Foundations of Fuzzy Sets

Lawrence N. Stout, Ulrich Höhle

Research output: Journal ArticleArticlepeer-review


This paper gives an overview of the origins of fuzzy set theory and the problems for the foundations of fuzzy sets arising from those origins and current practice. It then gives detailed accounts of categorical approaches using a closed structure to capture the fuzzy AND connective. Within these categories weak forms of subobject representations provide an internal second order logic. An approach to fuzzy real numbers and fuzzy topology is included to illustrate the use of this internal; second order theory.
Original languageAmerican English
JournalFuzzy Sets and Systems
StatePublished - 1991


  • Fuzzy sets
  • quasitopoi
  • footings
  • weak topoi.


  • Mathematics

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