Objective Weights Research Articles

Developing predictive framework for human thermal state based on multilevel fuzzy integrated assessment method: Local thermal radiation environments

Local thermal radiation in heat treating, glass melting workshops substantially affect the human thermal comfort and thermal responses, causing even the thermal health risks. The accessibility of an effective assessment of human thermal state is crucial for the thermal safety protection. A scoring for thermal state was developed based on the multilevel fuzzy integrated assessment method at three aspects: thermal environment (Air temperature and mean radiant temperature), physiological responses (Heart rate, sweat rate, auditory canal temperature, mean arterial pressure, and skin temperature), and psychological perceptions (Rating of perceived exertion and thermal perception). Scoring of thermal state (STS) was determined to be dependent on the objective weights of each index and the set of nonlinear weights. Twelve experimental cases, including air temperatures of 33 and 36 °C, mean radiant temperatures of 33.6 to 38.3 °C, and metabolic levels of 1.1, 2.9 and 4.3 met, simulated the situations of different work intensities with exposure to local thermal radiation, which were used for the validation of the STS. Results showed that the remarkable contributions of air temperature, radiant temperature, auditory canal temperature, heart rate, sweat rate, and perceived fatigue were the highest in the STS. The STS, validated with the PHS model and the PSI index, allows a well-assessed human thermal state because of its encompassing multifaceted characteristics. This study contributes to the evaluation of hot discomfort in local thermal radiation environments, revisiting the thermal comfort research method.

Geochemical fingerprints, evolution, and driving forces of groundwater in an alpine basin on Tibetan Plateau: Insights from unsupervised machine learning and objective weight allocation approaches

Study RegionTongde Basin, a typical alpine basin on the northeastern Tibetan Plateau Study focusResearch on the hydrochemical pattern and availability of groundwater is very limited in alpine regions, which greatly hinders the rational ulitilization and scientific management of groundwater resources. Multiple approaches integrating self-organizing map, K-means, entropy weight were employed to elucidate the distinct hydrochemical evolution patterns and controlling mechanisms of groundwater in alpine basins with dense human activities. New hydrological insights for the regionMultiple hydrochemical evolution patterns were discovered for groundwater in present alpine basin on northeastern Tibetan Plateau. Groundwater presents a gradual hydrochemical evolution from the piedmont to the riverside under the natural regulation with the increasing of TDS and major ions along the flow path. While, groundwater at some sporadic sites is featured with relatively high total alkalinity due to carbonate mineral dissolution. The riverine groundwaters are regulated by the strong hydrodynamic condition of river and demonstrate fresher hydrochemical characteristics. Groundwaters in the irrigation areas are featured by elevated nitrate levels with a maximum of 42.86mg/L, attributed to agricultural pollution inputs. A conceptual model was established to illustrate the distinct hydrochemical fingerprints, evolution patterns and controlling mechanisims of groundwater in alpine basins that with dense human activities. This research can enhance the understanding of groundwater chemical status, genesis and availability, and is beneficial for the conservation and sustainable management of groundwater resources in ecologically fragile alpine regions worldwide.

Weight discrimination ability during an action observation task is dependent on the type of muscle contraction

AbstractConcentric and eccentric contractions show different patterns of neural activity at both peripheral and cortical levels, which are thought to influence the perception of action properties such as the weight of objects moved by others. The aim of this study was to investigate how the type of muscle contraction influences weight estimation during action observation.Forty‐eight volunteers completed the Main experiment and the Control experiment. In the Main experiment, they performed a weight discrimination video task in which they watched videos of an actor moving two objects, a comparison, and a reference box, executing concentric or eccentric contractions and they had to indicate which box was the heaviest. Sensitivity analysis and psychometric functions were used to analyse the data. In the Control experiment, observers judged the actor's effort in moving the boxes.The results of the Main experiment showed that the weight discrimination sensitivity was higher in the eccentric condition for the light boxes. Conversely, for the heaviest boxes, discrimination sensitivity was higher in the concentric condition. These results were confirmed by the psychometric function analysis. The control experiment showed that the perceived difference in effort between the comparison and reference stimuli was greater in the eccentric than in the concentric condition for light stimuli.These results showed that the ability to evaluate the weight of the object involved in the observed action was influenced by the type of contraction and the amount of weight. The effort attributed to the actor influenced the observer's perception.

The effect of pleasurable emotions on weight perception.

Based on the broaden-and-build theory of positive emotions and embodied cognition theory, this study explored the effects of two different forms of pleasure on the perception of object weight through two experiments. Experiment 1 induced pleasure by having participants watch a funny video and further investigated the effect of pleasure on weight perception. The results showed that the weight estimation of the pleasure group participants was significantly lower than that of the calm group. Experiment 2 induced pleasure through embodied pleasure postures and further investigated the effect of pleasure on weight perception. The results showed that subjects in the embodied pleasure posture group had lighter weight estimates compared to the calm posture and no posture groups. This study suggests that pleasure affects individuals' perception of the weight of objects, and pleasure makes individuals more optimistic in their perception of object weight.

Assessment of Water Disaster Resilience in Mountainous Urban Metro Stations by Combination Weighting Method and Extension Cloud Model

Studying the resilience of metro stations in mountainous cities to heavy rain and flooding is of significant importance for enhancing the stability and safety of metro station operations. Considering the topographical and climatic characteristics of mountainous urban areas, this study analyzes the mechanisms through which heavy rain and flooding affect metro station resilience. Based on this analysis, 27 factors, influencing metro station resilience, are identified across 4 dimensions: absorptive capacity, resistance capacity, recovery capacity, and adaptive capacity. A water disaster resilience evaluation index system and corresponding rating standards are established for metro stations in mountainous cities. By combining the advantages of objective and subjective weighting, the combination weights of evaluation indicators are calculated using game theory. The extension theory is combined with the cloud model to establish a model for assessing the water disaster resilience of metro stations in mountainous urban areas. The applicability and feasibility of the model are validated through its implementation at Shapingba Station within Chongqing Rail Transit. The evaluation results obtained from the established model indicate a resilience level of IV for Shapingba metro station, reflecting a high level of resilience that aligns with real-world conditions. These findings further validate the proposed evaluation standards and the method for assessing the water disaster resilience of metro stations based on the combination weighting method and extension cloud model. This evaluation method considers the uncertainty in the evaluation process, demonstrating good feasibility and reliability. It offers a new perspective and methodology for assessing and analyzing the resilience of similar metro stations in mountainous cities.

Comprehensive Method for Supplier Selection in the Indonesian Leather Industry Considering Sustainable Development Goals Criteria

Objective: This pivotal research aims to rank raw material suppliers at an Indonesian leather company using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). It is based on Sustainable Development Goals (SDGs) criteria selected by many decision-makers through the Delphi method, with a compromise criteria weight between Methods based on Removal Effects of Criteria (MEREC) and Stepwise Weight Assessment Ratio Analysis (SWARA) II. Theoretical Framework: The global and national commitments of Sustainable Development Goals (SDGs) to improving society's welfare, including the sustainable use of resources, are not just theoretical concepts. They are practically applied in this research to guide supplier selection in the leather industry. These criteria are then weighted using objective weighting (MEREC) and subjective weighting (SWARA) II, and the results are compromised to form the basis for evaluating suppliers using TOPSIS. Method: The proposed method in this research consists of three stages. The first stage is selecting the SDGs criteria using the Delphi method, a structured communication technique involving experts. The second stage is weighting the criteria using MEREC for objective weighting and SWARA II for subjective weighting. The third stage is supplier evaluation using TOPSIS based on the weight of the compromised criteria. Results and Discussion: The ranking of leather raw material suppliers for Indonesian leather companies is Kediri, Rembang, Jombang, Cirebon, Wonogiri, Lumajang, Cianjur, and Sidoarjo. This ranking is based on the SDGs criteria. Responsible leather sourcing, eco-friendly tanning processes, water use audits, and waste management are the SDGs' criteria for selecting suppliers in the Indonesian leather industry. Responsible leather sourcing is the only sustainability criterion more important than the price criterion. This criterion directly affects the quality of the animal skin, which is why it is rejected. Research Implications: The manager should prioritize the SDGs criteria, such as the product's significance to the organization's survival over cost and other factors, which have become secondary due to high demand. Apart from rejecting and delivery factors, management also considers responsible leather sourcing. This means that good animal care impacts the reject factor, and management prioritizes this factor. The rejection criterion must be prioritized for the production process to operate efficiently. Originality/Value: It is imperative to establish a technique for managers in the Indonesian leather sector to choose sustainability suppliers incorporating Delphi, MEREC, SWARA II, and TOPSIS.

Comprehensive evaluation of water quality grades based on improved CRITIC and multidimensional connection cloud combination

AbstractThis study proposes a comprehensive water quality assessment method for nine major plateau lakes in Yunnan Province, based on an improved CRITIC method combined with a multidimensional connectivity cloud model. Key water quality monitoring indicators (NH3‐N, COD, TP, TN, permanganate index, DO, pH) were selected, and the weights were determined using the improved CRITIC method, highlighting the impact of NH3‐N, COD, and TP. These weights were then integrated with a multidimensional connectivity cloud model to classify lake water quality levels. The results indicated the following water quality grades for the lakes: Dianchi (III), Fuxian Lake (I), Erhai (II), Xingyun Lake (I), Qilu Lake (II), Yilong Lake (II), Lugu Lake (I), Yangzonghai (II), and Chenghai (II). Compared to five conventional methods, the proposed approach better addresses the issues of fuzziness, randomness, and discreteness in water quality indicators, avoiding the boundary selection problems inherent in traditional methods. By combining the improved CRITIC method with a multidimensional connectivity cloud model, the study achieves more precise and reliable evaluations through objective weighting and comprehensive consideration of multiple indicators. This method offers a more accurate reflection of lake water quality conditions and provides a scientific basis for water quality management and decision‐making, demonstrating significant potential for application in the field of environmental science.

Fermatean fuzzy distance and Sugeno–Weber operators-based SPC-MARCOS approach for sustainable supplier evaluation in the healthcare supply chain

The present work proposes a new decision support tool for assessing the sustainable suppliers in the healthcare supply chain. For this purpose, the classical Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) model is integrated with the Sugeno–Weber weighted averaging operators, modified symmetry point of criterion (SPC) model, rank sum (RS) tool and Fermatean fuzzy sets (FFSs), and named as the ‘FF-SPC-RS-MARCOS’ framework. The developed model firstly determines the decision experts’ weights through RS model. Second, novel Sugeno–Weber weighted operators are introduced to combine the experts’ opinions. Third, a unified weighting procedure is presented based on the combination of modified SPC approach for objective weight and RS method for subjective weight of attributes. To this aim, a novel distance measure is introduced for FFSs and further applied to compute the distance between aggregated Fermatean fuzzy numbers and symmetry point value of an attribute in the modified SPC approach. Further, a hybrid FF-SPC-RS-MARCOS approach is proposed to tackle the decision-making problems on FFSs setting. To elucidate the efficacy of the developed method, it is applied to a case study of sustainable supplier selection problem in the healthcare supply chain. The paper further conducts sensitivity investigation and comparison with existent approaches to test the stability and robustness of the ranking outcomes. This study shows how the proposed MARCOS method in combination with SPC and RS models can be used to prioritize the alternative suppliers in the healthcare supply chain. The introduced work provides a new methodology, which can help the practitioners and academics to evaluate suppliers with uncertain information and can also be employed to other areas facing similar types of decision-making problems.

Tea nanoparticles modified halloysite clay coated polyurethane sponge as multifunctional sensors

Tea, as one of the three major beverages in the world, has antioxidant, anti-cancer, inhibitory inflammation, immune regulation, diabetes prevention, antibacterial and other effects. In this study, black tea and FeCl3·6H2O were chelated to functionally modify the outer surface of halloysite clay nanotube (Hal). A new nanomaterial with excellent photothermal properties, tea nanoparticles@Hal, was successfully synthesized. Tea nanoparticles@Hal powder can raise to 225.8 °C in 25 s, and the corresponding solution can raise to 50.5 °C in 8 min with a photothermal efficiency of 77.3 %. The tea nanoparticles@Hal was assembled on the polyurethane (PU) sponges by simply soaking to prepare conductive sensor. The flexible sensor shows a fast response time (132.8 ms) and a long service time (400 cycles), which have wide range of applications. The resistance changes with the pressure is in a regular functional relationship, and the sensor can measure the weight of objects with high accuracy. In addition, the sensor can stably monitor various physiological activities of the human body. When finger is bent, the sensor can produce the difference output signals. The prepared tea nanoparticles@Hal/PU sensor has broad prospects in fields such as human-computer interaction and medical detection.

A new probabilistic linguistic decision-making process based on PL-BWM and improved three-way TODIM methods

Probabilistic linguistic term sets (PLTSs) provide a flexible tool to express linguistic preferences, which allow decision-makers to label linguistic information with different probabilities. In this paper, a method based on a PLTS is proposed to address multi-criteria decision-making problems (MCDM). We develop the theory of PLTSs and put forward a novel best–worst method (BWM), termed PL-BWM, based on PLTS. Our method fully reflects the preference information of decision-makers and accurately provides the importance level of the criteria. The combined weight of the criteria is obtained by merging PL-BWM-based subjective weights and similarity minimization-based objective weights. Upon introducing a three-way decision system to improve the TODIM method, a novel three-way TODIM method is proposed and showcased on an optimal new energy vehicle selection problem. The effectiveness and accuracy of the proposed method are verified by sensitivity analysis and comparative analysis. Our approach paves the way for new developments in solving MCDM problems and for novel applications in otherwise difficult ranking problems.

Do kea parrots infer the weight of objects from their movement in a breeze?

Weight, though it cannot be seen directly, pervades nearly every aspect of an animal's life. However, the extent to which non-human animals reason about the property of weight remains poorly understood. Recent evidence highlights birds as a promising group for testing this ability: for example, New Caledonian crows can infer the weight of objects after observing their movements in a breeze. Here, we tested for similar weight inference abilities in kea (Nestor notabilis), a parrot species known for its sophisticated problem-solving skills. Subjects were trained to exchange objects of a target weight (light or heavy) for a food reward. They were then allowed to observe pairs of novel objects (one light and one heavy) hung in front of an electric fan in both an experimental condition (fan on, light object moving) and a control condition (fan off, both objects motionless). The birds were subsequently presented with test trials in which they could use the information from the demonstration to select an object of their target weight. We found that, unlike New Caledonian crows, kea did not perform significantly better on trials in which they observed the objects' movements and discussed our findings within the context of the kea's highly explorative nature.

Analysis and Optimization of Laser Beam Welding Parameters for Aluminium Composite (Al-Zn-Cu Alloy) by Grey Relational Optimization

Aluminium and its composites are widely used in production to enhance the strength of lightweight objects. In this study, an AA7075/SiC composite was fabricated using a stir casting route. Multi-objective optimization and finite element analysis were performed with various process parameters on a manufactured aluminium composite (AA7075 + SiC) undergoing a laser beam welding process. Four welding parameters, i.e., pulse frequency, power, welding speed (transverse), and wire size were taken for laser welding as per the L-9 orthogonal array for experimental study. Tensile strength, deflection, temperature distribution, Rockwell hardness (fusion zone), and Rockwell hardness (heat affected zone) were taken as output parameters after welding. The standard deviation objective weighting–grey relational optimization method optimized the process parameter. ANSYS APDL 23 software was utilized to simulate the entire laser welding method with a cylindrical heat source to predict the temperature distribution in the butt-welded plates. This software uses finite element analysis and gives a deviation of only 5.85% for temperature distribution with experimental results. This study helps to understand the effect of various parameters on the welding strength of the aluminium composite.

Spatio-Temporal Variation in Pluvial Flash Flood Risk in the Lhasa River Basin, 1991–2020

The analysis of temporal and spatial variability in risk has garnered significant research attention, particularly regarding flash flood disasters in the context of warming and wetting conditions on the Qinghai–Tibetan Plateau. Focusing on the Lhasa River basin, this study develops a framework that integrates geographic information systems and a combined subjective–objective weighting approach to comprehensively assess flash flood risk despite limited observations. This paper investigates the distribution patterns of hazard, vulnerability, and the integrated risk of pluvial flash floods; demonstrates the reliability of the assessment results; and provides mitigation recommendations for disaster risk management at the county level. The results showed a trend in increasing flash flood risk in recent decades compared to the 1990s. Moreover, very-high- and high-risk areas were concentrated in downstream regions with frequent precipitation extremes and anthropogenic activity. From 1991 to 2020, the high to very high-risk areas gradually expanded from central Lhasa to neighbouring counties. This study contributes valuable insights into flash flood risk assessment cand mapping, which are crucial in terms of the protection of life and property in the plateau basin.

A Hybrid Multi-Attribute Decision-Making Method Considering Tourists' Behavioral Preferences for Customized Tours

A decision-making analysis method considering tourists' behavioral preferences is proposed to address the problem of hybrid multi-attribute decision making (HMDM) for customized tours in which attribute values are intuitionistic fuzzy numbers, interval numbers and real numbers. This method is presented through step-by-step instructions:1) construct an evaluation index system of the HMDM for customized tours; 2) convert the attribute values of different data types into normalized intuitionistic fuzzy numbers, and obtain their objective weights by calculating their intuitionistic fuzzy entropies; 3) use the intuitionistic fuzzy weighted average operator to aggregate all the converted attribute values of each customized scheme;4) calculate scores of aggregation values for customized schemes and rank these schemes accordingly under the scenarios where tourists express such behavioral preferences as caution, mildness and recklessness; and 5) apply the proposed method to an example case to prove its feasibility.

Research on the evaluation method for safety cognitive ability of workers in high-risk construction positions

PurposeSafety cognitive ability is a key factor influencing unsafe behavior. However, the existing achievements have not yet involved the division of the hierarchical relationship of factors influencing safety cognition and lack a quantitative evaluation system of safety cognitive ability. The purpose of this paper is to find out the deficiencies in the safety cognition of workers in high-risk construction positions and to provide practical suggestions for improving their safety cognitive ability and reducing unsafe behavior.Design/methodology/approachBased on the iceberg model, the factors influencing the safety cognitive ability of workers in high-risk construction positions and their hierarchical relationship were determined, and an evaluation index system consisting of four primary indicators and 20 secondary indicators was constructed. The game theory algorithm was used to optimize the subjective and objective weights of the indicators calculated by the sequential analysis method (G1) and the entropy weighting method (EWM) to obtain the optimal combination weight value. The Matlab software was used for cloud mapping and similarity calculation to determine the safety cognitive ability level of the object to be evaluated.FindingsThe research results indicate that the comprehensive level of safety cognitive ability of scaffolders in this construction project is at “Level III”, the fundamental factors and compliance factors are at “Level IV”, the auxiliary factors and driving factors are at “Level III”. This conclusion aligns with the situation learned from the previous field investigation, which validates the feasibility and scientificity of the proposed evaluation method.Research limitations/implicationsConsidering that the safety cognitive ability of construction workers is constantly changing, this study has not yet delved into the specific impacts of various influencing factors on the level of safety cognitive ability. Future research can utilize simulation software, such as MATLAB and Vensim, to construct dynamic simulation models that accurately simulate the changing rules of construction workers’ safety cognitive ability under the influence of different factors.Practical implicationsThis research broadens the application scope of the iceberg model, enriches the analysis model of the factors influencing the safety cognitive ability of workers in high-risk construction positions and provides a novel perspective for similar research. The safety cognitive ability evaluation method proposed in this paper can not only accurately evaluate the safety cognitive ability level of workers in high-risk positions such as scaffolders but also provide practical suggestions for improving the safety cognitive ability of workers, which is of great significance to improve the safety management level and reduce unsafe behavior in the construction field.Originality/valueThis research fills the research gap of workers in high-risk construction positions and the quantification of safety cognitive ability. The iceberg model is used to realize the hierarchical division of the factors influencing safety cognitive ability. Additionally, an evaluation method for the safety cognitive ability of workers in high-risk construction positions based on the game theory combination weighting method and cloud model is proposed, which realizes the quantitative evaluation of safety cognitive ability.

A novel multi-criteria decision making method to evaluate green innovation ecosystem resilience

Green innovation ecosystem resilience evaluation is crucial for ensuring sustainable development in dynamic environments. By comprehensively assessing resilience, it helps identify risks and facilitate effective responses, thus promoting sustainable development. To effectively evaluate the resilience of green innovation ecosystems, this paper proposes a model based on the interval-valued intuitionistic fuzzy multi-criteria decision-making (MCDM) method, designed to support decision-makers (DMs) in resilience evaluation. In this model, we improve the Criteria Importance Through Intercriteria Correlation (CRITIC) method by introducing Spearman's correlation coefficient to more accurately determine the objective weights of various indicators based on their interrelationships. Furthermore, we propose an Interval-Valued Intuitionistic Fuzzy Hybrid Average Aggregation (IVIFHAA) operator, which considers both the subjective and objective weight order for aggregating expert evaluation results. Additionally, a scoring function is introduced to generate ranked evaluation results. We also establish a resilience evaluation criteria system covering interconnectivity, sustainability, and diversity within green innovation ecosystems to assist DMs in resilience evaluation. Finally, to validate this method, we apply it to assess the resilience of regional green innovation ecosystems and compare it with other methods. The results demonstrate that the improved operator effectively reduces information loss and improves evaluation efficiency, while the improved CRITIC method handles outliers during the evaluation process.

A Decision-Making Model with Cloud Model, Z-Numbers, and Interval-Valued Linguistic Neutrosophic Sets

Interval-valued linguistic neutrosophic sets (IVLNSs), Z-numbers, and the trapezium cloud model are powerful tools for expressing uncertainty and randomness. This paper aims to combine these methodologies. First, we review relevant concepts and operators, introducing a novel combination of IVLNSs and Z-numbers, which establishes a new form of expression. Subsequently, we propose the Z-interval-valued linguistic neutrosophic set-trapezium–trapezium cloud (Z-IVLNS-TTC) model, designed to minimize information loss and distortion during quantification. A novel method for calculating the objective weight vector is then developed using multi-objective programming (MOP). Drawing inspiration from the TOPSIS method, we propose a new approach for calculating the distance between Z-IVLNS-TTCs based on the p-norm. Finally, a group decision-making problem is presented to demonstrate the practical application of the proposed method. To validate the effectiveness and feasibility of the method, sensitivity analysis and comparisons with existing approaches are conducted.

Risk assessment of transmission towers based on variable weight theory and matter-element extension model

Abstract The risk assessment of transmission towers is a critical approach to ensuring the safe and stable operation of power grids. In response to the increasingly frequent and severe impacts of seasonal permafrost on transmission towers in permafrost regions, this paper proposes a novel risk assessment method based on Variable Weight Theory and the Matter-Element Extension Model. By incorporating key influencing factors—such as the number of freeze-thaw cycles, soil moisture content, temperature fluctuations, soil dry density, melting settlement coefficient, and porosity ratio—an indicator system tailored to risk assessment in seasonal permafrost regions is established. Utilizing the Matter-Element Extension Model, this approach applies Variable Weight Theory to integrate both the best-worst method and the entropy weight method for calculating subjective and objective indicator weights. The risk level of the towers is then determined by their proximity to risk thresholds. Finally, a case study involving transmission towers in a specific region of a province in China is presented, where the assessment results are compared with the actual conditions to validate the rationality and effectiveness of the proposed method.

Construction Quality Evaluation of Concrete Structures in Hydraulic Tunnels Based on CWM-UM Modeling

The construction time of concrete structures in hydraulic tunnels is long, the construction environment is complex, and there are many influencing factors. The requirements for construction quality are high not only to meet the strength requirements but also to meet the design requirements of erosion resistance, crack resistance, and seepage resistance according to its specific operating environment. Therefore, evaluating the construction quality of concrete structures in hydraulic tunnels is of great significance. Considering the randomness and fuzziness of factors affecting the construction quality of concrete structures in hydraulic tunnels, this paper proposes a comprehensive evaluation model based on combined weighting (CWM) and uncertainty measurement theory (UM). The improved analytic hierarchy process (IAHP) and the CRITIC method are used to determine the subjective and objective weights of evaluation indicators. Combined weighting is based on the principle of minimum entropy, and the UM method is used to evaluate the construction quality level. Finally, taking a hydraulic tunnel as an example, its construction quality grade is calculated to be III, according to the evaluation model proposed in this paper, which matches the engineering reality, and a comparative study is made with the mixture element topology theory at the same time. It is verified that the evaluation model can scientifically and reasonably evaluate the construction quality level of concrete structures in hydraulic tunnels.

Tri-objective and multi-parameter geometric optimization of two-stage radioisotope thermoelectric generator based on NSGA-II

Radioisotope thermoelectric generator (RTG) is one of ideal power sources for deep space exploration due to the long service life and high stability. To further extend service life and improve electrical output, this study is first to simultaneously optimize electrical output and mechanical stability induced by thermal stress of the two-stage RTG using non-dominated sorting genetic algorithm-II. Skutterudite and bismuth telluride are used as the thermoelectric materials in hot-stage and cold-stage thermoelectric generators, respectively. The maximum von Mises stress of the skutterudite-stage (VonSKD) and bismuth telluride-stage (VonBT) thermoelectric generator and the conversion efficiency of the two-stage RTG (ηtwo) are set to the three objectives, and twelve geometrical parameters of two-stage RTG are used as variables. Electrical output and mechanical stability are simulated with COMSOL 6.0 Multiphysics software based on the finite element method. Results show that the ranges of ηtwo, VonSKD, and VonBT in the Pareto front are 4.81–7.57 %, 112.2–228.46 and 19.24–87.33 MPa, respectively, when the temperature difference is 300 K. TOPSIS decision-making method is used to select the specific optimal solution on the Pareto front according to the weight of the different objectives. Comparisons between tri- and bi-objective as well as single-stage optimization are also carried. Results show that there are strong influences among these three objectives. The performance of one objective would improve at the expense of the performance of the remaining objectives decrease if a larger weight was given. The VonSKD has the greatest importance among the three objectives, followed by ηtwo, and the smallest is VonBT. Skutterudite-stage thermoelectric generator should be particularly considered in the design of two-stage RTGs. The two-stage RTGs with different weight factors exhibit different electrical performances due to different geometrical parameters. This research can provide references for two-stage thermoelectric generators in more scenarios to improve electrical performances and extend service life.