Indistinguishability Operators via Yager t -norms and Their Applications to Swarm Multi-Agent Task Allocation

Maria-del-Mar Bibiloni-Femenias, José Guerrero, Juan-José Miñana and Oscar Valero
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Maria-del-Mar Bibiloni-Femenias: Department of Mathematics and Computer Science, University of the Balearic Islands, Ctra. de Valldemossa Km. 7.5, 07122 Palma, Baleares, Spain
José Guerrero: Department of Mathematics and Computer Science, University of the Balearic Islands, Ctra. de Valldemossa Km. 7.5, 07122 Palma, Baleares, Spain
Juan-José Miñana: Department of Mathematics and Computer Science, University of the Balearic Islands, Ctra. de Valldemossa Km. 7.5, 07122 Palma, Baleares, Spain
Oscar Valero: Department of Mathematics and Computer Science, University of the Balearic Islands, Ctra. de Valldemossa Km. 7.5, 07122 Palma, Baleares, Spain

Mathematics, 2021, vol. 9, issue 2, 1-21

Abstract: 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.

Keywords: Yager t -norm; indistinguishability operator; possibility theory; multi-agent; task allocation; Swarm Intelligence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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