# Labeled Fuzzy Rough Sets Versus Fuzzy Flow Graphs

### Leszek Rolka, Alicja Mieszkowicz-Rolka

#### Abstract

This paper presents the idea of labeled fuzzy rough sets which constitutes a novel approach to rough approximation of fuzzy information systems. The labeled fuzzy rough sets approach is compared with the fuzzy flow graph approach. The standard definition of fuzzy rough sets is based on comparing the elements of a universe by using a fuzzy similarity relation. This is a complex task, especially in the case of large universes. The idea of labeled fuzzy rough sets consists in comparison of elements of the universe to some ideals represented by linguistic values of attributes. Every element of the universe can be bound up with a linguistic label. Fuzzy rough approximations of any fuzzy set are obtained by describing its elements with the help of characteristic elements of linguistic labels. In this paper, new parameterized notions of the positive, boundary, and negative linguistic values are introduced.

#### References

- Dubois, D. and Prade, H. (1992). Putting rough sets and fuzzy sets together. In Slowi Áski, R., editor, Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, pages 203- 232, Boston Dordrecht London. Kluwer Academic Publishers.
- Mieszkowicz-Rolka, A. and Rolka, L. (2004). Fuzzy implication operators in variable precision fuzzy rough sets model. In Rutkowski, L. et al., editors, Artificial Intelligence and Soft Computing - ICAISC 2004. Lecture Notes in Artificial Intelligence, volume 3070, pages 498-503, Berlin Heidelberg New York. Springer-Verlag.
- Mieszkowicz-Rolka, A. and Rolka, L. (2006). Flow graphs and decision tables with fuzzy attributes. In Rutkowski, L. et al., editors, Artificial Intelligence and Soft Computing - ICAISC 2006. Lecture Notes in Artificial Intelligence, volume 4029, pages 268-277, Berlin Heidelberg New York. Springer-Verlag.
- Mieszkowicz-Rolka, A. and Rolka, L. (2014). Flow graph approach for studying fuzzy inference systems. Procedia Computer Science, 35:681-690. sciencedirect.com/science/journal/18770509/35.
- Mieszkowicz-Rolka, A. and Rolka, L. (2016). A novel approach to fuzzy rough set-based analysis of information systems. In Swai t?ek, J. et al., editors, Information Systems Architecture and Technology. Knowledge Based Approach to the Design, Control and Decision Support, volume 432 of Advances in Intelligent Systems and Computing, pages 173-183, Switzerland. Springer International Publishing.
- Pawlak, Z. (1991). Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Boston Dordrecht London.
- Pawlak, Z. (2005a). Flow graphs and data mining. In Peters, J. F. et al., editors, Transactions on Rough Sets III. Lecture Notes in Computer Science (Journal Subline), volume 3400, pages 1-36, Berlin Heidelberg New York. Springer-Verlag.
- Pawlak, Z. (2005b). Rough sets and flow graphs. In Sel?zak, D. et al., editors, Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Lecture Notes in Artificial Intelligence, volume 3641, pages 1-11, Berlin Heidelberg New York. Springer-Verlag.
- Radzikowska, A. M. and Kerre, E. E. (2002). A comparative study of fuzzy rough sets. Fuzzy Sets and Systems, 126:137-155.
- Zadeh, L. (1965). Fuzzy sets. Information and Control, 8:338-353.

#### Paper Citation

#### in Harvard Style

Rolka L. and Mieszkowicz-Rolka A. (2016). **Labeled Fuzzy Rough Sets Versus Fuzzy Flow Graphs** . In *Proceedings of the 8th International Joint Conference on Computational Intelligence - Volume 2: FCTA, (IJCCI 2016)* ISBN 978-989-758-201-1, pages 115-120. DOI: 10.5220/0006083301150120

#### in Bibtex Style

@conference{fcta16,

author={Leszek Rolka and Alicja Mieszkowicz-Rolka},

title={Labeled Fuzzy Rough Sets Versus Fuzzy Flow Graphs},

booktitle={Proceedings of the 8th International Joint Conference on Computational Intelligence - Volume 2: FCTA, (IJCCI 2016)},

year={2016},

pages={115-120},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006083301150120},

isbn={978-989-758-201-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 8th International Joint Conference on Computational Intelligence - Volume 2: FCTA, (IJCCI 2016)

TI - Labeled Fuzzy Rough Sets Versus Fuzzy Flow Graphs

SN - 978-989-758-201-1

AU - Rolka L.

AU - Mieszkowicz-Rolka A.

PY - 2016

SP - 115

EP - 120

DO - 10.5220/0006083301150120