Forward and backward fuzzy rule base interpolation using fuzzy geometry

[1] P. Baranyi, I. M. Bavelaar, R. Bubuˇska, L. T. K´oczy, A. Titli, H. B. Verbruggen, A method to invert a linguistic
fuzzy model, International Journal of Systems Science, 29(7) (1998), 711-721.

[2] P. Baranyi, T. D. Gedeon, L. T. K´oczy, A general interpolation technique in fuzzy rule bases with arbitrary membership functions, In Systems, Man, and Cybernetics, 1996, IEEE International Conference on, 1 (1996), 510-515.

[3] P. Baranyi, L. T. K´oczy, A general and specialised solid cutting method for fuzzy rule interpolation, Journal BUSEFAL, URA-CNRS, Universit´e Paul Sabatier, (1996), 13-22.

[4] P. Baranyi, D. Tikk, T. D. Gedeon, L. T. K´oczy, Alpha-cut interpolation technique in the space of regular conclusion,
9th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE’00), San Antonio, Texas, USA, 7-10 May, 2000,
478-482. ISBN: 0-7803-5877-5.

[5] R. E. Bellman, E. Richard, L. Asker Zadeh, Decision-making in a fuzzy environment, Management Science, 17(4)
(1970), B-141.

[6] S. Blaˇzic, I. Skrjanc, ˇ Design and stability analysis of fuzzy model-based predictive control-a case study, Journal of
Intelligent and Robotic Systems, 49(3) (2007), 279-292.

[7] D. Chakraborty, S. Das, Fuzzy geometry: Perpendicular to fuzzy line segment, Information Sciences, 468 (2018),
213-225.

[8] T. Chen, C. Shang, J. Yang, F. Li, Q. Shen, A new approach for transformation-based fuzzy rule interpolation, IEEE
Transactions on Fuzzy Systems, 28(12) (2019), 3330-3344.

[9] S. Das, D. Chakraborty, Conceptualizing fuzzy line as a collection of fuzzy points, Information Sciences, 598 (2022),
86-100.

[10] S. Das, D. Chakraborty, Graphical method to solve fuzzy linear programming, S´adhan´a, 47(4) (2022), 259.

[11] S. Das, D. Chakraborty, L. T. K´oczy, Linear fuzzy rule base interpolation using fuzzy geometry, International
Journal of Approximate Reasoning, 112 (2019), 105-118.

[12] S. Das, D. Chakraborty, L. T. K´oczy, Process of inversion in fuzzy interpolation model using fuzzy geometry, In
2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), (2020), 1-8.

[13] D. Dubois, Gradual rules and the approximation of control laws, Theoretical Aspects of Fuzzy Control, (1995),
147-181.

[14] D. Dubois, H. Prade, Gradual inference rules in approximate reasoning, Information Sciences, 61(1-2) (1992),
103-122.

[15] S. Jin, R. Diao, C. Quek, Q. Shen, Backward fuzzy rule interpolation, IEEE Transactions on Fuzzy Systems, 22(6)
(2014), 1682-1698.

[16] S. Jin, R. Diao, Q. Shen, α-cut-based backward fuzzy interpolation, In 2014 IEEE 13th International Conference on
Cognitive Informatics and Cognitive Computing, (2014), 211-218.

[17] S. Jin, Q. Shen, J. Peng, Backward fuzzy rule interpolation, Springer, 2019.

[18] Z. C. Johany´ak, S. Kov´acs, Fuzzy rule interpolation by the least squares method, In 7th International Symposium
of Hungarian Researchers on Computational Intelligence (HUCI 2006), (2006), 495-506.

[19] Z. C. Johany´ak, S. Kov´acs, Fuzzy rule interpolation based on polar cuts, In Computational Intelligence, Theory
and Applications, Springer, Berlin, Heidelberg, (2006), 499-511.

[20] Z. C. Johany´ak, S. Kov´acs, Polar-cut based fuzzy model for petrophysical properties prediction, Scientific Bulletin of
“Politehnica” University of Timisoara, Romania, Transactions on Automatic Control and Computer Science, 57(67)
(2008), 195-200.

[21] D. Hl´adek, J. Vascak, P. Sincak, Hierarchical fuzzy inference system for robotic pursuit evasion task, In Applied
Machine Intelligence and Informatics, 2008. SAMI 2008. 6th International Symposium on, (2008), 273-277.

[22] Z. Huang, Q. Shen, Scale and move transformation-based fuzzy interpolative reasoning: A revisit, In 2004 IEEE
International Conference on Fuzzy Systems (IEEE Cat. No. 04CH37542), 2 (2004), 623-628.

[23] Z. Huang, Q. Shen, Fuzzy interpolative reasoning via scale and move transformations, IEEE Transactions on Fuzzy
Systems, 14(2) (2006), 340-359.

[24] Z. Huang, Q. Shen, Fuzzy interpolation and extrapolation: A practical approach, IEEE Transactions on Fuzzy
Systems, 16(1) (2008), 13-28.

[25] L. K´oczy, K. Hirota, Approximate reasoning by linear rule interpolation and general approximation, International
Journal of Approximate Reasoning, 9(3) (1993), 197-225.

[26] L. T. K´oczy, S. Kov´acs, On the preservation of the convexity and piecewise linearity in linear fuzzy rule interpolation,
Tokyo Institute of Technology, Yokohama, Japan, Technical Reports TR, (1993), 93-94.

[27] L. T. K´oczy, S. Kov´acs, Shape of the fuzzy conclusion generated by linear interpolation in trapezoidal fuzzy rule
bases, In Proceedings of the 2nd European Congress on Intelligent Techniques and Soft Computing, Aachen, (1994),
1666-1670.

[28] L. T. K´oczy, S. Kov´acs, The convexity and piecewise linearity of the fuzzy conclusion generated by linear fuzzy rule
interpolation, Journal of BUSEFAL, 60 (1994), 23-29.

[29] S. Kov´acs, L. T. K´oczy, Application of interpolation-based fuzzy logic reasoning in behaviour-based control structures,
In Fuzzy Systems, 2004. Proceedings. 2004 IEEE International Conference on, 3 (2004), 1543-1548.

[30] F. Li, C. Shang, Y. Li, Q. Shen, Interpretable mammographic mass classification with fuzzy interpolative reasoning,
Knowledge-Based Systems, 191 (2020), 105279.

[31] F. Li, C. Shang, Y. Li, J. Yang, Q. Shen, Approximate reasoning with fuzzy rule interpolation: Background and
recent advances, Artificial Intelligence Review, 54(6) (2021), 4543-4590.

[32] H. Lv, F. Li, C. Shang, Q. Shen, W-Infer-polation: Approximate reasoning via integrating weighted fuzzy rule
inference and interpolation, Knowledge-Based Systems, (2022), 109995.

[33] E. H. Mamdani, S. Assilian, An experiment in linguistic synthesis with a fuzzy logic controller, International Journal
of Man-Machine Studies, 7(1) (1975), 1-13.

[34] J. M. Mendel, P. P. Bonissone, Critical thinking about explainable AI (XAI) for rule-based fuzzy systems, IEEE
Transactions on Fuzzy Systems, 29(12) (2021), 3579-3593.

[35] M. Mukaidono, L. Ding, Z. Shen, Approximate reasoning based on revision principle, In Proc. NAFIPS’90, 1 (1990),
94-97.

[36] R. E. Precup, S. Doboli, S. Preitl, Stability analysis and development of a class of fuzzy control systems, Engineering
Applications of Artificial Intelligence, 13(3) (2000), 237-247.

[37] Z. Saghian, A. Esfahanipour, B. Karimi, A novel Kumaraswamy interval type-2 TSK fuzzy logic system for subway
passenger demand prediction, Iranian Journal of Fuzzy Systems, 19(3) (2022), 69-87.

[38] Z. Shen, L. Ding, M. Mukaidono, Methods of revision principle, Proc. 5th IFSA World Congress, (1993), 246-249.

[39] M. Sugeno, T. Takagi, Multi-dimensional fuzzy reasoning, Fuzzy Sets and Systems, 9(1-3) (1983), 313-325.

[40] Y. Tsukamoto, An approach to fuzzy reasoning method, Advances in Fuzzy Set Theory and Applications, 137
(1979), 149.

[41] L. A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on Systems, Man, and Cybernetics, 1 (1973), 28-44.

[42] P. Zhang, Q. Shen, Dynamic TSK systems supported by fuzzy rule interpolation: An initial investigation, In 2020
IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), (2020), 1-7.

[43] M. Zhou, C. Shang, G. Li, L. Shen, N. Naik, S. Jin, J. Peng, Q. Shen, Transformation-based fuzzy rule interpolation
with mahalanobis distance measures supported by choquet integral, IEEE Transactions on Fuzzy Systems, (2022),
1-15.