Robustness on Intuitionistic Fuzzy Connectives
DOI:
https://doi.org/10.5540/tema.2014.015.02.0133Abstract
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.
References
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.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish in this journal agree to the following terms:
Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.
Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
author. This is in accordance with the BOAI definition of open access
Intellectual Property
All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.