Fuzzy functions: a fuzzy extension of the category SET and some related categories

• Höhle, Ulrich ^[1] ; Porst, Hans-E. ^[2] ; Sostak, Alexander P. ^[3]
  1. [1] University of Wuppertal

     University of Wuppertal

     Kreisfreie Stadt Wuppertal, Alemania

     
  2. [2] University of Bremen

     University of Bremen

     Kreisfreie Stadt Bremen, Alemania

     
  3. [3] University of Latvia

     University of Latvia

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 1, Nº. 1, 2000, págs. 115-127
• Idioma: inglés
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  • In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -> L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.