Email this article Robustness on Intuitionistic Fuzzy Connectives
Abstract
The main contribution of this paper is concerned with the robustness of intuitionistic fuzzy connectives in fuzzy reasoning. Starting with an evaluation of the sensitivity in $n$-order functions on the class of intuitionistic fuzzy sets, we apply the results in the intuitionistic $(S,N)$-implication class. The paper formally states that the robustness preserves the projection functions in such class.
Full Text:
PDFReferences
References
K. Atanassov and G. Gargov, Elements of Intuitionistic Fuzzy Logic. Part I, Fuzzy Sets and Systems, 95 (1989) 39–52.
K. H. Atanassov, and G. Gargov, Interval Valued Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 31 (1989) 343–349.
K. Atanassov, Intuitionistic Fuzzy Sets, Theory and Applications, Physica- Verlag, Heidelberg, 1999.
M. Baczyński, On some properties of intuitionistic fuzzy implication, EUSFLAT 2003 - 3rd Conference of the European Society for Fuzzy Logic and Technology (M. Wagenknecht and R. Hampel, eds.) pp. 168–171, Zittau, 2003.
B. Bedregal, G. Dimuro, R. Santiago, R. Reiser, On interval fuzzy S- implications, Information Sciences, 180 No. 8 (2010) 1373–1389.
H. Bustince, E. Barrenechea, V. Mohedano, Intuitionistic fuzzy implication op- ertors – an expression and main properties, Int. Journal of Uncertainty, Fuzzi- ness and Knowledge-Based Systems (IJUFKS), 12 No. 3 (2004) 387 – 406.
K. Cai, Robustness of fuzzy reasoning and σ−Equalities of Fuzzy Sets. IEEE Transaction on Fuzzy Systems, 9 No. 5 (2001) 738–750.
G. Cornelis, G. Deschrijver, and E. Kerre, On the Representation of Intuition- istic Fuzzy t-Norms and t-conorms, IEEE Transactions on Fuzzy Systems, 12 No. 1 (2004) 45–61.
Reiser and Bedregal
G. Cornelis, G. Deschrijver, and E. Kerre, Implications in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification and application, Int. Journal of Approximate Reasoning, 35 (2004) 55–95.
D. Dubois, W. Ostasiewisz and H. Prade, Fundamentals of Fuzzy Sets, Fuzzy Sets: History and Basic Notions, “The Handbook of Fuzzy Sets Series" ( Didier Dubois and Henri Prade, eds.), pp. 21-106 Kluwer, Boston, 2000.
J. Fodor and M. Roubens, “Fuzzy Preference Modelling and Multicriteria De- cision Support”, Dordrecht: Kluwer Academic Publisher, 1994.
J. Jin, Y. Li and C. Li, Robustness of fuzzy reasoning via locally equivalence measure. Information Sciences, 177 No. 22 (2007) 5103–5177.
Y. Li, D. Li, W. Pedrycz and J. Wu, An approach to measure the robustness of fuzzy reasoning, Int. Journal of Intelligent Systems, 20 No. 4 (2005) 393–413.
Y. Li, Approximation and robustness of fuzzy finite automata, Int. Journal of Approximate Reasoning, 47 No. 2 (2008) 247–257.
R. Reiser and B. Bedregal, Robustness of N-dual fuzzy connectives, “ Ad- vances in Intelligent and Soft Computing - EUROFUSE2011 - Fuzzy Methods for Knowledge-Based Systems”, CITAB Research Centre UTAD University, Régua, pp. 79–90, Springer, Heidelberg, 2011.
R. Reiser and B. Bedregal, Robustness of intuitionistic fuzzy connectives, “Proceedings of CNMAC 2012 - Congresso Nacional de Matemática Aplicada e Computacional”, SBMAC, Águas de Lindóia, pp. 1–10, 2012.
R. Santiago, B. Bedregal, and B. Acióly, Formal aspects of correctness and optimalityofintervalcomputations, FormalAspectsofComputing,182(2006) 231–243.
M. Ying, Perturbation on fuzzy reasoning, IEEE Transactions on Fuzzy Sys- tems, 7 (1999) 625–629.
Zadeh, L.A. (1965) Fuzzy sets, Information and Control, 15 No. 6 338–353.
L. Zhang and K. Cai, Optimal fuzzy reasoning and its robustness analysis, Int. Journal of Intelligent Systems, 19 No. 11 (2004) 1033–1049.
DOI: https://doi.org/10.5540/tema.2014.015.02.0133
Article Metrics
Metrics powered by PLOS ALM
Refbacks
- There are currently no refbacks.
Trends in Computational and Applied Mathematics
A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
Indexed in:
Desenvolvido por:
