Practical computing with interactive fuzzy variables

• A general-purpose Fuzzy Calculator is developed to propagate epistemic uncertainty through a function or model.
• Interactivity between fuzzy variables is accounted for by using t-norms or a possibilistic clustering algorithm.
• Results illustrate that the Fuzzy Calculator is an efficient tool to propagate epistemic uncertainty regarding non-interactive as well as interactive fuzzy input variables.

The importance of epistemic uncertainty in engineering is being recognized more and more. In this work, epistemic uncertainty is captured through the use of fuzzy variables, i.e. variables that are described in terms of possibility distributions. Taking into account epistemic uncertainty implies that one should also be able to propagate such uncertainty through increasingly complex models. In earlier work, we have developed a general tool, called Fuzzy Calculator, to propagate epistemic uncertainty regarding non-interactive fuzzy input variables. In reality, however, the fuzzy input variables of a model are often interactive. Taking into account this interactivity reduces the uncertainty on the fuzzy output variable and should therefore always be aimed for. However, the full determination of the joint possibility distribution of the fuzzy input variables is not an easy task. In literature, it is often claimed that triangular norms can be used to model interactivity between fuzzy variables. Making use of a generalization of Nguyen's alpha-cut approach, we have developed a general-purpose Fuzzy Calculator that is able to take into account interactivity modelled by a triangular norm. However, the absence of a general strategy to select an appropriate triangular norm often results in the use of other strategies to model interactivity in practice. Therefore, we have also applied our Fuzzy Calculator to a case study where the interactivity between the fuzzy input variables is identified through possibilistic clustering. The results illustrate that this Fuzzy Calculator is an efficient tool to propagate epistemic uncertainty regarding non-interactive as well as interactive fuzzy input variables.