Abstract
Our aim in this chapter is to give a brief overview of the main aspects of fuzzy logic. We introduce the concept of fuzzy logic and discuss its philosophical background. We argue that people encounter a phenomenon of indeterminacy which has two complementary facets, namely uncertainty and vagueness. Fuzzy logic is then considered as a mathematical model useful for modelling of the latter. Furthermore, we outline the theory of special structures, which are suitable for representation of the structure of truth values.
The research has been supported by the grant A1187901/99 of the GA AV ČR and the project VS96037 of the MŠMT of the Czech Republic.
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
Black, M. (1937). “Vagueness: An Exercise in Logical Analysis,” Philosophy of Science 4, 427–455. Reprinted in Int. J. of General Systems 17 (1990), 107–128.
Butnariu, D. and Klement, E. P. (1993). Triangular Norm-based Measures and Games with Fuzzy Coalitions. Dordrecht: Kluwer.
Chang, C. C. and Keisler, H. J. (1973). Model Theory, Amsterdam: North-Holland.
Cohen, P. M. (1965), Universal algebra, New York: Harper and Row.
van Dalen, D. (1994). Logic and Structure, Berlin: Springer.
Gottwald, S. (1993). Fuzzy Sets and Fuzzy Logic. Wiesbaden: Vieweg.
Gottwald, S.: A Treatise on Many-Valued Logics. Research Studies Press Ltd., Baldock, Herfordshire, UK (to appear)
Hajek, P. (1998). Metamathematics of fuzzy logic. Dordrecht: Kluwer.
Klir, G.J. and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications. New York: Prentice-Hall.
Mundici, D., Cignoli, R. and D’Ottaviano, I.M.L. (2000). Algebraic foundations of many-valued Reasoning. Dordrech: Kluwer.
Novak, V. (1992). The Alternative Mathematical Model of Linguistic Semantics and Pragmatics. New York: Plenum.
Novak, V. (1995), V. (1995). “Linguistically Oriented Fuzzy Logic Controller and Its Design,” Int. J. of Approximate Reasoning 1995, 12, 263–277.
Novak, V., Perfilieva, I. and J. Mockoi (1999). Mathematical Principles of Fuzzy Logic. Boston: Kluwer.
Vopénka, P. (1979). Mathematics In the Alternative Set Theory. Leipzig: Teubner.
Zadeh, L. A. (1965). “Fuzzy Sets,” Inf. Control. 8, 338–353.
Zadeh, L.A. (1975). “The concept of a linguistic variable and its application to approximate reasoning I, II, III,” Inf. Sci., 8, 199–257, 301–357; 9, 43–80.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Novák, V., Perfilieva, I. (2001). The Principles of Fuzzy Logic: Its Mathematical and Computational Aspects . In: Di Nola, A., Gerla, G. (eds) Lectures on Soft Computing and Fuzzy Logic. Advances in Soft Computing, vol 11. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1818-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1818-5_12
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1396-8
Online ISBN: 978-3-7908-1818-5
eBook Packages: Springer Book Archive