Fuzzy Euclidean Normed Spaces for Data Mining Applications

  • Sorin Nădăban Aurel Vlaicu University of Arad Romania, 310330 Arad, Elena Dragoi, 2 *Corresponding author: snadaban@gmail.com

Abstract

The aim of this paper is to introduce some special fuzzy norms on Kn and to obtain, in this way, fuzzy Euclidean normed spaces. In order to introduce this concept we have proved that the cartesian product of a finite family of fuzzy normed linear spaces is a fuzzy normed linear space. Thus any fuzzy norm on K generates a fuzzy norm on Kn. Finally, we prove that each fuzzy Euclidean normed space is complete. Fuzzy Euclidean normed spaces can be proven to be a suitable tool for data mining. The method is based on embedding the data in fuzzy Euclidean normed spaces and to carry out data analysis in these spaces.

References

[1] Bag, T., Samanta, S.K. (2003); Finite dimensional fuzzy normed linear spaces, Journal of uzzy Mathematics, 11(3): 687–705.

[2] Bag, T., Samanta, S.K. (2005); Fuzzy bounded linear operators, Fuzzy Sets and Systems, 51: 513–547.

[3] Dzitac, I., Moisil, I. (2008); Advanced AI techniques for web mining, Proceedings of the 0th WSEAS international conference on Mathematical methods, computational techniques, on-linear systems, intelligent systems, 343–346.

[4] Hüllermeier, E. (2005); Fuzzy methods in machine learning and data mining: Status and rospects. Fuzzy Sets and Systems, 156(3): 387–406.
http://dx.doi.org/10.1016/j.fss.2005.05.036

[5] Katsaras, A.K. (1984); Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12: 43–154.
http://dx.doi.org/10.1016/0165-0114(84)90034-4

[6] Nădăban, S., Dzitac, I. (2014); Atomic Decompositions of Fuzzy Normed Linear Spaces for avelet Applications, Informatica, (in press).

[7] Saadati, R., Vaezpour, S.M. (2005); Some results on fuzzy Banach spaces, J. Appl. Math. & Computing, 17(1-2): 475–484.

[8] Saadati, R., Park, J.H. (2006); Intuitionistic fuzzy Euclidean normed spaces, Communications n Mathematical Analysis, 1(2): 85–90.

[9] Saadati, R., Park, J.H. (2006); On the intuitionistic fuzzy topological spaces, Chaos, Solitons nd Fractals, 27: 331–344.

On the intuitionistic fuzzy topological spaces, Chaos, Solitons nd Fractals, 27: 331–344.

[10] Schweizer, B., Sklar, A. (1960); Statistical metric spaces, Pacific J. Math., 10: 314–334.
Published
2014-11-17
How to Cite
NĂDĂBAN, Sorin. Fuzzy Euclidean Normed Spaces for Data Mining Applications. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 10, n. 1, p. 70-77, nov. 2014. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/1564>. Date accessed: 27 sep. 2020. doi: https://doi.org/10.15837/ijccc.2015.1.1564.

Keywords

fuzzy norm, fuzzy Euclidean normed spaces, data mining