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The authors acknowledge financial support from FEDER/Ministerio de Ciencia, Innovacion y Universidades-Agencia Estatal de Investigacion/Proyecto PGC2018-095709-B-C21. This work is also partially supported by Programa Operatiu FEDER 2014-2020 de les Illes Balears, by project PROCOE/4/2017 (Direccio General d'Innovacio i Recerca, Govern de les Illes Balears) and by projects ROBINS and BUGWRIGHT2. These two latest projects have received funding from the European Union's Horizon 2020 research and innovation programme under grant agreements No 779776 and No 871260, respectively. This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein.

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Miñana, Juan-José;

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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.

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