ROBUSTNESS OF THE TRIPLE IMPLICATION INFERENCE METHOD BASED ON THE WEIGHTED LOGIC METRIC

[1] R. Belohlavek, Fuzzy Relational Systems, Foundations and Principles, Kluwer Academic
Publishers, Dordrecht, (2002), 40-116.
[2] K. Y. Cai, -equalities of fuzzy sets, Fuzzy Sets and Systems, 76(1) (1995), 97-112.
[3] K. Y. Cai, Robustness of fuzzy reasoning and -equalities of fuzzy sets, IEEE Transactions
on Fuzzy Systems, 9(5) (2001), 738-750.
[4] G. S. Cheng and Y. X. Fu, Error estimation of perturbations under CRI, IEEE Transactions
on Fuzzy Systems, 14(6) (2006), 709-715.
[5] S. S. Dai, D. W. Pei and S. M. Wang, Perturbation of fuzzy sets and fuzzy reasoning based
on normalized Minkowski distances, Fuzzy Sets and Systems, 189 (2012), 63-73.
[6] S. S. Dai, D. W. Pei and D. H. Guo, Robustness analysis of full implication inference method,
International Journal of Approximate Reasoning, 54(5) (2013), 653-666.
[7] D. Dubois, J. Lang and H. Prade, Fuzzy sets in approximate reasoning, parts 1 and 2, Fuzzy
Sets and Systems, 40(1) (1991), 143-244.
[8] P. Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, (1998),
27-29.
[9] D. H. Hong and S. Y. Hwang, A note on the value similarity of fuzzy systems variables,
Fuzzy Sets and Systems, 66(3) (1994), 383-386.
[10] E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Kluwer Academic Publishers,
Dordrecht, (2000), 4-6.
[11] J. Li and J. T. Yao, Theory of integral truth degrees of formula in SMTL propositional logic,
Acta Electronica Sinica, 41(5) (2013), 878-883.
[12] Y. M. Li, D. C. Li, W. Pedrycz and J. J. Wu, An approach to measure the robustness of fuzzy
reasoning, International Journal of Intelligent Systems, 20(4) (2005), 393-413.
[13] H. W. Liu and G. J. Wang, Continuity of triple I methods based on several implications,
Computers and Mathematics with Applications, 56(8) (2008), 2079-2087.
[14] H. W. Liu and G. J. Wang, A note on the unied forms of triple I method, Computers and
Mathematics with Applications, 52(10) (2006), 1609-1613.
[15] H. W. Liu and G. J. Wang, Unied forms of fully implicational restriction methods for fuzzy
reasoning, Information Sciences, 177(3) (2007), 956-966.

[16] H. W. Liu and G. J. Wang, Triple I method based on pointwise sustaining degrees, Computers
and Mathematics with Applications, 55(11) (2008), 2680-2688.
[17] M. X. Luo and N. Yao, Triple I algorithms based on Schweizer- Sklar operators in fuzzy
reasoning, International Journal of Approximate Reasoning, 54(5) (2013), 640-652.
[18] C. P. Pappis, Value approximation of fuzzy systems variables, Fuzzy Sets and Systems, 39(1)
(1991), 111-115.
[19] D. W. Pei, Unied full implication algorithms of fuzzy reasoning, Information Sciences,
178(2) (2008), 520-530.
[20] G. J. Wang, Non-classical Mathematical Logic and Approximate Reasoning, second ed., Sci-
ence Press, Beijing, China, (2008), 155-165.
[21] G. J.Wang, Introduction to Mathematical Logic and Resolution Principle, second ed., Science
Press, Beijing, China, (2006), 160-162.
[22] G. J. Wang and H. Wang, Non-fuzzy versions of fuzzy reasoning in classical logics, Informa-
tion Sciences, 138 (2001), 211-236.
[23] G. J. Wang and J. Y. Duan, On robustness of the full implication triple I inference method
with respect to ner measurements, International Journal of Approximate Reasoning, 55(3)
(2014),787-796.
[24] S. W. Wang and W. X. Zheng, Real Variable Function and Functional Analysis, Higher
Education Press, Beijing, China, (2005), 4-5.
[25] G. J. Wang, The full implication triple I method of fuzzy reasoning, SCIENCE CHINA Ser.
E 29 (1999), 43-53.
[26] G. J. Wang and J. Y. Duan, Two types of fuzzy metric spaces suitable for fuzzy reasoning,
Science China Information Sciences, 44(5) (2014), 623-632.
[27] G. J. Wang and L. Fu, Unied forms of triple I method, Computers and Mathematics with
Applications, 49(5) (2005), 923-932.
[28] G. J. Wang, Formalized theory of general fuzzy reasoning, Information Sciences, 160(1)
(2004), 251-266.
[29] R. R. Yager, On some new classes of implication operators and their role in approximate
reasoning, Information Sciences, 167(1-4) (2004), 193-216.
[30] M. S. Ying, Perturbation of fuzzy reasoning, IEEE Transactions on Fuzzy Systems, 7(5)
(1999), 625-629.
[31] L. A. Zadeh, Outline of a new approach to the analysis of complex systems and decision
processes, IEEE Transactions on Systems Man and Cybernetics, 3(1) (1973), 28-33.