Double Fuzzy Implications-Based Restriction Inference Algorithm

[1] M. Baczynski and B. Jayaram, Fuzzy implications (Studies in Fuzziness and Soft Computing,
Vol. 231), Springer, Berlin Heidelberg, 2008.
[2] 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.
[3] D. Dubois and H. Prade, Fuzzy sets in approximate reasoning, Part 1: Inference with possi-
bility distributions, Fuzzy Sets and Systems, 40 (1991), 143-202.
[4] J. Fodor, On contrapositive symmetry of implications in fuzzy logic, First European Congress
on Fuzzy and Intelligent Technologies, Aachen, (1993), 1342{1348.
[5] J. Fodor and M. Roubens, Fuzzy Preference Modeling and Multicriteria Decision Support,
Kluwer Academic Publishers, Dordrecht, 1994.
[6] S. Gottwald, A treatise on many-valued logics, Research Studies Press, Baldock, 2001.
[7] P. Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998.
[8] J. Hou, F. You and H. X. Li, Fuzzy systems constructed by triple I algorithm and their
response ability, Progress in Natural Science, 15 (2005), 29-37.
[9] B. Jayaram, On the law of importation (x ^ y) ! z  (x ! (y ! z)) in fuzzy logic, IEEE
Transactions on Fuzzy Systems, 16 (2008), 130-144.
[10] E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Kluwer Academic Publishers,
Dordrecht, 2000.
[11] H. X. Li, Probability representations of fuzzy systems, Science in China. Series F, 49 (2006),
339-363.
[12] H. X. Li, F. You and J. Y. Peng, Fuzzy controllers based on some fuzzy implication operators
and their response functions, Progress in Natural Science, 14 (2004), 15-20.
[13] H. W. Liu, Fully implicational methods for approximate reasoning based on interval-valued
fuzzy sets, Journal of Systems Engineering and Electronics, 21 (2010), 224-232.
[14] H. W. Liu and G. J. Wang, Continuity of triple I methods based on several implications,
Computers and Mathematics with Applications, 56 (2008), 2079-2087.
[15] H. W. Liu and C. Li, Fully implicational methods for interval-valued fuzzy reasoning
with multi-antecedent rules, International Journal of Computational Intelligence Systems,
4 (2011), 929-945.
[16] M. Mas, M. Monserrat, J. Torrens and E. Trillas, A survey on fuzzy implication functions,
IEEE Transactions on Fuzzy Systems, 15 (2007), 1107-1121.
[17] D. W. Pei, R0 implication: characteristics and applications, Fuzzy Sets and Systems, 131
(2002), 297-302.
[18] D. W. Pei, On the strict logic foundation of fuzzy reasoning, Soft Computing, 8 (2004),
539-545.
[19] D. W. Pei, Unied full implication algorithms of fuzzy reasoning, Information Sciences, 178
(2008), 520-530.
[20] D. W. Pei, Formalization of implication based fuzzy reasoning method, International Journal
of Approximate Reasoning, 53 (2012), 837-846.

[21] J. Y. Peng, Fully implicational triple I restriction algorithm for fuzzy reasoning based on
some familiar implication operators, Progress in Natural Science, 15 (2005), 539-546.
[22] H. Seki and M. Mizumoto, SIRMs connected fuzzy inference method adopting emphasis and
suppression, Fuzzy Sets and Systems, 215 (2013), 112-126.
[23] S. J. Song, C. B. Feng and C. X. Wu, Theory of restriction degree of triple I method with
total inference rules of fuzzy reasoning, Progress in Natural Science, 11 (2001), 58-66.
[24] S. J. Song, C. B. Feng and E. S. Lee, Triple I method of fuzzy reasoning, Computers and
Mathematics with Applications, 44 (2002), 1567-1579.
[25] Y. M. Tang and X. P. Liu, Dierently implicational universal triple I method of (1, 2, 2)
type, Computers and Mathematics with Applications, 59 (2010), 1965-1984.
[26] Y. M. Tang, F. J. Ren and Y. X. Chen, Reversibility of FMT-universal triple I method
based on IL operator, American Journal of Engineering and Technology Research, 11 (2011),
2763-2766.
[27] Y. M. Tang, F. J. Ren and Y. X. Chen, Universal triple I method and its application to textual
emotion polarity recognition, In: Third International Conference on Quantitative Logic and
Soft Computing, Xi'an, China, (2012), 189-196.
[28] L. X. Wang, A course in fuzzy systems and control, Prentice-Hall, Englewood Clis, NJ,
1997.
[29] G. J. Wang, Fully implicational triple I method for fuzzy reasoning, Science in China. Series
E, 29 (1999), 43-53.
[30] G. J. Wang and L. Fu, Unied forms of triple I method, Computers and Mathematics with
Applications, 49 (2005), 923-932.
[31] G. J. Wang and H. J. Zhou, Introduction to Mathematical Logic and Resolution Principle,
Science Press, Beijing and Alpha Science International Limited, Oxford, U.K., 2009.
[32] 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 (1973), 28{44.
[33] J. C. Zhang and X. Y. Yang, Some properties of fuzzy reasoning in propositional fuzzy logic
systems, Information Sciences, 180 (2010), 4661-4671.