The intrinsic stochasticity of manufacturing is one of the main factors that hinder system resilience. Planning and scheduling problems are typical examples plagued by uncertainties such as stochastic processing time, arrivals of new orders, and breakdowns of workstations. Frequent uncertainties disturb the workflow, and their cascading effects create chaos in the whole system. The transparency and traceability analytics in Cyber-Physical Manufacturing Systems (CPMS) bring new hope to tackle uncertainties. Inspired by the core spirit of Out-of-Order (OoO) Execution in CPU, this paper proposes a novel OoO architecture for resilient planning and scheduling in CPMS with real-time data analytics. Following OoO principles, multi-level instruction queues are constructed, under which manufacturing operations (instructions) are sequenced and performed by analyzing real-time dependencies and executability. This study contributes a new perspective to enhance decision resilience using real-time data in CPMS. Results validate the effectiveness and resilience of OoO under different levels of uncertainty, showing improvements in the on-time delivery rate and reductions in the average order flow time.

With the rapid development of smart manufacturing, the joint optimization of production, equipment maintenance, and product quality control has become key to improving manufacturing system performance. To formulate maintenance strategies for manufacturing systems, most studies use equipment degradation level as an indicator of whether maintenance actions should be initiated. However, product quality often deteriorates before equipment degradation is detected. This study develops a new joint optimization model based on quality information. First, we quantify a production quality risk indicator based on the deviation of key quality characteristics and potential risk and formulate a preventive maintenance strategy on that basis. Then, we construct a dual-objective optimization model using Pareto frontier analysis that accounts for both cost minimization and equipment availability in cycle maximization, aiming to improve the accuracy of maintenance strategies. Finally, the effectiveness of the proposed method is demonstrated through specific examples and sensitivity analysis, as well as a comparative study. The results show that the proposed method achieves the lowest total cost among the considered policies, while keeping a high availability comparable to existing policies. This outcome can provide decision support for the high-reliability, low-cost operation and maintenance of smart manufacturing systems.

Multiple response optimization (MRO) aims to obtain an optimal solution by optimizing several responses simultaneously for quality improvement. The preference parameters in the traditional MRO are exact real numbers. However, qualified uncertainties of marginally qualified responses can lead to preference parameters, such as the lower and upper bounds, to obtain interval forms. To solve the MRO involving conflicting responses using desirability functions under interval preference parameter, an intuitionistic fuzzy desirability function method (IFDFM) is proposed, which includes the experiments and data regression phase, the intuitionistic fuzzy desirability function set (IFDFS) construction phase, the optimization and decision-making phase. Compared with the existing desirability function methods, in the proposed method, the IFDFSs are introduced. Namely, after evaluating interval preference parameters with marginally qualified responses, the IFDFSs are constructed to measure the qualified uncertainties of multiple response performances based on the membership, non-membership and hesitant degrees. The proposed IFDFM is verified on the tire-tread compound problem. The results show that the IFDSs of the optimal solution obtained by the IFDFM can better measure the desirability uncertainties of the marginally qualified responses. By comparing results of the IFDFM under different combinations of marginally qualified responses, the influence orders of responses on optimal solutions are obtained, providing important information for developing quality improvement strategies.

This study considers a response surface methodology (RSM) variation in which a response has multiple central tendencies (MCTs) that can have multiple influences on a sheet metal part. This is formulated as a set response surface (SRS) problem, which, in industrial practice, is studied using the thinning ratio example. The set RSM (SRSM), consisting of three phases, is proposed to solve the SRS problem. The first phase is the problem definition and regional division phase, where based on the analysis of MCTs and response influence, a sheet metal part that needs quality improvement is divided intoqregions. The second phase is the experiment and data regression phase. The third phase is the optimization and interactive decision phase, where the condition relaxation strategy (CRS) is proposed, and relaxation is obtained based on the barrier and engineering requirement analysis. The optimization models are constructed for the (q+1)-level optimal solutions using the CRS. The proposed SRSM is verified by tests on the wrinkle and crack problem of the inner plate of the back door. A possible optimization model combination and trend analysis strategy is proposed to solve the CRS challenge for higher dimensions in the tendencies.

Flexible and reconfigurable manufacturing systems with independent multiskilled cells are pivotal for mass customization under volatile demand, yet internal/external uncertainties persistently disrupt planning, scheduling, and execution (PSE), causing idle time and workflow instability. This study proposes a hybrid synchronization framework with hierarchical real-time data feedback to address heterogeneous demand-capacity synchronization (HDCS), reconciling demand volatility, system reconfigurability, and dynamic human capacity. The framework first adopts the ticket-enabled queuing mechanism of the graduation intelligent manufacturing system (GiMS) to enable seamless PSE integration, ensuring resilient operations. Next, it hybridizes a global optimization model with local adjustment mechanisms, utilizing multigranularity data to balance global optimality and local practicality under uncertainty. Finally, it implements a human-cyber-physical digitalization architecture to establish smart human-machine collaborative assembly. Validated through a case study, the method enhances cost-efficiency by 1.7%, punctuality by 29.5%, and resource utilization by 3.9% compared to conventional rescheduling strategies, demonstrating superior adaptability to uncertainties. The results validate its effectiveness in advancing human-centric smart manufacturing aligned with Industry 5.0 objectives, offering an integrated solution to HDCS challenges through synergistic coordination of hierarchical control, hybrid optimization, and human-machine collaboration.

To solve multiple response optimization problems that often involve incommensurate and conflicting responses, a robust interactive desirability function approach is proposed in this article. The proposed approach consists of a parameter initialization phase and calculation and decision-making phases. It considers a decision maker's preference information regarding tradeoffs among responses and the uncertainties associated with predicted response surface models. The proposed method is the first to consider model uncertainty using an interactive desirability function approach. It allows a decision maker to adjust any of the preference parameters, including the shape, bound, and target of a modified robust function with consideration of model uncertainty in a single and integrated framework. This property of the proposed method is illustrated using a tire tread compound problem, and the robustness of the adjustments for the approach is also considered. The new method is shown to be highly effective in generating a compromise solution that is faithful to the decision maker's preference structure and robust to uncertainties associated with model predictions.

This paper uses the priority labels to express the detailed prioritized relationship between criteria and develops some scaled prioritized geometric aggregation operators, including the scaled prioritized geometric score (SPGS) operator and the scaled prioritized geometric averaging (SPGA) operator. We also present the uncertain scaled prioritized geometric scoring (USPGS) operator and the uncertain scaled prioritized geometric averaging (USPGA) operator. We investigate the properties of these operators and build the models to derive the weights by maximizing square deviations from a possible range to distinguish the candidate alternatives. The principal advantage of these scaled prioritized geometric aggregation operators is that they are very stable and satisfy monotonicity. Furthermore, we investigate approaches to multi-attribute decision making based on the proposed operators or models and examples are illustrated to show the feasibility and validity of the new approaches. Finally, some further discussions are given.

The Bonferroni mean (BM) was originally presented by Bonferroni and had been generalized by many researchers on Atanassov's intuitionistic fuzzy sets (AIFSs) for its capacity to capture the interrelationship between input arguments. Nevertheless, the forms of the combinations of the newly proposed interaction theory on AIFSs with BM are very single, and the existing BMs on AIFSs are not consistent with aggregation operations on the ordinary fuzzy sets. As complements to the existing generalizations of BM under Atanassov's intuitionistic fuzzy environment, this paper develops the extended Atanassov's intuitionistic fuzzy interaction Bonferroni mean (EIFIBM) and the extended weighted Atanassov's intuitionistic fuzzy interaction Bonferroni mean, which can evolve into a series of BMs by taking different generator functions that reflect the different preference attitudes of the decision makers. In addition, some of the EIFIBMs are consistent with aggregation operations on the ordinary fuzzy sets, and some of the EIFIBMs consider the interactions between the membership and nonmembership functions of different Atanassov's intuitionistic fuzzy sets; thus, they can be used in more decision situations. We investigate the properties of these new extensions and apply them to multiple-attribute decision-making problems with admissible orders. Finally, numerical examples show the validity and feasibility of the new approaches.

The geometric Bonferroni mean (GBM) can capture the interrelationships between input arguments, which is an important generalization of Bonferroni mean (BM). In this paper, we combine geometric Bonferroni mean (GBM) with the power geometric average (PGA) operator under intuitionistic fuzzy environment and present the intuitionistic fuzzy geometric power Bonferroni mean (IFPGBM) and the weighted intuitionistic fuzzy power geometric Bonferroni mean (WIFPGBM). The desirable properties of these new extensions of Bonferroni mean and their special cases are investigated. We list the detailed steps of multiple attribute group decision making with the developed IFPGBM or WIFPGBM, and give a comparison of the new extensions of Bonferroni mean by this paper with the corresponding existing intuitionistic fuzzy Bonferroni means. Finally, examples are illustrated to show the validity and feasibility of the new approaches.

The Bonferroni mean (BM) was originally presented by Bonferroni and had been generalized by many researchers for its capacity to capture the interrelationship between input arguments. Nevertheless, the existing intuitionistic fuzzy BMs only consider the effects of membership function or nonmembership function of different intuitionistic fuzzy sets (IFSs). As complements to the existing generalizations of BM under intuitionistic fuzzy environment, this paper also considers the interactions between the membership function and nonmembership function of different IFSs and develops the intuitionistic fuzzy interaction BM and the weighted intuitionistic fuzzy interaction BM. We investigate the properties of these new extensions of BM and discuss their special cases. Furthermore, the detailed steps of multiple attribute decision making with the presented operators under intuitionistic fuzzy environment are investigated and an example is illustrated to show the validity and feasibility of the new approach.

As a useful generalization of fuzzy sets, the hesitant fuzzy set is designed for situations in which it is difficult to determine the membership of an element to a set because of ambiguity between a few different values. In this paper, we define the ith-order polymerization degree function and propose a new ranking method to further compare different hesitant fuzzy sets. In order to obtain much more information in the process of group decision making, we combine the power average operator with the Bonferroni mean in hesitant fuzzy environments and develop the hesitant fuzzy power Bonferroni mean and the hesitant fuzzy power geometric Bonferroni mean. We investigate the desirable properties of these new hesitant fuzzy aggregation operators and discuss some special cases. The new aggregation operators are utilized to present techniques for hesitant fuzzy multiple attribute group decision making. Finally, a numerical example is provided to illustrate the effectiveness of the developed techniques.