Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems

Hybrid systems are dynamical systems with interacting discrete computation and continuous physical processes, which have become more common, more indispensable, and more complicated in our modern life. Particularly, many of them are safety-critical, and therefore are required to meet a critical safety standard. Invariant generation plays a central role in the verification and synthesis of hybrid systems. In the previous work, the fourth author and his coauthors gave a necessary and sufficient condition for a semi-algebraic set being an invariant of a polynomial autonomous dynamical system, which gave a confirmative answer to the open problem. In addition, based on which a complete algorithm for generating all semi-algebraic invariants of a given polynomial autonomous hybrid system with the given shape was proposed. This paper considers how to extend their work to non-autonomous dynamical and hybrid systems. Non-autonomous dynamical and hybrid systems are with inputs, which are very common in practice; in contrast, autonomous ones are without inputs. Furthermore, the authors present a sound and complete algorithm to verify semi-algebraic invariants for non-autonomous polynomial hybrid systems. Based on which, the authors propose a sound and complete algorithm to generate all invariants with a pre-defined template.     

Supply chain performance for deteriorating items with cooperative advertising

To study the effect of cooperative advertising on the supply chain of deteriorating items, this paper establishes a Stackelberg game model for a two-echelon deteriorating items supply chain composed of one manufacturer and one retailer under a given support program with an exogenous participation rate. The manufacturer as the leader determines the wholesale price and production rate, and the retailer as the follower determines the retail price and advertising strategies. The strategies of the players under the decentralized scenario and the centralized scenario are respectively characterized. Numerical simulations and sensitivity analysis are conducted to gain some managerial insights. It is shown that the pricing, advertising and production strategies are negatively correlated to deteriorating coefficient, and both the profit and the channel efficiency decrease with deteriorating coefficient; The interaction between price, advertising investment and production rate results in a higher retail price of the centralized channel compared to that of the decentralized channel; Implementing the cooperative advertising program does improve the performance of the supply chain in some cases and the participation rate roughly at 0.5 is most preferable, but it is also possible to distort incentive and damage the channel performance when the participation rate reaches a relatively high level.     

Dual hesitant fuzzy information aggregation with Einstein t-conorm and t-norm

Dual hesitant fuzzy set (DHFS) is a new generalization of fuzzy set (FS) consisting of two parts (i.e., the membership hesitancy function and the non-membership hesitancy function), which confronts several different possible values indicating the epistemic degrees whether certainty or uncertainty. It encompasses fuzzy set (FS), intuitionistic fuzzy set (IFS), and hesitant fuzzy set (HFS) so that it can handle uncertain information more flexibly in the process of decision making. In this paper, we propose some new operations on dual hesitant fuzzy sets based on Einstein t-conorm and t-norm, study their properties and relationships and then give some dual hesitant fuzzy aggregation operators, which can be considered as the generalizations of some existing ones under fuzzy, intuitionistic fuzzy and hesitant fuzzy environments. Finally, a decision making algorithm under dual hesitant fuzzy environment is given based on the proposed aggregation operators and a numerical example is used to demonstrate the effectiveness of the method.     

Risk reduction in a project portfolio

The positive impacts of managing projects as a portfolio are quantified by comparing the value of the integrated risk of a project portfolio and the aggregation of single project risks implemented separately. Firstly, the integrated risk is defined by proposing risky events based on set theory. Secondly, as projects interact with each other in a project portfolio, the integrated risk is evaluated by using a Bayesian network structure learning algorithm to construct an interdependent network of risks. Finally, the integrated risk of a practical case is assessed using this method, and the results show that the proposed method is an effective tool for calculating the extent of risk reduction of implementing a project portfolio and identifying the most risky project, so as to assist companies in making comprehensive decisions in the phase of portfolio selection and portfolio controlling.     

Feature network-driven quadrant mapping for summarizing customer reviews

With the rapid growth of e-commerce, customers increasingly write online reviews of the product they purchase. These customer reviews are one of the most valuable sources of information affecting selection of products or services. Summarizing these customer reviews is becoming an interesting area of research, inspiring researchers to develop a more condensed, concise summarization for users. However, most of the current efforts at summarization are based on general product features without feature’s relationship. As a result, these summaries either ignore feedback from customers or do a poor job of reflecting the opinions expressed in customer reviews. To remedy this summarization shortcoming, we propose a feature network-driven quadrant mapping that captures and incorporates opinions from customer reviews. Our focus is on construction of a feature network, which is based on co-occurrence and sematic similarities, and a quadrant display showing the opinions polarity of feature groups. Moreover, the proposed approach involves clustering similar product features, and thus, it is different from standard text summarization based on abstraction and extraction. The summarized results can help customers better understand the overall opinions about a product.     

Optimal bundling and pricing decisions for complementary products in a two-layer supply chain

This article explores bundling and pricing decisions for two complementary products in a two-layer supply chain consisting of a multi-product manufacturer and a retailer. We establish four different pricing models under cases of decentralized decision, while considering different portfolio-bundling strategies of the manufacturer and the retailer. A game-theoretical method is used to characterize the corresponding equilibrium outcomes in each scenario. By further analyzing and comparing the maximum profits of all four possible scenarios, optimal bundling and pricing decisions for the manufacturer and the retailer are obtained, respectively. Model extensions and numerical examples are enriched to highlight the factors affecting optimal decision-making. Finally, valuable and interesting managerial insights are summarized. Results show that the upstream manufacturer always profits more when he sells complementary products separately. However, the optimal bundling decision of the downstream retailer is jointly determined by product complementarity (as a major factor) and the difference of product profitability (as a secondary factor). Market power cannot exert an influence on both optimal bundling decisions, but it can partly affect pricing decisions.     

A partial robust optimization approach to inventory management for the offline-to-online problem under different selling prices

This study examines an optimal inventory strategy when a retailer markets a product at different selling prices through a dual-channel supply chain, comprising an online channel and an offline channel. Using the operating pattern of the offline-to-online (O2O) business model, we develop a partial robust optimization (PRO) model. Then, we provide a closed-form solution when only the mean and standard deviation of the online channel demand distribution is known and the offline channel demand follows a uniform distribution (partial robust). Specifically, owing to the good structural properties of the solution, we obtain a heuristic ordering formula for the general distribution case (i.e., the offline channel demand follows a general distribution). In addition, a series of numerical experiments prove the rationality of our conjecture. Moreover, after comparing our solution with other possible policies, we conclude that the PRO approach improves the performance of incorporating the internet into an existing supply chain and, thus, is able to adjust the level of conservativeness of the solution. Finally, in a degenerated situation, we compare our PRO approach with a combination of information approach. The results show that the PRO approach has more “robust” performance. As a result, a reasonable trade-off between robustness and performance is achieved.     

Consensus intuitionistic fuzzy group decision-making method for aircraft cockpit display and control system evaluation

A novel group decision-making (GDM) method based on intuitionistic fuzzy sets (IFSs) is developed to evaluate the ergonomics of aircraft cockpit display and control system (ACDCS). The GDM process with four steps is discussed. Firstly, approaches are proposed to transform four types of common judgement representations into a unified expression by the form of the IFS, and the features of unifications are analyzed. Then, the aggregation operator called the IFSs weighted averaging (IFSWA) operator is taken to synthesize decision-makers’ (DMs’) preferences by the form of the IFS. In this operator, the DM’s reliability weights factors are determined based on the distance measure between their preferences. Finally, an improved score function is used to rank alternatives and to get the best one. An illustrative example proves the proposed method is effective to valuate the ergonomics of the ACDCS.     

F-117A飞机外形隐身性能的研究

本文简要地介绍了美国隐身战斗机F—117A的有关情况,并模拟了F-117A的外形,制作了模型,经雷达测试后,得出在各姿态角下的雷达散射截面,用突防理论对F—117A进行隐身性能分析。并据此得出了应加强具有隐身性能材料研究的结论。     

单相介质受热管集中参数模型建模方法的改进

本文对工程中广泛应用的、以流体出口温度作为流体代表温度的单相介质受热管集中参数模型进行了深入分析,利用动态因子对模型进行改进。使模型精度明显提高,模型刚度大大下降。这一方法物理意义清楚。数学分析严密。既可以用于小偏差线性化模型,也可以用于大扰动非线性模型。具有较大工程实用价值。