Abstract
Abstract This paper is a comparison and contrast of approaches to many-valued mathematics offered by Fuzzy Set Theory and topos theory. It gives a survey of the categorical foundations of Fuzzy Set theory and related topoi. Topoi are not a basis for Fuzzy Set theory butthey do suggest appropriate directions to go and questions to ask for a synthesis which does provide a foundation. One possible structure which has a lopos-like internal logic and the rich variety of loggical connectives used in fuzzy sets is included.
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