The Pythagorean fuzzy set as an extension of the intuitionistic fuzzy set characterized by membership and nonmembership degrees has been introduced recently. Accordingly, the square sum of the membership and nonmembership degrees is a maximum of one. The Pythagorean fuzzy set has been previously applied to multiattribute group decision-making. This study develops a few aggregation operators for fusing the Pythagorean fuzzy information, and a novel approach to decision-making is introduced based on the proposed operators. First, we extend the generalized Bonferroni mean to the Pythagorean fuzzy environment and introduce the generalized Pythagorean fuzzy Bonferroni mean and the generalized Pythagorean fuzzy Bonferroni geometric mean. Second, a new generalization of the Bonferroni mean, namely, the dual generalized Bonferroni mean, is proposed by considering the shortcomings of the generalized Bonferroni mean. Furthermore, we investigate the dual generalized Bonferroni mean in the Pythagorean fuzzy sets and introduce the dual generalized Pythagorean fuzzy Bonferroni mean and dual generalized Pythagorean fuzzy Bonferroni geometric mean. Third, a novel approach to multiattribute group decision-making based on proposed operators is proposed. Lastly, a numerical instance is provided to illustrate the validity of the new approach.
Many forecasting techniques have been applied to sales forecasts in the retail industry. However, no one prediction model is applicable to all cases. For demand forecasting of the same item, the different results of prediction models often confuse retailers. For large retail companies with a wide variety of products, it is difficult to find a suitable prediction model for each item. This study aims to propose a dynamic model selection approach that combines individual selection and combination forecasts based on both the demand patterns and the out-of-sample performance for each item. Firstly, based on both metrics of the squared coefficient of variation (CV2) and the average inter-demand interval (ADI), we divide the demand patterns of items into four types: smooth, intermittent, erratic, and lumpy. Secondly, we select nine classical forecasting methods in the M-Competitions to build a pool of models. Thirdly, we design two dynamic weighting strategies to determine the final prediction, namely DWS-A and DWS-B. Finally, we verify the effectiveness of this approach by using two large datasets from an offline retailer and an online retailer in China. The empirical results show that these two strategies can effectively improve the accuracy of demand forecasting. The DWS-A method is suitable for items with the demand patterns of intermittent and lumpy, while the DWS-B method is suitable for items with the demand patterns of smooth and erratic.
A dynamic model for a double-bubble system in compressible liquid under the coupling effect of ultrasound and electrostatic field was developed here. In this study, we mainly discussed the effect of the interaction on the investigated bubble using the numerical solutions to the theoretic model. The variable parameters are the distance between bubble centers and the initial radius of the adjacent bubble. In addition, we applied approximate equations to analyse variations of the internal gas pressure and temperature of a bubble. We found that, the oscillation amplitude of a bubble with an adjacent bubble significantly reduces, compared to that of an isolated bubble.
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