Laplace operator, fuzzy transform, fuzzy partition, proximity

Simple and understandable representation is required in many research areas, but especially in mathematics. Therefore, we use existing possibilities of how to define Laplace operator and extend these by the possibility of representation of this operator by means of fuzzy transform. Fuzzy transform allows us to unify both - discrete and continuous - cases of definitions, which is one of the main advantages of this approach. Moreover, we show that this F-transform-based representation of the Laplace operator can be described in terms of well-known Laplace-Beltrami operator.