The random generation of fuzzy measures under complex linear constraints holds significance in various fields, including optimization solutions, machine learning, decision making, and property investigation. However, most existing random generation methods primarily focus on addressing the monotonicity and normalization conditions inherent in the construction of fuzzy measures, rather than the linear constraints that are crucial for representing special families of fuzzy measures and additional preference information. In this paper, we present two categories of methods to address the generation of linearly constrained fuzzy measures using linear programming models. These methods enable a comprehensive exploration and coverage of the entire feasible convex domain. The first category involves randomly selecting a subset and assigning measure values within the allowable range under given linear constraints. The second category utilizes convex combinations of constrained extreme fuzzy measures and vertex fuzzy measures. Then we employ some indices of fuzzy measures, objective functions, and distances to domain boundaries to evaluate the coverage performance of these methods across the entire feasible domain. We further provide enhancement techniques to improve the coverage ratios. Finally, we discuss and demonstrate potential applications of these generation methods in practical scenarios.

Abstract Question‐and‐answer (Q&A) sites improve access to information and ease transfer of knowledge. In recent years, they have grown in popularity and importance, enabling research on behavioral patterns of their users. We study the dynamics related to the casting of 7 M votes across a sample of 700 k posts on Stack Overflow, a large community of professional software developers. We employ log‐Gaussian mixture modeling and Markov chains to formulate a simple yet elegant description of the considered phenomena. We indicate that the interevent times can naturally be clustered into 3 typical time scales: those which occur within hours, weeks, and months and show how the events become rarer and rarer as time passes. It turns out that the posts' popularity in a short period after publication is a weak predictor of its overall success, contrary to what was observed, for example, in case of YouTube clips. Nonetheless, the sleeping beauties sometimes awake and can receive bursts of votes following each other relatively quickly.

There is a mutual resemblance between the behavior of users of the Stack Exchange and the dynamics of the citations accumulation process in the scientific community, which enabled us to tackle the outwardly intractable problem of assessing the impact of introducing “negative” citations. Although the most frequent reason to cite an article is to highlight the connection between the 2 publications, researchers sometimes mention an earlier work to cast a negative light. While computing citation‐based scores, for instance, the h‐index, information about the reason why an article was mentioned is neglected. Therefore, it can be questioned whether these indices describe scientific achievements accurately. In this article we shed insight into the problem of “negative” citations, analyzing data from Stack Exchange and, to draw more universal conclusions, we derive an approximation of citations scores. Here we show that the quantified influence of introducing negative citations is of lesser importance and that they could be used as an indicator of where the attention of the scientific community is allocated.