Ergonomic assessment of collaborative robot application based on IVIULWG operator

Abstract

Background

The rapid advancement of robotic technology is transforming the manufacturing industry, with collaborative robots (Cobots) increasingly deployed to improve productivity and reduce ergonomic risks. However, ensuring ergonomic compatibility between Cobots and human operators remains a critical challenge.

Objective

This study aims to evaluate the ergonomic impact of Cobot integration in industrial settings by developing a comprehensive assessment framework covering physical, cognitive, and organizational ergonomics.

Methods

An ergonomic evaluation framework was proposed and implemented using the interval-valued intuitionistic uncertain fuzzy (IVIUF) method to accommodate both quantitative data and qualitative judgments. The interval-valued intuitionistic uncertain linguistic weighted geometric (IVIULWG) aggregation operator was used to combine objective and subjective information with improved robustness and accuracy.

Results

The analysis revealed that dual-arm Cobots equipped with display interfaces exhibit superior ergonomic performance compared to other configurations. The IVIULWG approach effectively preserved and integrated both numerical measurements and linguistic assessments in the evaluation process.

Conclusions

The proposed methodology provides a scientifically rigorous and practical tool for the ergonomic evaluation of Cobots. These findings support more informed decisions in Cobot design and deployment, contributing to safer and more sustainable industrial operations.

Keywords

Cobots ergonomics evaluation IVIULWG multi-criteria evaluation human-robot interaction physical and cognitive ergonomics

Introduction

With the advent of the Industry 4.0 era, factory automation has become a crucial driver of growth in the manufacturing sector. Robots have long been a vital component of this automation process, with traditional industrial robots dominating the sector due to their efficiency and precision. However, as the demand for intelligent and flexible manufacturing grows, the limitations of conventional robots have become increasingly apparent. In recent years, a new trend has emerged in the industrial world—Cobots, or “Cobots,” are quickly becoming the favored choice for factory automation. Unlike traditional industrial robots, Cobots prioritize interaction and collaboration with human workers. They represent a fresh wave in industrial automation, signaling a new direction for the evolution of automation technologies.¹ According to an analysis by Grand View Research,² the compound annual growth rate for Cobot technology is expected to reach 32% from 2023 to 2030, with the global market size expanding from $1.58 billion in 2023 to $11.04 billion by 2030. As digitalization, artificial intelligence, and the manufacturing sector continue to advance rapidly, the Cobot industry has emerged as a major global growth area, with related research increasing year by year.

Academia has increasingly engaged in deeper discussions on the application and future opportunities of Cobots from technical, economic, and social perspectives. Technologically, a defining characteristic of collaborative robots lies in their capacity to operate in close coordination with human workers. Unlike traditional industrial robots, they do not require safety barriers or isolation measures, allowing them to share workspaces directly with humans.³ In many modern factories, Cobots are no longer mere mechanical substitutes but have evolved into “colleagues” for human workers.⁴ They assist in tasks requiring high levels of flexibility and creativity, making production processes more efficient and personalized. From a social perspective, Cobots are adept at performing monotonous, hazardous, or strenuous duties, thereby allowing human laborers to concentrate on functions that necessitate creativity, critical thinking, and social acumen.⁵ As populations age and many countries face labor shortages,⁶ Cobots can alleviate the physical strain on older workers, extending their working years and helping them maintain productivity.⁷ Moreover, Cobots provide new opportunities for individuals with physical disabilities to participate in the workforce, assisting with tasks such as heavy lifting or precise operations that would otherwise be challenging.⁸ Economically, Cobots excel at performing repetitive tasks quickly and accurately, reducing human error and waste, and thereby lowering production costs and increasing output.⁹ This boost in efficiency helps companies remain competitive in fiercely contested markets. Although the upfront investment in collaborative robots can be relatively high, in the long run, they reduce labor costs as they can work continuously without breaks or vacations, minimizing reliance on human resources.¹⁰ In regions suffering from severe labor shortages, Cobots offer a solution by enhancing productivity and ensuring that companies can meet production targets and market demands.¹¹ In conclusion, evaluating the effectiveness of Cobot applications from a managerial decision-making perspective, alongside research into relevant evaluation algorithms, represents foundational work in shaping technological innovation, market development, and application in this field. Such studies provide a crucial basis for informed management decisions.

Research on the impact evaluation of Cobot applications has yielded a wide range of findings, with scholars approaching the subject from diverse disciplines, research objectives, and perspectives. As a result, much of the research remains fragmented, and conclusions vary significantly. Notably, there is a gap in studies evaluating the application of Cobots from an ergonomic perspective. Regarding the impact of Cobots on production efficiency, most scholars agree that their use enhances productivity. For instance, George highlighted that Cobots can execute tasks faster and more accurately than human workers, thereby boosting productivity.¹² Cobots can operate ceaselessly without succumbing to fatigue, thereby reducing periods of inactivity and enhancing the general efficacy of production processes.¹¹ They can function during intermissions, transitions between shifts, and even throughout the night, guaranteeing the seamless operation of the manufacturing process. However, some studies present contrasting findings. For example, previous research indicated that when participants collaborate with Cobots instead of humans, their performance (in terms of products manufactured) is lower, and the time spent on collaborative activities is reduced.¹³ It is widely recognized in the academic community that, unlike conventional industrial robots, collaborative robots are designed with integrated safety features that allow for proximate operation alongside human workers without the need for physical barriers or complex protective systems. This enhanced level of safety promotes a reduced likelihood of accidents and injuries, fostering a safer workplace environment and potentially diminishing expenses linked to workplace incidents.^14,15 However, some scholars argue that the safety of Cobots is closely linked to their operating speed. For safety reasons, Cobots are often programmed to operate at speeds far below their full capability.¹⁶ When their movement speed is higher, they may pose a safety hazard to human collaborators.¹⁷ From an organizational perspective, Cobots offer greater convenience and flexibility than traditional industrial robots. They are typically smaller in size, take up less space, and can be flexibly deployed in limited workspaces, a feature that is especially advantageous for small and medium-sized enterprises (SMEs).¹⁸ However, despite their flexibility, Cobots generally lag behind traditional industrial robots in terms of load capacity and work speed.¹⁹ For high-load, high-intensity tasks, Cobots may not fully replace conventional heavy-duty industrial robots. While Cobots are engineered to possess user-friendly attributes, such as intuitive programming interfaces and seamless integration with current systems, which diminishes the necessity for specialized training or expertise, the preliminary expenses associated with procurement, setup, and training persist as substantial factors.^20,21 Researchers have different focuses when evaluating the ergonomic impact of Cobots, and consensus is lacking. This reflects the current state of research, where a comprehensive evaluation system for assessing the impact of Cobots has yet to be established. This study is grounded in the construction of a scientifically rigorous evaluation framework that synthesizes interdisciplinary insights to enable a comprehensive assessment of the ergonomic implications of collaborative robot applications.

Research on algorithms for evaluating the effectiveness of Cobot applications remains relatively sparse. Zhang et al. developed a dynamic human-robot integration algorithm based on a digital human dynamics model, aiming to proactively enhance safety in human–cobot interaction scenarios.²² Liau and Ryu employed genetic algorithms to optimize human-robot task distribution, aiming to shorten assembly duration while mitigating ergonomic risks.²³ Kinast et al. developed a genetic algorithm framework based on biased random-key encoding, aiming to optimize a weighted objective function that balances both production cost and makespan, thereby achieving concurrent minimization of these key performance metrics.²⁴ A significant challenge in current research is the lack of real-world application data for Cobots. Most efficiency data regarding Cobots comes from laboratory settings rather than industry, limiting the ability to analyze actual performance.²⁵ Even within the limited data available, while some metrics are quantifiable “crisp numbers” (e.g., changes in production efficiency), much of the data remains “fuzzy” and imprecise, such as employee satisfaction. There is an urgent need to develop algorithms and techniques that can retain both types of information-quantifiable and qualitative to the fullest extent possible. Additionally, most assessments of Cobots’ effectiveness are based on simulated experiments, and given the rapidly evolving nature of industrial technology and product development platforms, algorithms must consider the flexibility and scalability of their applications.

This study systematically evaluates the ergonomic impact of collaborative robot (Cobot) applications. Section 2 presents a comprehensive set of criteria for assessing the ergonomic implications of Cobots and constructs an evaluation index system, providing a foundational framework to support managerial decision-making and promote industrial development. Section 3 centers on formulating a rigorous algorithmic methodology designed to effectively manage the heterogeneity of data types encountered in ergonomic evaluation processes. Specifically, the IVIUL approach was adopted to effectively address the integration of precise quantitative data with imprecise linguistic evaluations. The integration of geometric weights led to the formulation of the IVIULWG operator, which ensures a balanced representation of objective and subjective data. In Section 4, a practical case study demonstrates the feasibility and effectiveness of the IVIULWG operator, offering a detailed analysis of the ergonomic performance of various Cobot designs. This empirical application highlights the advantages of dual-arm Cobots with display interfaces in ergonomic optimization. Finally, the study concludes with an integrative discussion that synthesizes the principal findings and proposes targeted suggestions for advancing future research in the domains of Cobot ergonomics and assessment methodologies.

Ergonomic evaluation for Cobots

The ergonomic evaluation of Cobots involves assessing their performance, efficiency, and impact on human users in environments where they work alongside humans. This research centers on assessing the ergonomic implications of Cobot deployment in intelligent manufacturing environments, with an emphasis on ensuring not only task efficiency but also safe and comfortable human-robot interaction. According to the International Ergonomics Association (IEA), ergonomics is typically classified into three primary domains: physical, cognitive, and organizational ergonomics.²⁶ Drawing from relevant literature and considering the logical framework of ergonomic evaluation in the context of smart manufacturing, this study builds an evaluation index system for Cobot ergonomics based on the IEA's classification. In selecting evaluation criteria, the study also takes into account the future directions for research and application of Cobots based on smart manufacturing technologies, as well as regulatory and policy trends.

Physical ergonomics

Physical ergonomics focuses on the analysis of human anatomical, anthropometric, physiological, and biomechanical attributes about physical tasks, aiming to enhance safety, operational efficiency, and user comfort across diverse working contexts.²⁶ This involves assessing how workplace design, tools, and equipment interact with the human body and identifying potential risks associated with repetitive tasks, awkward postures, or physical strain. In the context of Cobots, physical ergonomics plays a crucial role in evaluating and optimizing their impact on workers’ physical well-being and overall health after their integration into the workplace.²⁷

The evaluation of physical ergonomics in human-robot collaboration (HRC) systems focuses on reducing physical strain, preventing work-related musculoskeletal disorders (WMSDs), and enhancing operator performance. Cobots are specifically designed to complement human workers, taking over physically demanding or repetitive tasks while allowing operators to concentrate on tasks requiring cognitive input. This not only reduces biomechanical stress but also improves system performance and productivity.²⁸ For example, Cobots can be programmed to assist with lifting heavy objects, minimizing the physical burden on workers and reducing the risk of injury. Colim et al. analyzed assembly tasks in collaborative workstations and found that the risk of WMSDs significantly decreased across all observational assessment methods compared to traditional manual workstations.²⁹ Similarly, Palomba et al. employed the Rapid Upper Limb Assessment (RULA) tool to evaluate ergonomic conditions at Cobot-integrated workstations, revealing that RULA scores decreased by 50% on the left side and 57% on the right side of the body compared to traditional manual workstations, indicating substantial ergonomic improvement.³⁰

In addition to observational methods, advanced modeling approaches have been employed to optimize physical ergonomics in Cobot environments. Lorenzini et al. developed a full-body and joint-specific model that monitors operator fatigue levels in real-time.³¹ When joint fatigue surpasses a predefined threshold, the system triggers robotic assistance to adjust the worker's posture and reduce the biomechanical load, effectively preventing further fatigue accumulation and lowering the risk of chronic injury.

The integration of Cobots in the digital transformation of traditional manual workstations has been widely recognized as an effective strategy for improving workplace ergonomics. By reducing physical strain and minimizing biomechanical workload, Cobots not only enhance operators’ physical health but also contribute to safer, more efficient, and more productive work environments. This aligns with the broader goals of modern ergonomics to ensure sustainable human performance in increasingly automated and collaborative industrial settings.

Cognitive ergonomics

Cognitive ergonomics focuses on the analysis of how systems, tasks, and environments affect cognitive processes such as perception, memory, reasoning, and decision-making, aiming to optimize human-system interactions and improve performance, efficiency, and user experience.³² Cognitive ergonomics in Human-Robot Collaboration (HRC) systems is essential for optimizing human-cobot interaction by alleviating cognitive workload, reducing mental strain, and enhancing task efficiency. It emphasizes how psychological functions such as sensory perception, cognitive reasoning, and motor responses shape the operator's ability to effectively interact with and adapt to dynamic system components.³³

However, while reducing cognitive workload is generally associated with improved task performance and reduced strain, it is important to strike a balance. Excessive simplification of tasks may lead to under-stimulation and operator disengagement, potentially reducing situational awareness and job satisfaction. Therefore, effective cognitive ergonomic design in HRC should not only alleviate unnecessary mental burdens but also maintain sufficient cognitive engagement to sustain attention, motivation, and operator well-being during collaborative work.

One of the key challenges in HRC systems is ensuring that the cognitive demands placed on operators remain manageable, particularly when complex tasks require high levels of attention, problem-solving, and decision-making. The acceptability of human-robot interactions is heavily influenced by cognitive ergonomics, as excessive mental stress can lead to decreased performance and user dissatisfaction. By minimizing the cognitive strain associated with human-robot interactions, cognitive ergonomics not only improves operators’ mental well-being but also enhances collaborative efficiency.³⁴ Studies have shown that workers perceive Cobots as valuable tools that improve working conditions by providing physical and cognitive support, thereby reducing the stress associated with industrial tasks.³⁵

However, the cognitive demands in HRC systems are not without challenges. Panchetti et al. highlighted that integrating trust-based approaches in HRC systems reduces perceived task load and facilitates better collaboration.³⁶ Trust in the system allows operators to rely on the Cobot for assistance, thereby alleviating mental fatigue and improving overall system performance. On the other hand, Bouillet et al. pointed out that mechanical risks, such as sudden or unpredictable robot movements, may cause operators to adopt awkward postures or make rapid decisions to maintain control, leading to increased physical and cognitive strain.¹³ Similarly, Carissoli et al. found that as operators shift from collaborators to supervisors of Cobots, the increased demand for monitoring and managing robot behavior results in a higher cognitive workload, which can reduce situational awareness and attentional resources.³⁷

The redistribution of attentional resources in such supervisory roles presents significant cognitive costs, as operators must constantly monitor system status, detect anomalies, and make critical decisions in real-time.³⁸ These tasks become even more complex when operators are required to manage multiple robots or perform cognitively demanding operations under time constraints. The cognitive strain induced by such situations can compromise task performance and pose serious safety risks if not properly managed.

To overcome these challenges and promote effective human-robot collaboration, it is crucial to apply cognitive ergonomic principles that alleviate mental strain, enhance trust and transparency in Cobot behavior, and aid decision-making processes. Kim et al. emphasized that effective cognitive ergonomic strategies should be designed to alleviate cognitive strain, particularly when operators are faced with high-complexity tasks that require sustained attention and reasoning.³⁹ Hopko et al. further suggested that adapting task complexity to match operators’ cognitive capacities and providing real-time feedback and adaptive support mechanisms can significantly enhance human performance and system safety.⁴⁰

Ultimately, the integration of cognitive ergonomics in HRC systems ensures a more balanced human-robot relationship, promoting seamless interaction and reducing the cognitive and psychological burdens associated with increasingly complex technological environments.

Organizational ergonomics

Organizational ergonomics assesses how organizational structure, processes, policies, and culture affect employee efficiency, satisfaction, and health.⁴¹ In the context of Cobots, organizational ergonomics focuses on enhancing organizational productivity, employee well-being, and overall performance through scientific work design, effective performance evaluation, a positive organizational culture, good working environments and facilities, and efficient leadership and management.⁴² The research from Brun and Wioland,³⁸ which surveyed workers’ activities and perceptions of HRC, revealed that all employees believed the collaborative system had an impact on the organization. A significant majority of workers (75%) acknowledged that the introduction of Cobots enhanced workplace conditions and boosted confidence, offering support and alleviating stress and fatigue. Lambrechts et al. highlighted that phased planning for Cobot integration is essential, as employees frequently express reluctance due to insufficient information, experience, and communication.⁴³ Workers across different age groups view Cobots not as replacements but as independent “colleagues,” describing interactions with them as pleasant, engaging, and satisfying.⁴⁴ Some researchers have found that employee satisfaction with most aspects of their jobs remained roughly the same before and after the introduction of robots.⁴⁵ The advancement of automation within industrial settings has been shown in various studies to evoke concern among 40% of the workforce about the potential replacement of their roles by intelligent machines. This apprehension regarding job displacement is noted to have adverse effects on employee satisfaction levels.⁴⁶ High job satisfaction, which is positively associated with fluent human-Cobot interaction, fosters collaboration not only among employees but also between employees and Cobots, thereby enhancing overall productivity.⁴⁷ How to improve employee satisfaction after the introduction of Cobots, thereby maximizing their potential in enhancing productivity, product quality, and employee work experience, is a key consideration when evaluating the impact of Cobot applications.

Based on the aforementioned analysis and review, this study has developed an ergonomic evaluation index system for Cobots, as shown in Table 1.

Table 1.

Ergonomic evaluation index system for Cobots.

Dimensionality	Index	References
A₁ Physical ergonomics	A₁₁ Human's comfort level in working postures	⁴⁸
	A₁₂ Reasonableness of human's workspace layout	^49,50
	A₁₃ Human's physical workload level	⁵¹
	A₁₄ Human's safety conditions at work	²⁸
	A₁₅ Support for manual tasks for the human	⁵²
	A₁₆ HRC efficiency level	⁵³
A₂ Cognitive ergonomics	A₂₁ Human's attention allocation	⁵⁴
	A₂₂ Human's decision support	⁵⁵
	A₂₃ Human's level of cognitive load	⁵⁶
	A₂₄ Human's Perception of Robot Reliability	⁵⁷
	A₂₅ Human's perception of HRI usability	⁵⁸
	A₂₆ Human awareness of the surrounding environment	^59,60
	A₂₇ Human's job satisfaction	⁶¹
A₃ Organizational ergonomics	A₃₁ Task allocation in HRC	⁶²
	A₃₂ Coordination in HRC	⁶³
	A₃₃ Flexibility of work arrangements in HRC	⁶⁴
	A₃₄ Comfort level of the environment in HRC	⁶⁵

Development of IVIULWG operator for ergonomic evaluation of Cobots

The ergonomic evaluation metrics for Cobots are primarily derived from two types of data sources. The initial classification comprises traditional monitoring information, statistical figures, and experimental data, exemplified by metrics like “HRC efficiency level” and “Task allocation in HRC”, all encompassed within the domain of “crisp data”. The prevalent attribute exhibited by this category of data is that, notwithstanding its various manifestations including absolute figures, relative figures, and proportions, it maintains distinct numerical values and measurable depictions, facilitating unambiguous evaluations of its efficacy measures. The subsequent classification delineates a fusion of subjective and objective appraisals, such as “human's job satisfaction” and “human's comfort level in working postures”. Given that the application of Cobots is still in a growth phase within the industry, the industry standards and measurement criteria for these metrics exhibit some ambiguity. However, the potential range of values for this data remains clear based on previous research findings.

In light of the data types and characteristics, this study selects the interval-valued intuitionistic uncertain fuzzy (IVIUF) for evaluating the impact of Cobot applications. The IVIULWG, developed by considering geometric weights, can accurately convey the intuitive hesitations of evaluators regarding subjective aspects while also integrating all initial information to produce applicable evaluation results objectively. The intuitionistic validation and invalidation of IVIUF demonstrate remarkable flexibility, enabling automatic modifications as industry norms solidify, ergonomic investigations broaden, and pertinent quantitative criteria evolve progressively. In other words, this algorithm demonstrates strong sustainability.

Definition of IVIUF

The IVIUF semantic data and its operator are components of fuzzy multi-criteria decision-making techniques, which align with decision-making methodologies distinguished by uncertainty and ambiguity. This study is based on the intuitive fuzzy sets, interval-valued fuzzy sets, and their operational rules, forming the IVIUF semantic representation that incorporates both interval values and intuitive fuzzy sets.^66,67 The construction of this IVIUF semantic has three key features. First, all evaluations and judgments exhibit three-dimensional data, consisting of the judgment result, affirmation of the judgment result, and hesitancy about it. Second, the judgment result can be effectively described using interval values, where a larger range indicates greater ambiguity. Third, there is an understanding of the accuracy and inaccuracy of the formed judgments, which are likely to lie within any subset of the interval (0,1).

This study compiles relevant research findings to establish the following definition of IVIUF:

Definition 1:

Let S be a set of an odd number of uncertain linguistic evaluation sets $S = {S_{1}, S_{2}, \dots, S_{2 n - 1}}$ . The uncertain linguistic variable of IVIUF is defined as any subset interval $\tilde{S} = [S_{θ ({\tilde{a}}_{j})}, S_{τ ({\tilde{a}}_{j})}]$ , where $S_{θ ({\tilde{a}}_{j})}, S_{τ ({\tilde{a}}_{j})} \in S$ and are in ascending order. $S_{θ ({\tilde{a}}_{j})}$ represents the lower-level evaluation in the ascending order, while $S_{τ ({\tilde{a}}_{j})}$ represents the higher level.

Definition 2:

The intuitionistic perception confirmation state established for the uncertain linguistic variable $\tilde{S}$ is referred to as the membership interval value. Conversely, the intuitionistic uncertainty is referred to as the non-membership interval value. The membership interval $\tilde{u} = [u^{L} ({\tilde{a}}_{j}), u^{U} ({\tilde{a}}_{j})]$ consists of fuzzy evaluation values arranged in ascending order (where j represents the evaluation dimension), such that $u^{L} ({\tilde{a}}_{j}) < u^{U} ({\tilde{a}}_{j})$ . The non-membership interval $\tilde{v} = [v^{L} ({\tilde{a}}_{j}), v^{U} ({\tilde{a}}_{j})]$ reflects the intuitionistic perception uncertainty of the uncertain linguistic variable $\tilde{S}$ , also arranged in ascending order, with $v^{L} ({\tilde{a}}_{j}) < v^{U} ({\tilde{a}}_{j})$ . Given the allowance for hesitation factors, it holds that $0 \leq u^{L} ({\tilde{a}}_{j}) + v^{L} ({\tilde{a}}_{j}) \leq 1$ , $0 \leq u^{U} ({\tilde{a}}_{j}) + v^{U} ({\tilde{a}}_{j}) \leq 1$ .⁶⁸

Definition 3:

The description format of the IVIUF evaluation indicators is given by: $\tilde{a} = {[S_{θ ({\tilde{a}}_{1})}, S_{τ ({\tilde{a}}_{1})}], [u^{L} ({\tilde{a}}_{1}), u^{U} ({\tilde{a}}_{1})], [v^{L} ({\tilde{a}}_{1}), v^{U} ({\tilde{a}}_{1})]}$ . When examining a matrix comprising various variables, objects, and attributes, it can be succinctly defined as: ${\tilde{A}}_{i j} = ([S_{α_{i j}}, S_{β_{i j}}],$ $([a_{i j}, b_{i j}], [c_{i j}, d_{i j}]))$ , where i represents the number of evaluation objects and j represents the evaluation dimensions.

This study employs the IVIUF semantic expression for two main reasons. The initial step involves adeptly delineating the data attributes of both precise and indistinct values inherent in the ergonomic evaluation metrics. Additionally, the IVIUF methodology retains the factual evaluation intervals associated with precise and indistinct values, emphasizing the intuitive essence of subjective evaluations within ergonomic indicators. This results in richer state information and stronger mathematical properties.

IVIUF semantic transformation of evaluation indicators for coobot ergonomics effects

Step 1 “crisp” numbers in the evaluation indicator system

The ergonomic evaluation indicators for Cobots often adhere to established national grading standards, or they may rely on industry experts to form authoritative grading criteria. For such “crisp” data, intervals can be delineated based on these standards, classifying them into an odd number of ranges that progress from poor to excellent, with smaller interval labels indicating lower evaluations. If an indicator falls between two grade values, it is represented by the interval $[s_{θ ({\tilde{a}}_{1})}, s_{τ ({\tilde{a}}_{1})}]$ ; if it exists within a single evaluation range, it is represented as $[s_{θ ({\tilde{a}}_{1})}, s_{θ ({\tilde{a}}_{1})}]$ . The maximum interval could be $[s_{1}, s_{5}]$ or any subset of that interval. The interval values corresponding to “crisp” numbers are formed based on precise numerical values, endowing their membership and non-membership degrees with considerable objectivity.

Various countries and industries have established specific standards and regulations about the evaluation indicator system for human physical load levels. For instance, the International Organization for Standardization (ISO) has developed a series of guidelines-such as ISO 11228 for manual handling and ISO 7243 for thermal environments-that provide frameworks for assessing and managing physical workload. One such standard is the Strain Index, which assesses the physical workload on the hands and provides explicit classifications for different load levels. If the Duration of Exertion constitutes less than 10% of the work cycle time, it is assigned a score of 0.5, corresponding to an interval value of (0.98, 1] in IVIUF semantics. If we categorize into five intervals, the classification for “Duration of Exertion < 10%” would be set at Level 1, while the range “10–29%” would correspond to Level 2. Similarly, we can delineate levels 1 through 5 for varying proportions of Duration of Exertion, representing intervals S₁-S₂-S₃-S₄-S₅, which correlate to the characteristics of “Excellent, Above Average, Average, Below Average, Poor”. In instances of heightened precision in data, the degrees of membership and non-membership are delineated as (1, 1) and (0, 0) correspondingly. Conversely, under conditions of significant ambiguity in the operational context, these may be articulated as (0.2, 0.4) and (0.5, 0.6).

Step 2 “fuzzy” numbers in the evaluation indicator system

To date, opinions remain divided on whether the application of Cobots reduces or increases cognitive load levels. Consequently, many evaluations are based on “fuzzy” information. Therefore, subjective expert experience is still essential for assessment. We believe that even with diverse evaluation perspectives among experts, aggregating their assessments and averaging the results can still provide a general industry consensus on the cognitive ergonomics of such Cobots.

For instance, in the indicator system, the user work satisfaction metric (A₂₇) can be evaluated through a collective expert judgment. The evaluation values can be methodically categorized into a series of non-uniform judgment intervals, ranging from poor to excellent. In cases where the assessment values are derived through stratified sampling or comparative analysis, it becomes imperative to ascertain the equitable dispersion of these intervals. Subject matter specialists may be consulted to provide intuitive assessments on the levels of inclusion and exclusion grounded in their expert knowledge and perspectives.

Implementation of the IVIULWG algorithm

Based on Definitions 1–3 in Section 3.1 of the IVIUF framework, as well as the ergonomics evaluation index system for Cobots developed in this paper, the evaluation matrix ${\tilde{A}}_{i j}$ can be derived. Recognizing that this evaluation matrix comprises both “crisp” and “fuzzy” numbers, it is crucial to retain the maximum amount of initial evaluation information. The algorithmic framework is enhanced through the integration of geometric weights within the assessment matrix, consequently leading to the formulation of the IVIULWG operator. This operator is designed to effectively preserve both the objective and subjective information contained in the initial evaluation, leading to more scientifically grounded and objective mathematical conclusions.

Based on relevant research findings, we define the IVIUF variables as follows:

{\tilde{a}}_{1} = {[s_{θ ({\tilde{a}}_{1})}, s_{τ ({\tilde{a}}_{1})}], [u^{L} ({\tilde{a}}_{1}), u^{U} ({\tilde{a}}_{1})], [v^{L} ({\tilde{a}}_{1}), v^{U} ({\tilde{a}}_{1})]}

{\tilde{a}}_{2} = {[s_{θ ({\tilde{a}}_{2})}, s_{τ ({\tilde{a}}_{2})}], [u^{L} ({\tilde{a}}_{2}), u^{U} ({\tilde{a}}_{2})], [v^{L} ({\tilde{a}}_{2}), v^{U} ({\tilde{a}}_{2})]}

The fundamental operational rules are expressed as follows in equations (1) to (5):

\begin{aligned} {\tilde{a}}_{1} + {\tilde{a}}_{2} = & {[s_{θ ({\tilde{a}}_{1}) + θ ({\tilde{a}}_{2})}, s_{τ ({\tilde{a}}_{1}) + τ ({\tilde{a}}_{2})}], \\ [1 - (1 - u^{L} ({\tilde{a}}_{1})) (1 - u^{L} ({\tilde{a}}_{2})), \\ 1 - (1 - u^{U} ({\tilde{a}}_{1})) (1 - u^{U} ({\tilde{a}}_{2}))], \\ [v^{L} ({\tilde{a}}_{1}) v^{L} ({\tilde{a}}_{2}), v^{U} ({\tilde{a}}_{1}) v^{U} ({\tilde{a}}_{2})]} \end{aligned}

(1)

\begin{aligned} {\tilde{a}}_{1} \otimes {\tilde{a}}_{2} = & {[s_{θ ({\tilde{a}}_{1}) \times θ ({\tilde{a}}_{2})}, s_{τ ({\tilde{a}}_{1}) \times τ ({\tilde{a}}_{2})}], \\ [u^{L} ({\tilde{a}}_{1}) u^{L} ({\tilde{a}}_{2}), u^{U} ({\tilde{a}}_{1}) u^{U} ({\tilde{a}}_{2})], \\ [1 - (1 - v^{L} ({\tilde{a}}_{1})) (1 - v^{L} ({\tilde{a}}_{2})), \\ 1 - (1 - v^{U} ({\tilde{a}}_{1})) (1 - v^{U} ({\tilde{a}}_{2}))]} \end{aligned}

(2)

\begin{aligned} λ {\tilde{a}}_{1} & = {[s_{θ ({\tilde{a}}_{1}) \times λ}, s_{τ ({\tilde{a}}_{1}) \times λ}] [1 - {(1 - u^{L} ({\tilde{a}}_{1}))}^{λ}, \\ 1 - {(1 - u^{U} ({\tilde{a}}_{1}))}^{λ}], [{(v^{L} ({\tilde{a}}_{1}))}^{λ}, {(v^{U} ({\tilde{a}}_{1}))}^{λ}]} \end{aligned}

(3)

\begin{aligned} {\tilde{a}}_{1}^{λ} & = {[s_{{(θ ({\tilde{a}}_{1}))}^{λ},} s_{(τ ({\tilde{a}}_{1}))^{λ}}], [{(u^{L} ({\tilde{a}}_{1}))}^{λ}, {(u^{U} ({\tilde{a}}_{1}))}^{λ}], \\ [1 - {(1 - v^{L} ({\tilde{a}}_{1}))}^{λ}, 1 - {(1 - v^{U} ({\tilde{a}}_{1}))}^{λ}]} \end{aligned}

(4)

{\tilde{a}}_{1}^{λ_{1}} \otimes {\tilde{a}}_{2}^{λ 2} = ({\tilde{a}}_{1})^{λ_{1} + λ_{2}}

(5)

If ${\tilde{a}}_{1} = {[s_{θ ({\tilde{a}}_{1})}, s_{τ ({\tilde{a}}_{1})}], [u^{L} ({\tilde{a}}_{1}), u^{U} ({\tilde{a}}_{1})], [v^{L} ({\tilde{a}}_{1}), v^{U} ({\tilde{a}}_{1})]}$ (where $j = 1, 2, \dots, n$ ) represents a set of IVIUF variables, we developed the IVIULWG operator by incorporating geometric weighting factors into the generalized correlation aggregation operator based on IVIUF information.

Assuming ω = ( $ω_{1}, ω_{2}, \dots, ω_{n}$ ) is the weighting vector for ${\tilde{a}}_{j} (j = 1, 2, \dots, n)$ and $ω_{j} \in [0, 1]$ with $\sum_{j = 1}^{n} ω_{j} = 1$ , the general calculation rules for the IVIULWG operator are given by equations (6) to (8).

\begin{aligned} IVIULWG ({\tilde{a}}_{1}, {\tilde{a}}_{2} \dots \dots {\tilde{a}}_{n}) = [{\overset{\underset{n}{j = 1}}{\otimes}}_{{(s_{(α_{j})})}^{ω_{j}}}, {\overset{\underset{n}{j = 1}}{\otimes}}_{{(s_{(β_{j})})}^{ω_{j}}}], \\ [\prod_{j = 1}^{n} {(a_{j})}^{ω_{j}}, \prod_{j = 1}^{n} {(β_{j})}^{ω_{j}}], \\ [1 - \prod_{j = 1}^{n} {(1 - c_{j})}^{ω_{j}}, 1 - \prod_{j = 1}^{n} {(1 - d_{j})}^{ω_{j}}] \end{aligned}

(6)

\begin{aligned} Λ ({\tilde{a}}_{1}, {\tilde{a}}_{2} \dots \dots {\tilde{a}}_{n}) = \sum_{j = 1}^{n} ω_{j} {\tilde{a}}_{j} \\ = & {[s_{x_{n}}, s_{y_{n}}], [1 - \prod_{j = 1}^{n} {(1 - u^{L} ({\tilde{a}}_{j}))}^{ω_{j}}, 1 - \prod_{j = 1}^{n} {(1 - u^{U} ({\tilde{a}}_{j}))}^{ω_{j}}], [\prod_{j = 1}^{n} {(v^{L} ({\tilde{a}}_{j}))}^{ω_{j}}, \prod_{j = 1}^{n} {(v^{U} ({\tilde{a}}_{j}))}^{ω_{j}}]}, \\ where x_{n} = & \sum_{j = 1}^{n} ω_{j} θ ({\tilde{a}}_{j}), y_{n} = \sum_{j = 1}^{n} ω_{j} τ ({\tilde{a}}_{j}) \end{aligned}

(7)

ω i + 1 = \frac{C_{n - 1}^{i}}{2^{n - 1}} (i = 0, 1, \dots, n - 1)

(8)

Based on the aforementioned calculation rules, we can derive a comprehensive description of a specific evaluation objective from a multi-dimensional, multi-target IVIUF evaluation matrix,⁶⁹ expressed as $\tilde{a} = {[s_{θ (\tilde{a})}, s_{τ (\tilde{a})}], [u^{L} (\tilde{a}), u^{U} (\tilde{a})], [v^{L} (\tilde{a}), v^{U} (\tilde{a})]}$ . By applying the IVIULWG operator, we can obtain the expected value $E (\tilde{a})$ for decision-making. This expected value serves as an operator in Multi-Criteria Decision Analysis; while the numerical value itself does not carry evaluative significance, it can be directly used for comparison. The IVIUL evaluation information domain is governed by an ascending order regulation, where a higher expected value signifies a superior evaluation outcome. The calculation rule is detailed in equation (9):

\begin{aligned} E (\tilde{a}) = & \frac{1}{2} \times (\frac{u^{L} (\tilde{a}) + u^{U} (\tilde{a})}{2} + 1 - \frac{v^{L} (\tilde{a}) + v^{U} (\tilde{a})}{2}) \times S_{\frac{(θ (\tilde{a}) + τ (\tilde{a}))}{2}} \\ = & S_{(θ (\tilde{a}) + τ (\tilde{a}) \times [u^{L} (\tilde{a}) + u^{U} (\tilde{a}) + 2 - v^{L} (\tilde{a}) - v^{U} (\tilde{a})]) / 8} \end{aligned}

(9)

The application of interval-valued intuitionistic uncertain linguistic (IVIUL) semantics enables the seamless integration and management of both “crisp” and “fuzzy” numerical attributes in the ergonomic evaluation of collaborative robot (Cobot) applications. This approach addresses the inherent complexity of mixed data types, ensuring comprehensive and accurate assessments. By employing a generalized correlation aggregation operator based on IVIUL information and incorporating geometric weighting, the proposed IVIULWG operator preserves both objective “crisp” values and subjective “fuzzy” data. This dual-information retention significantly enhances the reliability and precision of evaluation outcomes. The IVIULWG operator proves to be a valuable instrument for conducting comparative numerical evaluations, hierarchical ranking, and categorical classification among diverse entities, thereby facilitating complex decision-making tasks within managerial and industrial environments.

Example verification and discussion

Example verification

The current market offers four main types of Cobots: single-arm Cobots (e.g., YuMi IRB 14050), dual-arm Cobots (e.g., YuMi IRB 14000), single-arm Cobots with a display (e.g., Sawyer), and dual-arm Cobots with a display (e.g., Rethink). Enterprises must make decisions about which type of Cobot to adopt based on ergonomics-related data for each category. For simplicity, the types are labeled as T₁ for single-arm Cobots, T₂ for dual-arm Cobots, T₃ for single-arm Cobots with a display, and T₄ for dual-arm Cobots with a display. This case study uses the IVIULWG operator to evaluate and prioritize these types.

Step 1: preparation of evaluation data

Based on the criteria specified in Table 1 for the evaluation index system, data or information pertinent to the application of the four categories of Cobots can be acquired from industry platforms, official brand websites, simulations, and real-world measurements. This data, alongside industry regulations and current industrial standards, serves as the basis for evaluation. The next step involves selecting five experts to provide evaluations based on IVIUF semantics. For the assessment, the experts will use an uncertainty linguistic evaluation set with five ascending intervals corresponding to the following qualitative terms: {S₁, S₂, S₃, S₄, S₅}={Poor, Below Average, Average, Above Average, Excellent}. These terms will guide the experts in evaluating the different types of Cobots across the provided criteria.

During the process of expert evaluation, indicators within the evaluation system exhibiting “crisp” characteristics are initially categorized into five interval values according to industry data norms. Subsequently, five experts utilize actual data from various types of Cobots to establish the respective interval values. The expert information is shown in Table 2. The expert panel consisted of five individuals, including four university researchers specializing in ergonomics and human-robot interaction, and one senior engineer with extensive experience in Cobot-integrated industrial settings. While this composition ensured professional expertise and methodological rigor, we acknowledge that the panel was relatively skewed toward academic perspectives. As such, it may not fully reflect the priorities and concerns of frontline workers, especially regarding safety and comfort in real production contexts. Due to access limitations and procedural constraints, workers were not directly included in the formal evaluation phase of this study. However, we fully recognize the value of their insights and intend to incorporate worker feedback in future studies through participatory ergonomic approaches, such as field observations, structured interviews, or user-centered assessments. The resultant membership and non-membership intervals are characterized by a high level of objectivity. Conversely, indicators demonstrating “fuzzy” characteristics are evaluated by experts through a direct assessment of interval values based on their professional expertise and intuition. Furthermore, these experts assign membership and non-membership details according to their intuitive judgments. The overall assessment values for the four categories of Cobots are determined through comprehensive evaluations provided by the five experts. In this study, equal weights are unilaterally assigned to the evaluations conducted by the experts.

Table 2.

Background information of the interviewed experts.

No.	Position	Work experience/year	Familiarity with HRC	Research direction
1	Lecturer	7	Familiar with	Human-computer interaction
2	Lecturer	10	Know well	Human factor
3	Lecturer	6	Familiar with	Human-computer interaction
4	Postdoctoral	8	Know well	Human factor
5	Engineer	12	Know well	Human-computer interaction

After processing, for the four types of Cobots, the evaluation matrices for the five experts (E₁, E₂, E₃, E₄, E₅) on the environmental impact evaluation index system can be obtained as 5*17 matrices, as shown in Table 3. Due to space constraints, other tabular data will be uploaded as necessary attachments.

Table 3.

Evaluation scores of four types of Cobots by expert E₁.

	T₁	T₂	T₃	T₄
A₁₁	<[s₃,s₄],[0.7,0.9],[0.05,0.1]>	<[s₃,s₄],[0.6,0.8],[0.1,0.2]>	<[s₃,s₄],[0.6,0.75],[0.15,0.25]>	<[s₃,s₄],[0.7,0.85],[0.1,0.1]>
A₁₂	<[s₄,s₅],[0.8,0.9],[0.05,0.1]>	<[s₄,s₅],[0.85,0.9],[0.05,0.1]>	<[s₄,s₅],[0.8,0.9],[0.1,0.1]>	<[s₄,s₅],[0.8,0.9],[0.1,0.1]>
A₁₃	<[s₂,s₃],[0.7,0.85],[0.1,0.15]>	<[s₃,s₄],[0.6,0.7],[0.15,0.2]>	<[s₃,s₄],[0.6,0.75],[0.15,0.25]>	<[s₂,s₃],[0.6,0.75],[0.15,0.25]>
A₁₄	<[s₁,s₂],[0.8,0.9],[0.1,0.1]>	<[s₄,s₅],[0.85,0.9],[0.05,0.1]>	<[s₄,s₅],[0.7,0.9],[0.0,0.1]>	<[s₃,s₄],[0.7,0.9],[0.05,0.1]>
A₁₅	<[s₃,s₄],[0.8,0.9],[0.1,0.1]>	<[s₃,s₄],[0.85,0.9],[0.1,0.1]>	<[s₁,s₂],[0.6,0.75],[0.2,0.25]>	<[s₂,s₃],[0.6,0.75],[0.2,0.25]>
A₁₆	<[s₂,s₃],[0.8,0.9],[0.1,0.1]>	<[s₃,s₄],[0.85,0.9],[0.1,0.1]>	<[s₂,s₃],[0.6,0.75],[0.2,0.25]>	<[s₃,s₄],[0.6,0.75],[0.2,0.25]>
A₂₁	<[s₄,s₅],[0.7,0.85],[0.1,0.15]>	<[s₁,s₂],[0.6,0.7],[0.15,0.2]>	<[s₃,s₄],[0.9,0.95],[0.05,0.05]>	<[s₁,s₂],[0.9,0.95],[0.05,0.05]>
A₂₂	<[s₁,s₂],[0.6,0.75],[0.2,0.25]>	<[s₁,s₂],[0.85,0.9],[0.05,0.1]>	<[s₂,s₃],[0.9,0.95],[0.05,0.05]>	<[s₂,s₃],[0.9,0.95],[0.0,0.05]>
A₂₃	<[s₂,s₃],[0.6,0.75],[0.2,0.25]>	<[s₂,s₃],[0.85,0.9],[0.1,0.1]>	<[s₃,s₄],[0.9,0.95],[0.05,0.05]>	<[s₃,s₄],[0.9,0.95],[0.05,0.05]>
A₂₄	<[s₂,s₃],[0.6,0.75],[0.2,0.25]>	<[s₁,s₂],[0.85,0.9],[0.05,0.1]>	<[s₄,s₅],[0.9,0.95],[0.05,0.05]>	<[s₁,s₂],[0.9,0.95],[0.05,0.05]>
A₂₅	<[s₁,s₂],[0.8,0.9],[0.15,0.1]>	<[s₃,s₄],[0.85,0.9],[0.05,0.1]>	<[s₂,s₃],[0.9,0.95],[0.05,0.05]>	<[s₃,s₄],[0.9,0.95],[0.05,0.05]>
A₂₆	<[s₃,s₄],[0.7,0.85],[0.1,0.15]>	<[s₂,s₃],[0.85,0.9],[0.05,0.1]>	<[s₃,s₄],[0.8,0.9],[0.05,0.1]>	<[s₂,s₃],[0.8,0.9],[0.05,0.1]>
A₂₇	<[s₃,s₄],[0.8,0.9],[0.1,0.1]>	<[s₂,s₃],[0.85,0.9],[0.1,0.1]>	<[s₄,s₅],[0.8,0.9],[0.1,0.1]>	<[s₂,s₃],[0.8,0.9],[0.1,0.1]>
A₃₁	<[s₂,s₃],[0.6,0.75],[0.1,0.25]>	<[s₂,s₃],[0.6,0.7],[0.15,0.2]>	<[s₂,s₃],[0.8,0.9],[0.1,0.1]>	<[s₁,s₂],[0.8,0.9],[0.1,0.1]>
A₃₂	<[s₂,s₄],[0.6,0.75],[0.15,0.25]>	<[s₁,s₂],[0.6,0.7],[0.15,0.2]>	<[s₁,s₂],[0.6,0.75],[0.15,0.25]>	<[s₁,s₂],[0.6,0.75],[0.2,0.25]>
A₃₃	<[s₂,s₅],[0.6,0.75],[0.15,0.25]>	<[s₁,s₂],[0.6,0.7],[0.2,0.2]>	<[s₁,s₂],[0.6,0.75],[0.15,0.25]>	<[s₂,s₃],[0.6,0.75],[0.2,0.25]>
A₃₄	<[s₃,s₄],[0.7,0.85],[0.1,0.15]>	<[s₂,s₃],[0.6,0.7],[0.1,0.2]>	<[s₃,s₄],[0.8,0.9],[0.1,0.1]>	<[s₂,s₃],[0.8,0.9],[0.05,0.1]>

Step2: IVIUF evaluation of cobot types

We first assign the same subjective weights to the primary indicators A₁, A₂, A₃, and the secondary indicators A_ij (i = 1, 2, 3, j = 1, 2,…,7) in the ergonomic evaluation index system for Cobots. According to the calculation rules of the IVIULWG operator, we can compute the comprehensive attribute values ${\tilde{E}}_{T i}^{k}$ (where E represents the expected value, k indicates the expert number, and T_i represents the different types of Cobots), which reflect the IVIUF evaluations from different experts for each type of Cobot.

{\tilde{E}}_{T 1}^{1} =< [s_{2.35}, s_{3.60}], [0.70, 0.84], [0.11, 0.16] >

{\tilde{E}}_{T 1}^{2} =< [s_{2.35}, s_{3.60}], [0.55, 0.73], [0.14, 0.24] >

{\tilde{E}}_{T 1}^{3} =< [s_{2.51}, s_{4.31}], [0.52, 0.76], [0.00, 0.23] >

{\tilde{E}}_{T 1}^{4} =< [s_{2.17}, s_{3.17}], [0.59, 0.69], [0.17, 0.24] >

{\tilde{E}}_{T 1}^{5} =< [s_{1.91}, s_{3.49}], [0.28, 0.38], [0.15, 0.30] >

{\tilde{E}}_{T 2}^{1} =< [s_{2.35}, s_{3.60}], [0.76, 0.83], [0.10, 0.14] >

{\tilde{E}}_{T 2}^{2} =< [s_{2.35}, s_{3.60}], [0.53, 0.71], [0.16, 0.23] >

{\tilde{E}}_{T 2}^{3} =< [s_{3.01}, s_{4.83}], [0.67, 0.86], [0.00, 0.14] >

{\tilde{E}}_{T 2}^{4} =< [s_{2.17}, s_{3.17}], [0.59, 0.69], [0.17, 0.24] >

{\tilde{E}}_{T 2}^{5} =< [s_{2.93}, s_{4.10}], [0.33, 0.62], [0.14, 0.28] >

{\tilde{E}}_{T 3}^{1} =< [s_{2.35}, s_{3.60}], [0.77, 0.88], [0.00, 0.12] >

{\tilde{E}}_{T 3}^{2} =< [s_{2.35}, s_{3.60}], [0.59, 0.69], [0.17, 0.24] >

{\tilde{E}}_{T 3}^{3} =< [s_{3.29}, s_{4.86}], [0.59, 0.69], [0.17, 0.24] >

{\tilde{E}}_{T 3}^{4} =< [s_{2.02}, s_{3.06}], [0.59, 0.69], [0.17, 0.24] >

{\tilde{E}}_{T 3}^{5} =< [s_{2.09}, s_{3.80}], [0.27, 0.61], [0.14, 0.30] >

{\tilde{E}}_{T 4}^{1} =< [s_{2.35}, s_{3.60}], [0.77, 0.88], [0.00, 0.12] >

{\tilde{E}}_{T 4}^{2} =< [s_{2.11}, s_{3.11}], [0.49, 0.68], [0.13, 0.24] >

{\tilde{E}}_{T 4}^{3} =< [s_{3.59}, s_{4.82}], [0.67, 0.88], [0.00, 0.12] >

{\tilde{E}}_{T 4}^{4} =< [s_{2.06}, s_{3.06}], [0.59, 0.69], [0.17, 0.24] >

{\tilde{E}}_{T 4}^{5} =< [s_{3.06}, s_{4.81}], [0.32, 0.62], [0.14, 0.28] >

Step 3: comprehensive evaluation of IVIUF

Based on the IVIULWG operator, the integrated comprehensive attribute values ${\tilde{E}}_{T i}^{k}$ can yield the collective comprehensive attribute values ${\tilde{E}}_{T i}$ for different types of Cobots. The positional variable is determined using the criterion $w_{i + 1} \frac{C_{n - 1}^{i}}{2^{n - 1}} (i = 0, 1, \dots, n - 1)$ . After calculation, the expert IVIUF comprehensive evaluations ${\tilde{A}}_{T i}$ for each type of Cobot is summarized as follows:

{\tilde{A}}_{T 1} =< [s_{2.26}, s_{3.63}], [0.55, 0.71], [0.00, 0.23] >

{\tilde{A}}_{T 2} =< [s_{2.56}, s_{3.86}], [0.57, 0.74], [0.00, 0.21] >

{\tilde{A}}_{T 3} =< [s_{2.42}, s_{3.78}], [0.59, 0.77], [0.00, 0.19] >

{\tilde{A}}_{T 4} =< [s_{2.63}, s_{3.88}], [0.60, 0.78], [0.00, 0.18] >

Step 4: comprehensive evaluation of cobot ergonomics

By calculating the total expected ergonomic evaluation values for Cobots T₁, T₂, T₃, T₄, we obtain E( ${\tilde{A}}_{T 1}$ )=S_2.231, E( ${\tilde{A}}_{T 2}$ )=S_2.485, E( ${\tilde{A}}_{T 3}$ )=S_2.450, E( ${\tilde{A}}_{T 4}$ )=S_2.597. Based on the optimization requirements, we rank the ergonomic expected values, resulting in E(S_T4)>E(S_T2)>E(S_T3)>E(S_T1). This indicates that the ergonomic comprehensive evaluation for the T₄ type of Cobot, namely the dual-arm robot with a screen, is the most optimal, which is consistent with previous studies.^70–72

Discussion

According to the findings of this study, the dual-arm robot with a screen performs the best in ergonomic comprehensive evaluations. In contrast to other robotic configurations, the dual-arm design more closely replicates the functional dynamics of human hands, thereby enhancing the robot's capacity to perform intricate operations such as grasping, assembling, and fine-tuning with greater precision and adaptability.⁷³ In contrast to single-arm robots, dual-arm robots can collaborate effectively to manage intricate operational workflows, such as multi-step assembly or the handling of complex objects. This humanoid design reduces the operator's learning curve and enhances both efficiency and precision.⁷⁴ Furthermore, the dual-arm design enables more flexible and coordinated operations.⁷⁵ For instance, one arm can stabilize an object while the other performs tasks, making this configuration particularly well-suited for scenarios that require precise coordination, thereby improving both efficiency and the quality of task completion.

It is noteworthy that the Cobots equipped with screens rank higher than those without, indicating that intuitive visual feedback is crucial for the ergonomic evaluation of Cobots. The screen design provides operators with real-time task feedback, allowing them to clearly understand the robot's status and progress. This not only enhances control and safety during operations—particularly in complex tasks where operators can quickly identify and address anomalies—but also enables operators to conveniently input commands or adjust task parameters, thereby reducing reliance on external control devices. Research by Liu et al. indicated that Cobots with screens require more attention resources and greater cognitive effort compared to those without screens.⁷⁶ However, Onnasch and Hildebrandt suggested that humanoid robots can foster a higher level of trust among users during human-robot interactions, improving the perceived reliability of the robots.⁷⁷

From an organizational ergonomics perspective, dual-arm Cobots equipped with screens demonstrate greater flexibility and adaptability compared to single-arm counterparts, thereby optimizing their effectiveness in collaborative human-robot work environments. Whether in assembly on production lines, logistics handling, or delicate medical operations, these robots can perform tasks with high efficiency and precision. Rodríguez and Suárez studied the integration of motion and task allocation in dual-arm robotic systems, where each part of the robot performs independent tasks in chaotic environments.⁷⁸ Yu et al. proposed a collaborative control strategy for dual-arm robots during assembly tasks to reduce the effort required by humans to move the “master” arm.⁷⁹ The results of this study also indicate that the optimal ergonomic evaluation of dual-arm Cobots with screens suggests that this type can significantly enhance efficiency in practical production. The dual-arm design allows robots to perform multitasking simultaneously, reducing downtime in production processes. Moreover, the screen design enhances monitoring and feedback mechanisms for tasks, aiding in timely adjustments and workflow optimization.

While cobots demonstrate clear advantages in enhancing efficiency, safety, and ergonomics, their effectiveness is not uniformly applicable across all manufacturing settings. The success of cobot deployment is influenced by a range of contextual factors, including task complexity, production requirements, infrastructure readiness, and the level of human-robot collaboration. Cobots tend to be particularly effective in environments characterized by repetitive, physically strenuous, or ergonomically taxing tasks, where their integration can alleviate human workload and improve consistency. Conversely, in settings involving high task variability or requiring nuanced human judgment and adaptability, the current generation of cobots may be less suitable without further advances in artificial intelligence and adaptive control systems. Additionally, workspace layout, product type, and existing workflows significantly shape the feasibility of cobot integration. Therefore, while cobots hold strong potential, especially for small- and medium-sized enterprises seeking flexible automation solutions, their deployment should be carefully evaluated to ensure alignment with specific operational needs.

Limitations

Although this study, based on the developed IVIULWG operator, provides a detailed analysis of the ergonomic evaluations of different types of Cobots, there are still some limitations. First, the study primarily focuses on a few typical Cobots. While it encompasses various types, including single-arm, dual-arm, with and without screens, the sample selection is relatively limited. There are many more types and models of Cobots in the market that may exhibit different ergonomic characteristics, which were not included in this research. Therefore, the generalizability of the results may be constrained. Second, although multiple ergonomic indicators (such as operational flexibility, user experience, production efficiency, etc.) are covered, not all potential influencing factors have been comprehensively considered. For example, psychological stress, fatigue from prolonged use, and users’ long-term adaptability have not been thoroughly assessed, yet these factors also significantly impact ergonomic evaluations. Another limitation of this study is its reliance on expert evaluations in the ergonomic assessment process, which may introduce subjective bias and affect the objectivity of the results. While expert judgment is valuable for interpreting complex ergonomic factors, it can lead to variability in evaluations. Future research should focus on incorporating a greater volume of real-world data, such as sensor-based biomechanical measurements and workplace observation records, to enhance the reliability and accuracy of the findings. Although the expert panel ensured methodological rigor, it was predominantly composed of academic professionals, with limited representation from frontline production workers. As a result, the evaluation may not fully capture worker-centered concerns, particularly regarding practical safety and comfort. Due to access and procedural constraints, workers were not directly involved in this study's formal assessment phase. Future research will aim to incorporate participatory ergonomic methods to address this gap.

Conclusions

The research commences by formulating an extensive ergonomic evaluation index system tailored for Cobots in the realm of corporate management decision-making. Emphasizing the amalgamation of precise and ambiguous figures in the index system, it introduced the IVIULWG operator by incorporating the fuzzy interval value attributes of IVIUF semantic data. A case study demonstrated the ergonomic assessment of different types of Cobots involving five experts, three evaluation dimensions, and 17 evaluation indicators, confirming the feasibility and applicability of the proposed evaluation approach. The results indicated that dual-arm Cobots with screens achieve the best overall ergonomic evaluation. This suggests that these robots excel not only in physical ergonomics but also in user experience, production efficiency, and adaptability. This design enhances the human-robot collaborative environment, offering substantial ergonomic benefits in real-world applications.

Footnotes

Acknowledgments

We are grateful to all the industry experts for this study. As well, we are pleased to extend our gratitude to the editors and reviewers for their valuable comments.

Ethical considerations

This study has been approved by the Ethics Committee of Dalian Maritime University.

Author contributions

AU1: Writing – original draft, Visualization, Software, Methodology, Formal analysis, Data curation, Conceptualization, Project administration. AU2: Data curation, Methodology, Validation. AU3: Writing – review & editing, Visualization, Methodology, Supervision, Project administration. AU4: Software, Methodology, Investigation, Validation.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by China Postdoctoral Science Fund (No.2024M760318), the 2025 Doctoral Research Start-up Project of Liaoning Province (Funded by Liu Li), the 1st Batch of 2024 MOE of PRC Industry-University Collaborative Education Program (Number: 230805329290236), Liaoning Province economic and social development research topic (No. 2025lslqnkt-042), the Natural Science Research Project of Anhui Educational Committee (Grant number: 2023AH050934), and the National Natural Science Foundation of China (Grant number: 72401003), the Humanities and Social Science Fund of the Ministry of Education of China (grant number 21YJA630041).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

Data available on request / reasonable request.

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