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The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.

Learning and making decisions in a complex uncertain multiagent environment like RoboCup Soccer Simulation 3D is a non-trivial task. In this paper, a probabilistic approach to handle such uncertainty in RoboCup 3D is proposed, specifically a Naive Bayes classifier. Although its conditional independence assumption is not always accomplished, it has proved to be successful in a whole range of applications. Typically, the Naive Bayes model assumes discrete attributes, but in RoboCup 3D the attributes are continuous. In literature, Naive Bayes has been adapted to handle continuous attributes mainly using Gaussian distributions or discretizing the domain, both of which present certain disadvantages. In the former, the probability density of attributes is not always well-fitted by a normal distribution. In the latter, there can be loss of information. Instead of discretizing, the use of a Fuzzy Naive Bayes classifier is proposed in which attributes do not take a single value, but a set of values with a certain membership degree. Gaussian and Fuzzy Naive Bayes classifiers are implemented for the pass evaluation skill of 3D agents. The classifiers are trained with different number of training examples and different number of attributes. Each generated classifier is tested in a scenario with three teammates and four opponents. Additionally, Gaussian and Fuzzy approaches are compared versus a random pass selector. Finally, it is shown that the Fuzzy Naive Bayes approach offers very promising results in the RoboCup 3D domain.

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