Abstract
In this paper, we introduce the operations of union, intersection, and complement for preorder-based fuzzy sets. The given operations are even capable of dealing with fuzzy sets that have membership degrees coming from different preordered sets. This enables us to handle the difficult situation in which one has different people giving judgements and they all like to use their own language and expressions.
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
Preview
Unable to display preview. Download preview PDF.
References
Birkhoff, G.: Lattice Theory, Colloquim publications, 3rd edn. vol. XXV, American Mathematical Society (AMS), Providence, Rhode Island (1995)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)
Goguen, J.A.: L-fuzzy sets. Journal of Mathematical Analysis and Applications 18, 145–174 (1967)
Järvinen, J.: Lattice theory for rough sets. In: Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 400–498. Springer, Heidelberg (2007)
Järvinen, J., Kortelainen, J.: A unifying study between modal-like operators, topologies, and fuzzy sets. Fuzzy Sets and Systems 158, 1217–1225 (2007)
Kortelainen, J.: On relationship between modified sets, topological spaces and rough sets. Fuzzy Sets and Systems 61, 91–95 (1994)
Lowen, R.: Fuzzy Set Theory: Basic Concepts, Techniques and Bibliography. Kluwer Academic Publishers, Norwell, MA (1996)
Steiner, A.K.: The lattice of topologies: structure and complementation. Transactions of the American Mathematical Society 122, 379–398 (1966)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Zadeh, L.A.: From computing with numbers to computing with words – from manipulation of measurements to manipulation of perceptions. International Journal of Applied Mathematics and Computer Science 12, 307–324 (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Järvinen, J. (2007). Set Operations for L-Fuzzy Sets. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds) Rough Sets and Intelligent Systems Paradigms. RSEISP 2007. Lecture Notes in Computer Science(), vol 4585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73451-2_24
Download citation
DOI: https://doi.org/10.1007/978-3-540-73451-2_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73450-5
Online ISBN: 978-3-540-73451-2
eBook Packages: Computer ScienceComputer Science (R0)