Abstract
We sketch two constructions of universes of fuzzy sets, which are closed under ‘fuzzification’, i.e. each containing its fuzzy subsets. Both constructions use in different degree fuzzy logic, which is also used to formulate and prove properties of the fuzzy sets and functions of these universes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
R. Giles, “Lukasiewicz logic and fuzzy set theory” Internat. J. Man-Machine Studies 8, 313–327 (1976).
S. Gottwald, “A cumulative system of fuzzy sets” Set Theory Hierarchy Theory, Mem. Tribute A. Mos-towski, Bierutowice 1975, Lect. Notes Math. 537, 109–119 (1976).
D. Klaua, “Über einen zweiten Ansatz zur mehrwertigen Mengenlehre” Monatsber. Deutsche Akad. Wiss. Berlin 8, 161–177 (1966).
C. V. Negoita and D. A. Ralescu, Applications of Fuzzy Sets to Systems Analysis (Birkh äuser, Basel-Stuttgart, 1975).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 The World Organisation of General Systems and Cybernetics
About this chapter
Cite this chapter
Gottwald, S. (1978). Universes of Fuzzy Sets, Closed Under Fuzzification. In: Rose, J. (eds) Current Topics in Cybernetics and Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93104-8_229
Download citation
DOI: https://doi.org/10.1007/978-3-642-93104-8_229
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-93106-2
Online ISBN: 978-3-642-93104-8
eBook Packages: Springer Book Archive