A General Framework for Ordering Fuzzy Sets
Orderings and rankings of fuzzy sets have turned out to play a fundamental role in various disciplines. Throughout the previous 25 years, a lot a different approaches to this issue have been introduced, ranging from rather simple ones to quite exotic ones. The aim of this paper is to present a new framework for comparing fuzzy sets with respect to a general class of fuzzy orderings. This approach includes several known techniques based on generalizing the crisp linear ordering of real numbers by means of the extension principle, however, in its general form, it is applicable to any fuzzy subsets of any kind of universe for which a fuzzy ordering is known - no matter whether linear or partial.
KeywordsConvex Hull Residuated Lattice Fuzzy Subset Fuzzy Relation Triangular Norm
Unable to display preview. Download preview PDF.
- 1.R. Babuška. Construction of fuzzy systems—interplay between precision and transparency. In Proc. ESIT 2000, pages 445–452, Aachen, 2000.Google Scholar
- 3.U. Bodenhofer. A Similarity-Based Generalization of Fuzzy Orderings, volume C 26 of Schriftenreihe der Johannes-Kepler- Universität Linz. Universitätsverlag Rudolf Trauner, 1999.Google Scholar
- 5.U. Bodenhofer and P. Bauer. Towards an axiomatic treatment of “interpretability”. In Proc. IIZUKA2000, pages 334–339, Iizuka, October 2000.Google Scholar
- 12.E. E. Kerre, M. Mareš, and R. Mesiar. On the orderings of generated fuzzy quantities. In Proc. IPMU’98, volume 1, pages 250–253, 1998.Google Scholar
- 14.E. P. Klement, R. Mesiar, and E. Pap. Triangular Norms, volume 8 of Trends in Logic. Kluwer Academic Publishers, Dordrecht, 2000.Google Scholar
- 17.R. Kruse, J. Gebhardt, and F. Klawonn. Foundations of Fuzzy Systems. John Wiley & Sons, New York, 1994.Google Scholar