Robustness of f- and g-generated Fuzzy (Co)Implications: The Yager's (Co)Implication Case Study

This paper studies the robustness of intuitionistic fuzzy implications in fuzzy reasoning based on Atanassov's intuitionistic fuzzy logic. Starting with an evaluation of the sensitivity in representable fuzzy negations, we apply the results in the Yager's classes of fuzzy implications called the f- and g-generated fuzzy implications. The paper formally states that the robustness preserves the projection functions in such class and also discusses their corresponding dual operators.

[1]  Witold Pedrycz,et al.  An approach to measure the robustness of fuzzy reasoning: Research Articles , 2005 .

[2]  Humberto Bustince,et al.  Intuitionistic Fuzzy Implication Operators - An Expression And Main Properties , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[3]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[4]  Ronald R. Yager,et al.  On some new classes of implication operators and their role in approximate reasoning , 2004, Inf. Sci..

[5]  J. Fodor On fuzzy implication operators , 1991 .

[6]  Michal Baczynski,et al.  Yager's classes of fuzzy implications: some properties and intersections , 2007, Kybernetika.

[7]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[8]  Michal Baczynski,et al.  Fuzzy Implications , 2008, Studies in Fuzziness and Soft Computing.

[9]  Benjamín R. C. Bedregal,et al.  Towards robustness and duality analysis of intuitionistic fuzzy aggregations , 2015, 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[10]  Chunquan Li,et al.  Robustness of fuzzy reasoning via logically equivalence measure , 2007, Inf. Sci..

[11]  J. Fodor Contrapositive symmetry of fuzzy implications , 1995 .

[12]  George Gargov,et al.  Elements of intuitionistic fuzzy logic. Part I , 1998, Fuzzy Sets Syst..

[13]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[14]  Vladik Kreinovich,et al.  A new class of fuzzy implications. Axioms of fuzzy implication revisited , 1998, Fuzzy Sets Syst..

[15]  Balasubramaniam Jayaram,et al.  Bandler–Kohout Subproduct With Yager’s Classes of Fuzzy Implications , 2012, IEEE Transactions on Fuzzy Systems.

[16]  Chris Cornelis,et al.  On the representation of intuitionistic fuzzy t-norms and t-conorms , 2004, IEEE Transactions on Fuzzy Systems.

[17]  Renata Reiser,et al.  Robustness on intuitionistic fuzzy connectives , 2014 .

[18]  Michal Baczynski On some properties of intuitionistic fuzzy implications , 2003, EUSFLAT Conf..

[19]  Etienne E. Kerre,et al.  Smets-magrez Axioms for R-implicators in Interval-valued and Intuitionistic Fuzzy Set Theory , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[20]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[21]  Michal Baczynski,et al.  (S, N)- and R-implications: A state-of-the-art survey , 2008, Fuzzy Sets Syst..

[22]  Regivan H. N. Santiago,et al.  Canonical representation of the Yager’s classes of fuzzy implications , 2013, Computational and Applied Mathematics.

[23]  Keyun Qin,et al.  Robustness of fuzzy connectives and fuzzy reasoning , 2013, Fuzzy Sets Syst..

[24]  Mingsheng Ying,et al.  Perturbation of fuzzy reasoning , 1999, IEEE Trans. Fuzzy Syst..

[25]  Yongming Li,et al.  Approximation and robustness of fuzzy finite automata , 2008, Int. J. Approx. Reason..

[26]  Witold Pedrycz,et al.  An approach to measure the robustness of fuzzy reasoning , 2005, Int. J. Intell. Syst..

[27]  Benjamín R. C. Bedregal,et al.  Robustness of N-Dual Fuzzy Connectives , 2011, Eurofuse.

[28]  Yongjian Xie,et al.  Robustness of interval-valued fuzzy inference , 2011, Inf. Sci..