Abstract
A characterization of fuzzy bags with fuzzy integers (ℕf) provides a general framework in which sets, bags, fuzzy sets and fuzzy bags are treated in a uniform way. In bag theory, the difference between two bags A and B is the relative complement of A intersection B to A. With fuzzy bags defined on ℕf, this difference does not always exist and, in such a case, only approximations of the exact result can be defined. The problem comes from the fact that the fuzzy bag model considered so far is based on positive fuzzy integers. In this paper, we show that fuzzy relative integers (ℤf) offer a well-founded framework in which the difference of two fuzzy bags is always defined.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bosc P., Rocacher D., “About difference operations on fuzzy bags”, 9 th Inter. Conf. IPMU, pp 1441–1546, 2002.
Dubois D., Prade H., “Inverse operations for fuzzy numbers”, Proc. IFAC symp. On fuzzy information, knowledge representation and decision analysis, Marseille, pp 391–396, 1983.
Dubois D., Prade H., “Fuzzy set theoretic differences and inclusions and their use in the analysis of fuzzy equations”, Control and Cybernetics, vol 13, n° 3, 1984.
Dubois D., Prade H., “Fuzzy cardinality and modeling of imprecise quantification”, Fuzzy Sets and Systems, 16,3, pp 199–230, 1985.
Miyamoto S., “Fuzzy Multisets and Fuzzy Clustering of Documents”, 10 th Inter. Conf. on Fuzzy Systems, (FUZZ IEEE’01), 2001.
Sanchez E., “Solutions of fuzzy equations with extended operations”, Fuzzy Set and Systems, 12, pp 237–248, 1984.
Rocacher D., “On the use of fuzzy numbers in flexible querying”, 9 th IFSA World Cong. and 20 th NAFIPS Inter. Conf., pp 2440–2445, 2001.
Yager R., “On the Theory of Bags”, Inter. J. of General Systems, vol. 13, pp 23–27, 1986.
Zadeh L. A., “A computational approach to fuzzy quantifiers in natural languages”, Comp. Math. App., vol. 9, pp 149–184, 1983.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bosc, P., Rocacher, D. (2003). About Zf, the Set of Fuzzy Relative Integers, and the Definition of Fuzzy Bags on Zf . In: Bilgiç, T., De Baets, B., Kaynak, O. (eds) Fuzzy Sets and Systems — IFSA 2003. IFSA 2003. Lecture Notes in Computer Science, vol 2715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44967-1_10
Download citation
DOI: https://doi.org/10.1007/3-540-44967-1_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40383-8
Online ISBN: 978-3-540-44967-6
eBook Packages: Springer Book Archive