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I have the book Artificial Intelligence: A Modern Approach (by Stuart Rusell). I am reading chapter 16, "Making simple decisions", but I do not get the main idea of the utility theory, can you provide a detailed example?

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Utility functions are a product of Utility Theory which is one of the disciplines that helps to address the challenges of building knowledge under uncertainty. It is often combined with the probabilistic theory to create decision-theoretic agents. Utility Theory lays out the foundation to create and evaluate Utility Functions. Typically, Utility Theory uses the notion of Expected Utility (EU) as a value that represents the average utility of all possible outcomes of a state, weighted by the probability that the outcome occurs. 

For more knowledge, refer the following link:

https://www.cs.brandeis.edu/~psyc/ai/decision/utility.htm

Here you can refer the following link for knowing the Applications of Utility Theory in Artificial Intelligence Research:

https://link.springer.com/chapter/10.1007/978-3-642-46609-0_17

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