Towards fuzzy linguistic Markov chains

In this contribution we deal with the problem of doing computations with a Markov chain when the information about transition probabilities is expressed linguistically. This could be the case, for instance, if the process we are modeling is described by a human expert, for whom the use of linguistic labels is easier than being forced to give inexact numerical probabilities which, in turn, may yield an unstable chain. We address the uncertainty of linguistic judgments by introducing fuzzy probabilities, and carry on the calculation of the linguistic stationary distribution of the chain by resorting to an existing fuzzy approach with restricted matrix multiplication. Preliminary results are very promising and deserve further research.