Bayesian networks, Fuzzy set theory, Probabilistic Inference

Our work is motivated by the applications of probabilistic models in the social sciences, in which surveys and questionnaires are typically used to collect respondents’ opinions via a Likert scale. The dividing lines between the states on the Likert scale are vague, so it is natural to interpret them using fuzzy numbers instead of integers. We treat the true model variables as hidden continuous variables, the values of which are observed only through their fuzzified counterparts. This approach seems more conceptually appropriate in the context of surveys and questionnaires, since the modeled variables are continuous by nature but are only observed on a fuzzy, discrete scale. Probabilistic inference with continuous variables is challenging when the assumption of normality of the variables’ distribution is violated, which is particularly true for variables modeling polarizing issues. We approximate continuous, multidimensional probability distributions using an F-transform composedof basic functions with central points, called nodes, at a multidimensional grid. We illustrate the suggested approach using a small Bayesian network model of data from the survey “Dividing Lines in Czech Society.”

Our work is motivated by the applications of probabilistic models in the social sciences, in which surveys and questionnaires are typically used to collect respondents’ opinions via a Likert scale. The dividing lines between the states on the Likert scale are vague, so it is natural to interpret them using fuzzy numbers instead of integers. We treat the true model variables as hidden continuous variables, the values of which are observed only through their fuzzified counterparts. This approach seems more conceptually appropriate in the context of surveys and questionnaires, since the modeled variables are continuous by nature but are only observed on a fuzzy, discrete scale. Probabilistic inference with continuous variables is challenging when the assumption of normality of the variables’ distribution is violated, which is particularly true for variables modeling polarizing issues. We approximate continuous, multidimensional probability distributions using an F-transform composedof basic functions with central points, called nodes, at a multidimensional grid. We illustrate the suggested approach using a small Bayesian network model of data from the survey “Dividing Lines in Czech Society.”