Fuzzy Topologies Induced by Fuzzy Relation Based Modifiers

@inproceedings{Cock2001FuzzyTI,
  title={Fuzzy Topologies Induced by Fuzzy Relation Based Modifiers},
  author={Martine De Cock and Etienne E. Kerre},
  booktitle={Fuzzy Days},
  year={2001}
}
In this paper we highlight the specific meaning of images of fuzzy sets under fuzzy relations in the context of fuzzy topology. More precisely we show that fuzzy modifiers taking direct and superdirect images of fuzzy sets under fuzzy pre-orderings are respectively closure and interior operators, inducing fuzzy topologies. Furthermore we investigate under which conditions the same applies to the recently introduced general closure and opening operators based on arbitrary fuzzy relations. 

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References

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Showing 1-10 of 16 references

Images under Fuzzy relations: A Master-Key to Fuzzy Applications

M. De Cock, M. Nachtegael, E. E. Kerre
Ruan, D., Abderrahim, H. A., D’hondt, P., Kerre, E. E. (eds.): Intelligent Techniques and Soft Computing in Nuclear Science and Engineering, Proceedings of FLINS 2000. World Scientific • 2000

Modelling Linguistic Modifiers Using Fuzzy-Rough Structures

M. De Cock, A. Radzikowska, E. E. Kerre
Proceedings of IPMU2000 • 2000

On Links between Fuzzy Morphology and Fuzzy Rough Sets

M. Nachtegael, A. Radzikowska, E. E. Kerre
Proceedings of IPMU2000 • 2000

Linguistic Modifiers: an overview

E. E. Kerre, M. De Cock
Chen, G., Ying, M., Cai, K.-Y. (eds.): Fuzzy Logic and Soft Computing. Kluwer Academic Publishers • 1999

Interpreting Linguistic Hedges by Concepts of Functional Analysis and Mathematical Logic

H. Thiele
Proceedings of EUFIT’98, volume I • 1998

Fuzzy Topology

L. Ying-Ming, L. Mao-Kang
Advances in Fuzzy Systems - Applications and Theory Vol. 9. World Scientific, Singapore, New Jersey, London, Hong Kong • 1997

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