid development of the new energy vehicle industry has resulted in a significant number of waste electric vehicle batteries (WEVBs) reaching the end of their useful life. The recycling of these batteries holds both economic and environmental value. As policy is a critical factor influencing the recycling of waste electric vehicle batteries, its role in the network warrants deeper investigation. Based on this, this study integrates both subsidy and penalty policy into the design of the waste electric vehicle battery reverse logistics network (RLN), aiming to examine the effects of single policy and policy combinations, thereby filling the research gap in the existing literature that predominantly focuses on single-policy perspectives. Considering multiple battery types, different recycling technologies, and uncertain recycling quantities and qualities, this study develops a fuzzy mixed-integer programming model to optimize cost and carbon emission. The fuzzy model is transformed into a deterministic equivalent form using expected intervals, expected values, and fuzzy chance-constrained programming. By normalizing and weighting the upper and lower bounds of the multi-objective functions, the model is transformed into a single-objective optimization problem. The effectiveness of the proposed model and solution method was validated through an empirical study on the construction of a waste electric vehicle battery reverse logistics network in Zhengzhou City. The experimental results demonstrate that combined policy outperforms single policy in balancing economic benefits and environmental protection. The results provide decision-making support for policymakers and industry stakeholders in optimizing reverse logistics networks for waste electric vehicle batteries. Full article

This study discusses the planning of a regional-scale water–food nexus (WFN) system using an inexact fuzzy chance constraint programming (IFCCP) method. The IFCCP approach can handle uncertainties expressed as interval and fuzzy parameters, as well as the preferences of decision makers. An inexact fuzzy chance constraint programming-based water–food nexus (IFCCP-WFN) model has been developed for the City of Jinan with the consideration of various restrictions related to water and land availability, as well as food and vegetable demands. Solutions for the planting areas for different crops in different periods have been generated under the different preferences of decision makers. The water resource availability would be the priority factor affecting the WFN system under demanding conditions, in which wheat cultivation would be dominated by this factor under fuzzy confidence levels of 0.2 and 0.5, and the planting area of corn would be determined by this factor under high fuzzy confidence levels (e.g., 0.8). In addition, the reliability of irrigation would decrease with increasing fuzzy confidence levels under demanding conditions, limiting the planting areas for crops and leading to a decreasing trend of the system benefit. Adequate water resources would be available for irrigation under optimistic conditions, implying no significant contributions to the planting schemes. Nevertheless, increasing food loss rates would result in more planting areas to satisfy food requirements and thus a greater system benefit under advantageous conditions. Compared with the developed IFCCP-WFN model, the interval-linear-programming-based water–food nexus (ILP-WFN) model can merely reflect the lower and upper bounds of uncertain parameters and neglects the inherent distributional information within the fuzzy parameters. Thus, the ILP-WFN model is unable to reveal the inherent impacts of the fuzzy parameters on the resulting planting strategies. Full article

In research of a better description for information uncertainty, Z-numbers, which are related to both the objective information and the subjective criticism, were first conceptualized by Zadeh. Because of its neologism, there have been multitudinous attempts toward continuation and expansion of the prototype. In this paper, we mainly study varieties of theoretical preparations for classical Z-numbers and derive the maximum expected linear programming model of Z-numbers, which are constructed on the basis of reliability conversion factors and proliferation on applications due to their simplicity. Firstly, by means of transforming Z-numbers into LR fuzzy intervals through their reliability variable, the credibility distribution and inverse distribution of converted Z-numbers are stated precisely. Then, the operational law of independent variables and its expected value can be derived via credibility distribution. The maximum expected Z-number linear programming model is determined on the basis of previous theoretical preparations, and it transforms from a classical Z-number chance-constrained model into a crisp one. Finally, with the aim of improving the programming method, its application in pragmatic practice with the realistic examples of a supplier section and optimal portfolio problems are enumerated to interpret the effectiveness of our model. Full article

The water environment restoration project portfolio (WERP) selection is discussed in this paper. By complying with the analysis of the project’s multidimensional property and operation mode, this paper develops the chance constraint and the management constraint of the WERP from the perspectives of public service and enterprise operation. In addition, the multi-objective mixed integer linear programming model is constructed by combining the expectation method and the fuzzy chance constraint programming method. The results demonstrate that: (1) Our proposed method successfully circumvents the occurrence of local objective optimization within a specific confidence interval, thereby achieving a balance between economic and water environment restoration objectives; (2) including fuzzy chance constraints in our proposed method significantly diminishes the risk of exceeding the WERP capacity, thereby ensuring the effectiveness of water environment restoration by adopting a market-based approach. However, further examination of the impact of various sub-projects in WERP is necessary, along with the integration of novel evolutionary algorithms to enhance the efficiency of our model. Full article

In this paper, an uncertain interval stochastic fuzzy chance constraint land use optimal allocation method is proposed and applied to solve the problem of land use planning in river basins. The UISFCL-LUP method is an aggregation of interval parametric programming, fuzzy linear programming and chance constraint programming which can cope with uncertain problems such as interval value, fuzzy set and probability. In this paper, the uncertain mathematical method is explored and studied in the optimal allocation of land use in the next two planning periods of Nansihu Lake Basin in China. Moreover, it was proved that ISFCL-LUP can deal with the uncertainty of interval, membership function and probability representation and can also be used to solve the land use planning and land use strategy analysis under uncertain conditions. On the basis of model calculations, we obtained the optimal allocation results for six types of land use in four regions over two planning periods based on different environmental constraints. The results show that the optimized λ value (that is, the degree of satisfaction with all the model conditions) is in the range of [0.54, 0.79] and the corresponding system benefits are between [18.4, 20.4] × 1012 RMB and [96.7, 109.3] × 1012 RMB. The results indicate that land managers can make judgments based on the different socio-economic development needs of different regions and determine strategic land use allocation plans under uncertain conditions. At the same time, the model obtained interval solutions under different system satisfaction and constraint violation probabilities, which helps land managers to analyze the importance of land system optimization and sustainable development more deeply. Full article

In scientific journals, it is increasingly common to find articles presenting methods for solving problems not based on idealistic mathematical models containing perfectly accurate coefficient values that cannot be obtained in practice, but on models in which coefficient values are affected by uncertainty and are expressed in the form of intervals, fuzzy numbers, etc. However, solving tasks with interval coefficients is not fully mastered, and a number of such problems cannot be solved by currently known methods. There is undeniably a research gap here. The article presents a method for solving problems governed by the quadratic interval equation and shows how to find the tolerant optimal control value of such a system. This makes it possible to solve problems that could not be solved before. The paper introduces a new concept of the degree of robustness of the control to the set of all possible multidimensional states of the system resulting from its uncertainties. The method presented in the article was applied to an example of determining the optimal value of nitrogen fertilization of a sugar beet plantation, the vegetation of which is under uncertainty. It would be unrealistic to assume precise knowledge of crop characteristics here. The proposed method allows to determine the value of fertilization, which gives a chance to obtain the desired yield for the maximum number of field conditions that can occur during the growing season. Full article

Water scarcity has become a major impediment to economic development, and a scientifically sound water allocation plan is essential to alleviate water scarcity. An opportunity constraint approach is introduced to optimise the uncertainty of the minimum regional development level under five hydrological scenarios, and an interval-fuzzy two-stage chance-constraint model (IFTSC) is constructed to improve the reliability of the model results. The correlation of each stochastic parameter in the IFTSC model with the water allocation results and the economic benefits of the Tingjiang River basin is analysed by the Pearson correlation coefficient method. Simulation results from the IFTSC model show a downward trend in overall water scarcity and an upward trend in overall economic benefits in the Tingjiang River basin. Taking the dry water scenario as an example, the water shortage in the industrial sector decreases by 9.7%, and the overall economic benefits of the Tingjiang River basin increase by 41.58 × 108 CNY. The results of the correlation analysis based on Pearson’s correlation coefficient show that water allocation is strongly positively correlated with variables such as water price and regional minimum development requirements, and economic efficiency is strongly positively correlated with unit scale output value and losses caused by water shortage. This paper provides constructive suggestions and guiding directions for the rational allocation of water resources in the Tingjiang River basin through a detailed analysis of the results and identification of the main stochastic parameters in the water allocation process. Full article

Renewable energy sources (RES) generation has huge environmental and social benefits, as a clean energy source with great potential. However, the difference in the uncertainty characteristics of RES and electric–thermal loads poses a significant challenge to the optimal schedule of an integrated energy system (IES). Therefore, for the different characteristics of the multiple uncertainties of IES, this paper proposes a type-II fuzzy interval chance-constrained programming (T2FICCP)-based optimization model to solve the above problem. In this model, type-II fuzzy sets are used to describe the uncertainty of RES in an IES, and interval numbers are used to describe the load uncertainty, thus constructing a T2FICCP-based IES day-ahead economic scheduling model. The model was resolved with a hybrid algorithm based on interval linear programming and T2FICCP. The simulations are conducted for a total of 20 randomly selected days to obtain the advance operation plan of each unit and the operation cost of the system. The research results show that the T2FICCP optimization model has less dependence on RES output power and load forecasting error, so can effectively improve the economy of IES, while ensuring the safe and stable operation of the system. Full article

Due to population growth and human activities, water shortages have become an increasingly serious concern in the North China Plain, which has become the world’s largest underground water funnel. Because the yield per unit area, planting area of crops, and effective precipitation in the region are uncertain, it is not easy to plan the amount of irrigation water for crops. In order to improve the applicability of the uncertainty programming model, a hybrid LSTM-CPP-FPP-IPP model (long short-term memory, chance-constrained programming, fuzzy possibility programming, interval parameter programming) was developed to plan the irrigation water allocation of irrigation system under uncertainty. The LSTM (long short-term memory) model was used to predict crop yield per unit area, and CPP-FPP-IPP programming (chance-constrained programming, fuzzy possibility programming, interval parameter programming) was used to plan the crop area and the effective precipitation under uncertainty. The hybrid model was used for the crop production profit of winter wheat and summer corn in five cities in the North China Plain. The average absolute error between the model prediction value and the actual value of the yield per unit area of winter wheat and summer maize in four cities in 2020 was controlled within the range of 14.02 to 696.66 kg/hectare. It shows that the model can more accurately predict the yield per unit area of crops. The planning model for the benefit of irrigation water allocation generated three scenarios of rainfall level and four planting intentions, and compared the planned scenarios with the actual production benefits of the two crops in 2020. In a dry year, the possibility of planting areas for winter wheat and summer corn is optimized. Compared with the traditional deterministic planning method, the model takes into account the uncertain parameters, which helps decision makers seek better solutions under uncertain conditions. Full article

This work focuses on the study of robust no-wait flow shop scheduling problem (R-NWFSP) under the interval-valued fuzzy processing time, which aims to minimize the makespan within an upper bound on total completion time. As the uncertainty of actual job processing times may cause significant differences in processing costs, a R-NWFSP model whose objective function involves interval-valued fuzzy sets (IVFSs) is proposed, and an improved SAA is designed for its efficient solution. Firstly, based on the credibility measure, chance constrained programming (CCP) is utilized to make the deterministic transformation of constraints. The uncertain NWFSP is transformed into an equivalent deterministic linear programming model. Then, in order to tackle the deterministic model efficiently, a simulated annealing algorithm (SAA) is specially designed. A powerful neighborhood search method and new acceptance criterion are applied to find better solutions. Numerical computations demonstrate the high efficiency of the SAA. In addition, a sensitivity analysis convincingly shows that the applicability of the proposed model and its solution strategy under interval-valued fuzzy sets. Full article

In order to take into account cost and timeliness and enhance accuracy testing, this study developed the fuzzy number and membership function, using the confidence interval of ratio operating performance index. Subsequently, according to the statistical test rules and the application of the fuzzy number and membership function, a fuzzy evaluation decision model for the operating performance index is proposed, to evaluate if the business performance reaches the needed level. Based on the abovementioned, the evaluation model in this study took into account not only timeliness but also accuracy, so that it could grasp the opportunity of improvement for operating organizations with poor operating performance after being evaluated. This fuzzy evaluation decision model for the operating performance index constructs a fuzzy membership function retrieved from an index’s confidence interval, reducing the chance of miscalculation due to sampling mistakes and improving the efficiency of evaluation. Finally, in order to facilitate the application of readers and the industry, this paper uses cases to explain the proposed fuzzy verification method. On the whole, the model proposed in this paper is a data-based auxiliary tool for the service operating performance improvement strategy. Full article

The western region of Jilin Province is an ecologically fragile area with scarce water resources. The effective allocation of the limited water resources in order to obtain a higher ecological service value is an urgent requirement. In this paper, an interval fuzzy, double-sided chance-constrained, stochastic programming (IFDCP) model was used based on the interconnected river system network project in the western Jilin Province. With the objective of maximizing the value of regional ecological services, the water diversion and supplement schemes were optimized and adjusted. The model results showed that the restored water surface area of all lakes and ponds in the western region of Jilin Province was higher than the initially planned scheme in the high flow year. The water surface area fulfilled the minimum constraints, but did not fulfill the initial scheme in the normal flow year. In the low flow year, the lower limit of some of the regions had to be decreased in order to meet the allocation of the limited water resources. The proportion of floodwater resource utilization gradually increased with an increase in the flood amount. The ecological service value produced in the normal and high flow years was found to be higher than the initial scheme. The marsh wetland can produce higher ecological service value. Therefore, the core of the model optimization was introducing more water to the marsh wetland after fulfilling the basic consumption of ponds and the reed wetland. In addition, the IFDCP model was more flexible in water diversion and supplement as compared to other models that had been developed previously. Full article

This paper developed a type-2 fuzzy interval chance constrained programming model for optimizing a crop area, which integrated chance constrained programming and type-2 fuzzy interval programming. The developed model was then applied to a case study in Wuwei City, Gansu Province, China, and the maximization of economic benefit was selected as the planning objective. Furthermore, different water-saving irrigation modes were considered as the development mode. A series of optimal irrigation water and planting structure schemes were obtained under different violation probabilities in each water-saving scenario. The obtained results could be helpful to make decisions on the planting structure and the optimal use of irrigation water and land resources under multiple uncertainties. Full article

The electronics industry in Taiwan has achieved a complete information and communication technology chain with a firm position in the global electronics industry. The integrated-circuit (IC) packaging industry chain adopts a professional division of labor model, and each process (including wafer dicing, die bonding, wire bonding, molding, and other subsequent processes) must have enhanced process capabilities to ensure the quality of the final product. Increasing quality can also lower the chances of waste and rework, lengthen product lifespan, and reduce maintenance, which means fewer resources invested, less pollution and damage to the environment, and smaller social losses. This contributes to the creation of a green process. This paper developed a complete quality evaluation model for the IC packaging molding process from the perspective of a green economy. The Six Sigma quality index (SSQI), which can fully reflect process yield and quality levels, is selected as a primary evaluation tool in this study. Since this index contains unknown parameters, a confidence interval based fuzzy evaluation model is proposed to increase estimation accuracy and overcome the issue of uncertainties in measurement data. Finally, a numerical example is given to illustrate the applicability and effectiveness of the proposed method. Full article