Paper:

# A Trust Evaluation of Networks Utilizing Matrix Operations Based on *t*-norms and *t*-conorms

## Masaya Nohmi, Aoi Honda, and Yoshiaki Okazaki

Kyushu Institute of Technology, Iizuka, Fukuoka, 820-8502, Japan

*t*-norm, fuzzy matrix, fuzzy graph, trust evaluation, fuzziness

A new scheme for numerical trust evaluation of networks is proposed. Matrix operations based on *t*-norms and *t*-conorms are used for the evaluation. The algebraic properties of the matrix operations are studied. Fuzzy graphs, in which nodes are linked with some membership value, are proposed, using the matrices as adjacent matrices. Furthermore, the fuzzinesses of the trustability distribution are calculated.

*t*-norms and

*t*-conorms,”

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.16, No.1, pp. 154-161, 2012.

- [1] R. Hemasinha, N. R. Pal, and J. C. Bezdek, “The determinant of a fuzzy matrix with respect to t and co-t norms,” Fuzzy Sets and Systems, Vol.87, pp. 297-306, 1997.
- [2] M. Z. Ragab and E. G. Emam, “The determinant and adjoint of a square fuzzy matrix,” Fuzzy Sets and Systems, Vol.61, pp. 297-307, 1994.
- [3] K. Fukuchi, A. Honda, M. Nohmi, and Y. Okazaki, “Trust evaluations of networks employing t-norms and t-conorms,” Trans. of Heart and Mind 2008, pp. 35-39, 2008. (in Japanese)
- [4] M. Garcia, G. Navarro-Arribas, S. N. Foley, V. Torra, and J. Borrell, “Flexible Security Inter-Domain Interoperability Through Attribute Conversion,” Information Sciences, Vol.181, No.16, pp. 3491-3507, 2011.
- [5] J. Nin, B. Carminati, E. Ferrari, and V. Torra, “Computing reputation for collaborative private networks,” Proc. of the 33rd Annual IEEE Int. Computer Software and Applications Conf., COMPSAC 2009, Seattle, Washington, pp. 246-253, July 20-24, 2009. ISBN: 978-0-7695-3726-9
- [6] J. Nin and V. Torra, “Possibilistic Reasoning for Trust-Based Access Control Eforcement in Social Networks,” Proc. FUZZ-IEEE 2010/WCCI , Barcelona, 2010. ISBN: 978-1-4244-6919-2
- [7] M. Nohmi, A. Honda, and Y. Okazaki, “Matrix operations derived from t-norms and t-conorms and applications,” J. of Japan Society for Fuzzy Theory and Intelligent Informatics, Vol.22, No.4, pp. 472-480, 2010. (in Japanese)
- [8] M. Nohmi, A. Honda, and Y. Okazaki, “Algebraic Properties ofMatrix Operations Derived from t-norms and t-conorms and Applications to Trust Evaluation of Networks,” Proc. of Modeling Decisions for Artificial Intelligence 2010, 2010. (CD-ROM Ver.)
- [9] N. Nakajima, “All the Features of t-norms,” Fuzzy Soft Science Series, Soft Science Research Division of Japan Society for Fuzzy Theory and Intelligent Informatics, 2001. (in Japanese)

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.