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The possibility function-based grey clustering model has evolved into a complete approach for dealing with uncertainty evaluation problems. Existing models still have problems with the choice dilemma of the maximum criteria and instances when the possibility function may not accurately capture the data's randomness. This study aims to propose a multi-stage skewed grey cloud clustering model that blends grey and randomness to overcome these problems.

First, the skewed grey cloud possibility (SGCP) function is defined, and its digital characteristics demonstrate that a normal cloud is a particular instance of a skewed cloud. Second, the border of the decision paradox of the maximum criterion is established. Third, using the skewed grey cloud kernel weight (SGCKW) transformation as a tool, the multi-stage skewed grey cloud clustering coefficient (SGCCC) vector is calculated and research items are clustered according to this multi-stage SGCCC vector with overall features. Finally, the multi-stage skewed grey cloud clustering model's solution steps are then provided.

The results of applying the model to the assessment of college students' capacity for innovation and entrepreneurship revealed that, in comparison to the traditional grey clustering model and the two-stage grey cloud clustering evaluation model, the proposed model's clustering results have higher identification and stability, which partially resolves the decision paradox of the maximum criterion.

Compared with current models, the proposed model in this study can dynamically depict the clustering process through multi-stage clustering, ensuring the stability and integrity of the clustering results and advancing grey system theory.

Recently several authors have concentrated their efforts in developing models to determine the economic lot size for multi‐stage systems. This is due to the fact that an increasing number of organisations are implementing material requirements planning systems. Numerous models have been developed and tested on problems with finite and rolling horizons and with deterministic time varying demand patterns.

The optimal payment in the whole operation and maintenance period of water environment treatment PPP projects has become the main approach to realize sustainable development of projects. This study is aimed at constructing an effective payment model for the whole life period of projects to achieve win-win among all stakeholders, so as to provide a theoretical reference and managerial implications for the public sector in the whole operation and maintenance period.

In the whole operation and maintenance period of water environment treatment PPP projects, this article investigates how the public sector optimizes the payment in the whole operation and maintenance period of projects. Firstly, the projects' whole operation and maintenance period is divided into several stages according to the performance appraisal period. And then, the multi-stage dynamic programming model is constructed to design the payment construct model for the public sector in each performance appraisal stage. The payment from the public sector is the decision variable, and the deduction from the private sector is a random variable.

The optimal payment model showed that the relatively less objective weight of public sector leaded to its relatively more total payment and vice versa. Therefore, the sustainable development of the projects can only be ensured when the objective weights both of them should be balanced. Additionally, the deduction from the performance appraisal of private sector plays an important role in the model construction. The larger deduction the private sector undertakes, the smaller profits private sector has. Since the deduction at each stage is a random variable, the deduction varies with the different probability distributions obeyed by the practical deduction in each stage.

The findings from this study have provided theoretical and application references, and some managerial implications are also given. First, the improvement of the pricing system of public sector should be accelerated. Second, the reasonable profit of the private sector must be guaranteed. While pursuing the maximization of social benefits, the public sector should make full use of the price sharing mechanism in the market and supervise the real income situation of the private sector. Third is increasing the public to participate in pricing. Additionally, it is a limitation that the deduction is assumed to conform to a uniform distribution in this study. Other probability distributions on deduction can be essentially further sought, so as to be more line with the actual situation of the projects.

The optimal payment in whole operation and maintenance period of the projects has become an important issue, which is a key to project success. This study constructs a multi-stage dynamic programming model to optimize payment in the whole period of projects. Additionally, this study adds its value through deeply developing the new theories of optimal payment to more suitable for the practical problems, so that to optimize the design of payment mechanism. Meanwhile, a valuable reference for public and private sectors is provided to ensure the sustainable development of the projects.

Three simple, single pass multi‐stage lot‐sizing heuristics are examined using simulation. The heuristics are based on using different cost policies in single stage lot‐sizing procedures when applied to a multi‐stage setting. The focus is on the echelon holding cost policy and its performance relative to using “full value” holding costs and McLaren's adjusted setup costs. It is shown that echelon holding costs can lead to an extremely poor overall cost performance. A simple measure that will detect situations for which the echelon holding cost policy is potentially not suitable is suggested and evaluated. Application of the proposed measure results in substantial cost improvements for the echelon holding cost policy; despite this, the policy was outperformed by the MLSA policy in most cases. More research is needed, however, before any conclusive evidence can be presented on the effectiveness of echelon holding costs in multi‐stage lot‐sizing.

Stereo vision is an attractive perception technique for mobile robots navigation. Stereo matching is a crucial part of stereo vision and its precision dominates the precision of reconstruction. Based on a geometry constraint applicable to natural terrain, the purpose of this paper is to present a multi‐stage stereo matching algorithm to improve matching accuracy.

In the multi‐stage matching algorithm, points with larger intensity gradient are matched in earlier stages. Using several constraints and statistical means, information from earlier stages is utilized to assist in matching of later stages to improve matching accuracy.

The multi‐stage matching algorithm improves the matching accuracy of stereo pairs of natural terrain in various conditions.

The algorithm demonstrates advantages over area‐matching algorithm both in matching accuracy and computation efficiency. However, if used for real‐time navigation, it still needs the assistance of specialized hardware or window selection technique.

The algorithm is able to produce dense disparity maps of natural terrain with fairly high accuracy and can be used for the navigation of planetary rover or other outdoor mobile robots.

The paper provides a new approach to produce accurate and dense disparity maps of natural terrain, which laid the foundation for its use in outdoor mobile robots navigation.

The purpose of this paper is to explore the functionality of multistage programming approach on network supply chain structure.

The general supply chain structure is considered and the supply chain planning model is developed using a two stage programming approach. The same model is extended to cover the applicability and advantages of a multi‐stage programming approach.

A multi‐period supply chain model for new product launches under uncertain demand for supply chain network structure has been developed. The model allows simultaneous determination of optimum procurement quantity, production quantity across the different plants, transportation routes and the outsourcing cost in case of shortages. The proposed multi‐stage model is compared with the standard two‐stage model by examining the difference between the objective values of two solutions. The research clearly shows the importance of the multi‐stage model as compared to the two‐stage programming model.

The models developed here are limited to covering demand uncertainty, whereas real supply chain exhibits different uncertainties like capacity, processing time, etc. This can be the future direction for extending the work.

The model is very useful in designing and planning the supply chain in an uncertain environment. The model allows the adjustment of the production plan as time progresses and uncertainties become resolved.

The model uses a scenario approach to address the supply chain planning problem for a supply chain network structure under an uncertain environment and compares the two‐solution approach for a set of problems. Generally supply chain costs are in millions of dollars and the saving using multi‐stage programming can be significant.

The literature of organizational change hints that adaptability and inertia not only counterbalance but also reinforce each other, and the inertia-adaptability balance over time is nonlinear. The author aims to address this view more clearly by presenting a multi-stage conceptual model that delineates how adaptability and inertia take turns to override each other. In addition, data collected from over 400 nonprofit organizations within the USA were used to test this model.

This study uses polynomial regression to examine the multi-stage conceptual model. More precisely, it tests how organizational age influences an organization's innovativeness, managerial risk aversion, and red tape.

The findings support the multi-stage conceptual model. The results imply that organizational ecology and rational adaptation are mutually compatible perspectives in explaining organizational age dynamics.

This study introduces a multi-stage model that more clearly examines how adaptability and inertia counterbalance and reinforce over time. More importantly, the author empirically examines the nonlinear organizational age dynamics using quantitative data.

The purpose of this paper is to develop some weight determining methods for hesitant fuzzy multi-criterion decision making (MCDM) in which the preference information on attributes is collected over different periods.

Based on the proposed weight determining methods and dynamic hesitant fuzzy aggregation operators, an approach is developed to solve the hesitant fuzzy multi-stage multi-attribute decision-making problem where all the preference information of attributes over different periods is represented in hesitant fuzzy values.

In order to determine the weights associated with dynamic hesitant fuzzy operators, the authors propose the improved maximum entropy method and the minimum average deviation method.

This paper does not consider the multi-stage multi-criteria group decision-making problem.

An example concerning the evaluation of rangelands is given to illustrate the validation and efficiency of the proposed approach. It should be stated that the proposed approach can also be implemented into other multi-stage MCDM problems.

The concept of hesitant fuzzy variable (HFV) is defined. Some operational laws and properties of the HFVs are given. Moreover, to fuse the multi-stage hesitant fuzzy information, the aggregation operators of hesitant fuzzy sets are extended to that of the HFVs.

This article proposes a novel hybrid simulation model for understanding the complex tobacco use behavior.

The model is developed by embedding the concept of the multistage learning-based fuzzy cognitive map (FCM) into the agent-based model (ABM) in order to benefit from advantageous of each methodology. The ABM is used to represent individual level behaviors while the FCM is used as a decision support mechanism for individuals. In this study, socio-demographic characteristics of individuals, tobacco control policies, and social network effect are taken into account to reflect the current tobacco use system of Turkey. The effects of plain package and COVID-19 on tobacco use behaviors of individuals are also searched under different scenarios.

The findings indicate that the proposed model provides promising results for representing the mental models of agents. Besides, the scenario analyses help to observe the possible reactions of people to new conditions according to characteristics.

The proposed method combined ABM and FCM with a multi-stage learning phases for modeling a complex and dynamic social problem as close as real life. It is expected to contribute for both ABM and tobacco use literature.

Aiming at the problem that the transmission mechanism of the assembly error of the multi-stage rotor with saddle surface type is not clear, the purpose of this paper is to propose a deep belief network to realize the prediction of the coaxiality and perpendicularity of the multi-stage rotor.

First, the surface type of the aero-engine rotor is classified. The rotor surface profile sampling data is converted into image structure data, and a rotor surface type classifier based on convolutional neural network is established. Then, for the saddle surface rotor, a prediction model of coaxiality and perpendicularity based on deep belief network is established. To verify the effectiveness of the coaxiality and perpendicularity prediction method proposed in this paper, a multi-stage rotor coaxiality and perpendicularity assembly measurement experiment is carried out.

The results of this paper show that the accuracy rate of face type classification using convolutional neural network is 99%, which meets the requirements of subsequent assembly process. For the 80 sets of test samples, the average errors of the coaxiality and perpendicularity of the deep belief network prediction method are 0.1 and 1.6 µm, respectively.

Therefore, the method proposed in this paper can be used not only for rotor surface classification but also to guide the assembly of aero-engine multi-stage rotors.