Foundations of a set theory for fuzzy sets. 40 years of development

Abstract

Besides their importance for applications, fuzzy sets as generalized sets call for a set theoretic understanding.

This paper concisely surveys the different types of approaches toward this foundational problem which have been offered during the 40 years since fuzzy sets first have appeared in print.

Keywords:

• fuzzy set theory
• universes of fuzzy sets
• axiom systems for fuzzy sets
• categories of fuzzy sets

Notes

¹ Personal communication from Klaua to this author: the discussion happened after a colloquium talk Menger had given in East Berlin in the mid-1960s.