In this paper, we propose a family of indistinguishability operators, that we have called Yager Possibilitic Response Functions (YPRFs for short), as an appropriate tool for allocating tasks to a collective of agents. In order to select the best agent to carry out each task, we have used the so-called response threshold method, where each agent decides the next task to perform following a probabilistic Markov process and, in addition, involves a response function which models how appropriate the task is for the agent. In previous works, we developed a new response threshold method which incorporates the use of indistinguishability operators as response functions and possibility theory instead of probability, for task allocation from a very general perspective without taking into account the specific characteristics of the agents except their limitations to carry out a task. Such an allocation is modelled by means of possibilistic, instead of probabilisitic, Markov chains. We show that possibilistic Markov chains outperform its probabilistic counterparts for the aforementioned propose. All the indistinguishability operators considered in previous papers were not able to take into account the agents’ restrictions for moving from a task to another one, or equivalently to carry out a task instead of another one. In order to avoid this handicap, we introduce a new kind of response functions, YPRFs, which are modelled by means of indistinguishability operators obtained via Yager t-norms. This new type of response functions drops to zero when an agent, due to its limitations, is not able to execute a task and, therefore, is able to model a generic multi-agent system with restrictions. The performed simulation, under Matlab, allows us to compare the results obtained using the new YPRFs with those obtained applying celebrated response functions also generated via indistinguishability operators (that we call Original Possibilitic Response Functions, OPRFs for short). Moreover, the results confirm that the YPRFs are able to take into account agent’s restrictions while the OPRFs are not able. Finally, in the light of the experimental results, we can confirm that those systems modelled.

中文翻译：

---

通过Yager t范数的可区分性算子及其在群体多Agent任务分配中的应用

在本文中，我们提出了一个不可区分的算子族，我们将其称为Yager可能响应函数（简称YPRF），作为将任务分配给一组Agent的合适工具。为了选择执行每个任务的最佳代理，我们使用了所谓的响应阈值方法，其中每个代理根据概率马尔可夫过程决定要执行的下一个任务，此外，还涉及一个响应函数，该函数对任务适合代理。在先前的工作中，我们开发了一种新的响应阈值方法，该方法结合了使用不可区分算符作为响应函数和可能性理论，而不是概率，从非常笼统的角度考虑任务分配，而不考虑代理的特定特征（执行任务的局限性除外）。这种分配是通过可能性而不是概率的马尔可夫链建模的。我们表明，对于上述提议，可能性马尔可夫链优于其概率对应物。先前论文中考虑的所有不可区分性运算符都无法考虑代理程序从一项任务转移到另一项任务，或者等效地执行一项任务而不是另一项任务的限制。为了避免这种障碍，我们引入了一种新型的响应函数YPRF，这些函数通过Yager获得的不可区分运算符进行建模 这种分配是通过可能性而不是概率的马尔可夫链建模的。我们表明，对于上述提议，可能性马尔可夫链优于其概率对应物。先前论文中考虑的所有不可区分性运算符都无法考虑代理程序从一项任务转移到另一项任务，或者等效地执行一项任务而不是另一项任务的限制。为了避免这种障碍，我们引入了一种新型的响应函数YPRF，这些函数通过Yager获得的不可区分运算符进行建模 这种分配是通过可能性而不是概率的马尔可夫链建模的。我们表明，对于上述提议，可能性马尔可夫链优于其概率对应物。先前论文中考虑的所有不可区分性运算符都无法考虑代理程序从一项任务转移到另一项任务，或者等效地执行一项任务而不是另一项任务的限制。为了避免这种障碍，我们引入了一种新型的响应函数YPRF，这些函数通过Yager获得的不可区分运算符进行建模 先前论文中考虑的所有不可区分性运算符都无法考虑代理程序从一项任务转移到另一项任务，或者等效地执行一项任务而不是另一项任务的限制。为了避免这种障碍，我们引入了一种新型的响应函数YPRF，这些函数通过Yager获得的不可区分运算符进行建模 先前论文中考虑的所有不可区分性运算符都无法考虑代理程序从一项任务转移到另一项任务，或者等效地执行一项任务而不是另一项任务的限制。为了避免这种障碍，我们引入了一种新型的响应函数YPRF，这些函数通过Yager获得的不可区分运算符进行建模t范数 当代理由于其局限性而无法执行任务，因此能够建模具有限制的通用多代理系统时，这种新型的响应功能将降至零。在Matlab下执行的仿真使我们能够将使用新YPRF所获得的结果与通过著名的响应函数所获得的结果进行比较，这些函数也通过可区分性运算符生成（我们将其称为原始可能响应函数，简称OPRF）。此外，结果证实，YPRF可以考虑代理的限制，而OPRF则不能。最后，根据实验结果，我们可以确认这些系统已建模。