Fuzzy Markov Chains and Experiments with FuzzRank, an Alternative to PageRank
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The theory of Markov chains has been applied successfully in several situations, for example in the PageRank algorithm which powers Google search. In this thesis we study the foundations of fuzzy logic and Markov chains before introducing fuzzy Markov chains. Fuzzy Markov chains were introduced in 1970 as an alternative to the usual Markov chains and have some interesting properties that may make them more desirable for some applications. We will consider some of these properties and see how they differ from the usual Markov chains. We will also study an application of fuzzy Markov chains called FuzzRank, a twist on the aforementioned PageRank algorithm used for web search. Finally, we will consider a further generalization of the fuzzy Markov chains where we allow some flexibility in the operations we use during matrix multiplication to compute our results.