Response-threshold methods stand out among the different developed swarm-like methodologies that address the task allocation problem, which must be faced in multi-robot systems in order to assign to each robot the best task to perform at each instant of time. In many real missions the tasks have associated deadlines. However, the literature only contains a few swarm methodologies, and thus response-threshold methods, tackling tasks with deadlines. Motivated by this fact, in this paper, we propose a new task allocation strategy inspired by response-threshold methods which deals with tasks with time deadlines, models stimuli using fuzzy sets and, in addition, in which each robot makes the decision about the best task to perform through the celebrated Bellman-Zadeh fuzzy optimization technique. An extensive number of simulations have been carried out in order to evaluate the quantitative performance of the swarm system based on the new approach. The results confirm that the proposed mathematical approach is able to model the evolution of the system when tasks with deadlines are under consideration. We have also observed competitive performance on a fleet of real robots, which corroborates the results derived from the simulations.

Many fields in applied sciences, like Artificial Intelligence and Computer Science, use aggregation methods to provide new generalized metrics from a collection of old ones. Thus, the problem of merging by means of a function a collection of generalized metrics into a single one has been recently studied in depth. Moreover, the mipoint sets for a generalized metric involving fuzzy sets have shown a great potential in medical diagnosis and decision making since it models the concept of “compromise” or “middle way” between two positions. Joining these facts, the aim of this paper is to provide a general framework for the study of midpoint sets for quasimetrics via aggregation theory. In particular, we determine the properties that an aggregation function must satisfy to characterize the midpoint set for a quasimetric generated by means of the fusion of a collection of quasimetrics in terms of the midpoint sets for each of the quasimetrics that are merged. In fact, this study generalizes the results for metrics in this context that are retrieved as a particular case of the exposed theory. Finally, some particular results for generalized metrics defined for fuzzy sets are proved.