Abstract
The “fuzzy” approach to the question of cardinality of a fuzzy set offers a very adequate and complete cardinal information in the form of a convex fuzzy set of ordinary cardinal numbers (of nonnegative integers, in the finite case). The existing studies of that approach, however, are restricted to cardinalities of fuzzy sets with the classical min and max operations. In this paper, we like to present a generalization of FGCounts to triangular norm-based fuzzy sets. Some remarks about an analogous generalization of FLCounts and FECounts will be given, too.
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
Dubois, D., Prade, H.: Fuzzy Cardinality and the Modeling of Imprecise Quantification. Fuzzy Sets and Systems 16 (1985) 199–230
Gottwald, S.: Many-Valued Logic and Fuzzy Set Theory. In: Hôhle, U., Rodabaugh, S.E. (eds.): Mathematics of Fuzzy Sets. Logic, Topology, and Measure Theory. Kluwer Acad. Publ., Boston Dordrecht London (1999) 5–89
Ling, C.H.: Representation of Associative Functions, Publ. Math. Debrecen 12 (1965) 189–212
Liu, Y., Kerre, E.E.: An Overview of Fuzzy Quantifiers. Part I: Interpretation. Fuzzy Sets and Systems 95 (1998) 1–21
Lowen, R.: Fuzzy Set Theory. Basic Concepts, Techniques and Bibliography. Kluwer Acad. Publ., Dordrecht Boston London (1996)
Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic. CRC Press, Boca Raton (1997)
Weber, S.: A General Concept of Fuzzy Connectives, Negations and Implications Based on t-Norms and t-Conorms. Fuzzy Sets and Systems 11 (1983) 115–134
Wygralak, M.: Fuzzy Cardinals Based on the Generalized Equality of Fuzzy Subsets. Fuzzy Sets and Systems 18 (1986) 143–158
Wygralak, M.: Vaguely Defined Objects. Representations, Fuzzy Sets and Nonclassical Cardinality Theory. Kluwer Acad. Publ., Dordrecht Boston London (1996)
Wygralak, M.: Questions of Cardinality of Finite Fuzzy Sets. Fuzzy Sets and Systems 102 (1999) 185–210
Wygralak, M.: Triangular Operations, Negations, and Scalar Cardinality of a Fuzzy Set. In: Zadeh, L.A., Kacprzyk, J. (eds.): Computing with Words in Information/Intelligent Systems 1. Foundations. Physica-Verlag, Heidelberg New York (1999) 326–341
Wygralak, M.: Fuzzy Sets with Triangular Norms and their Cardinality Theory. Fuzzy Sets and Systems, submitted
Zadeh, L.A.: A Theory of Approximate Reasoning. In: Hayes, J.E., Michie, D., Mikulich, L.I. (eds.): Machine Intelligence 9. Wiley, New York (1979) 149–184
Zadeh, L.A.: A Computational Approach to Fuzzy Quantifiers in Natural Languages. Comput. and Math. with Appl. 9 (1983) 149–184
Zadeh, L.A.: From Computing with Numbers to Computing with Words–From Manipulation of Measurements to Manipulation of Perceptions. IEEE Trans. on Circuits and Systems–I: Fundamental Theory and Appl. 45 (1999) 105–119
Zadeh, L.A.: Fuzzy Logic = Computing with Words. In: Zadeh, L.A., Kacprzyk, J. (eds.): Computing with Words in Information/Intelligent Systems 1. Foundations. Physica-Verlag, Heidelberg New York (1999) 3–23
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wygralak, M., Pilarski, D. (2000). FGCounts of Fuzzy Sets with Triangular Norms. In: Hampel, R., Wagenknecht, M., Chaker, N. (eds) Fuzzy Control. Advances in Soft Computing, vol 6. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1841-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1841-3_8
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1327-2
Online ISBN: 978-3-7908-1841-3
eBook Packages: Springer Book Archive