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Irrational-behavior-proof (IBP) conditions are important aspects to keep stable cooperation in dynamic cooperative games. In this paper, we focus on the establishment of IBP conditions. Firstly, the relations of three kinds of IBP conditions are described. An example is given to show that they may not hold, which could lead to the fail of cooperation. Then, based on a kind of limit characteristic function, all these conditions are proved to be true along the cooperative trajectory in a transformed cooperative game. It is surprising that these facts depend only upon the individual rationalities of players for the Shapley value and the group rationalities of players for the core. Finally, an illustrative example is given.

Exploring consumer preferences for a product is essential for the enterprise in product improvement. Many studies have been conducted in consumer preference. However, few studies have concentrated on evaluating the product and service characteristics of a specific product, to facilitate product and service improvements. This study proposes a systematic research framework for exploring major product and service features that reflect consumer preferences based on the online reviews. By creatively integrating quantitative studies of multiple linear regression and meta-analysis, this study expects to generate a feature-based preference importance ranking. Furthermore, by adopting an importance-satisfaction analysis, we can draw a matrix that is valuable in product improvement. Coupled with the preference rankings, implications for competitive strategies that facilitate product improvement can be drawn. The effectiveness of this methodology is verified by a case study of laptop on the basis of the online reviews from amazon.cn.

The experience of consumers for products has great effect on the pre-sale strategy. Based on this, the paper studies the selection and pricing of multi-channel marketing models consisting of a brewer, an electronic retailer and a traditional retailer, constructing the non-cooperative game model of brewers and retailers with equal status in four contexts. Finally, the result shows that the introduction of direct channel is beneficial to increase the brewer’s revenue. When the pre-sale marginal revenue is greater than two times the average spot-sale marginal revenue, the total profit of supply chain will achieve the best under mode I. i.e. both the brewer and e-retailer adopt pre-sale strategy.

According to the actual situation of investor network, a SE2IR rumor spreading model with hesitating mechanism is proposed, and the corresponding mean-field equations is obtained on scale-free network. In this paper, we first combine the theory of spreading dynamics and find out the basic reproductive number R0. And then analyzes the stability of the rumor-free equilibrium and the final rumor size. Finally, we discuss random immune strategies and target immune strategies for the rumor spreading, respectively. Through numerical simulation, we can draw the following conclusions: Reducing the fuzziness and attractiveness of invest market rumor can effectively reduce the impact of rumor. And the target immunization strategy is more effective than the random immunization strategy for the communicators in the invest investor network.

In order to distinguish with effect different hesitant fuzzy elements (HFEs), we introduce the asymmetrical relative entropy between HFEs as a distance measure for higher discernment. Next, the formula of attribute weights is derived via an optimal model according to TOPSIS from the relative closeness degree constructed by the discerning relative entropy. Then, we propose the concept of co-correlation degree from the viewpoint of probability theory and develop another new formula of hesitant fuzzy correlation coefficient, and prove their similar properties to the traditional correlation coefficient. To make full use of the existing similarity measures including the ones presented by us, we consider aggregation of similarity measures for hesitant fuzzy sets and derive the synthetical similarity formula. Finally, the derived formula is used for netting clustering analysis under hesitant fuzzy information and the effectiveness and superiority are verified through a comparison analysis of clustering results obtained by other clustering algorithms.

In this paper, Noether’s theorem and its inverse theorem are proved for the fractional variational problems based on logarithmic Lagrangian systems. The Hamilton principle of the systems is derived. And the definitions and the criterions of Noether’s symmetry and Noether’s quasi-symmetry of the systems based on logarithmic Lagrangians are given. The intrinsic relation between Noether’s symmetry and the conserved quantity is established. At last an example is given to illustrate the application of the results.