On the computer certification of fuzzy numbers

The formalization of fuzzy sets in terms of corresponding membership functions is already available in machine-verified mathematical knowledge base. We show how it can be extended to provide the development of fuzzy numbers fully benefitting from the existing framework. The flexibility which is offered by automated proof-assistants allowed us to overcome some initial difficulties. Although fuzziness stems from the same background as rough set theory, i.e. incomplete or imprecise information, both formal approaches are substantially different.