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Appl. Sci. 2017, 7(10), 963; doi:10.3390/app7100963

Indistinguishability Operators Applied to Task Allocation Problems in Multi-Agent Systems

Department of Mathematics and Computer Science, University of the Balearic Islands, Ctra. de Valldemossa Km. 7.5, 07122 Palma, Baleares, Spain
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Received: 2 August 2017 / Revised: 1 September 2017 / Accepted: 16 September 2017 / Published: 21 September 2017
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Abstract

In this paper we show an application of indistinguishability operators to model response functions. Such functions are used in the mathematical modeling of the task allocation problem in multi-agent systems when the stimulus, perceived by the agent, to perform a task is assessed by means of the response threshold model. In particular, we propose this kind of operators to represent a response function when the stimulus only depends on the distance between the agent and a determined task, since we prove that two celebrated response functions used in the literature can be reproduced by appropriate indistinguishability operators when the stimulus only depends on the distance to each task that must be carried out. Despite the fact there is currently no systematic method to generate response functions, this paper provides, for the first time, a theoretical foundation to generate them and study their properties. To validate the theoretical results, the aforementioned indistinguishability operators have been used to simulate, with MATLAB, the allocation of a set of tasks in a multi-robot system with fuzzy Markov chains. View Full-Text
Keywords: task allocation; multi-agents; multi-robot; swarm; response function; t-norm; additive generator; indistinguishability operator; distance task allocation; multi-agents; multi-robot; swarm; response function; t-norm; additive generator; indistinguishability operator; distance
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MDPI and ACS Style

Guerrero, J.; Miñana, J.-J.; Valero, O.; Oliver, G. Indistinguishability Operators Applied to Task Allocation Problems in Multi-Agent Systems. Appl. Sci. 2017, 7, 963.

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