Abstract
In this paper, a recall of the similarity-based view of interpolative reasoning considered as an analogical scheme of reasoning introduced by Bernadette Bouchon-Meunier and her colleagues. Based on this, an extension of this replacement is presented that finely corrects the validity by choosing a similar observation that non only guarantees convexity, but also a gradual behaviour with respect to a specifity measure.
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Notes
- 1.
A very restrictive version of fuzzy decision base rules, however, it enables us to lighten the notations and focus only on the important properties we want to highlight.
- 2.
Any approach used to defuzzify a fuzzy set (for instance, those used in fuzzy control) can be used to define the location of a fuzzy set. In particular, some approaches could be used in case of non-triangular or non-trapezoidal fuzzy sets.
References
Bouchon-Meunier, B., Delechamp, J., Marsala, C., Mellouli, N., Rifqi, M., Zerrouki, L.: Analogy and interpolation in the case of sparse rules. In: Eurofuse, SIC’99, pp. 132–136. Budapest, Hungary (1999)
Bouchon-Meunier, B., Delechamp, J., Marsala, C., Rifqi, M.: Several forms of fuzzy analogical reasoning. In: Proceedings of the IEEE International Conference on Fuzzy Systems, FUZZ-IEEE’1997, pp. 45–50. Barcelona, Spain (1997)
Bouchon-Meunier, B., Delechamp, J., Marsala, C., Rifqi, M.: Analogy as a basis of various forms of approximate reasoning. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds.) Uncertainty in Intelligent and Information Systems, vol. 20, pp. 70–79. World Scientific (2000)
Bouchon-Meunier, B., Dubois, D., Marsala, C., Prade, H., Ughetto, L.: A comparative view of interpolation methods between sparse fuzzy rules. In: IFSA’01 World Congress, pp. 2499–2504. Vancouver, Canada (2001)
Bouchon-Meunier, B., Esteva, F., Godó, L., Rifqi, M., Sandri, S.: A principled approach to fuzzy rule base interpolation using similarity relations. In: EUSFLAT–LFA 2005, pp. 757–763. Barcelona, Spain (2005)
Bouchon-Meunier, B., Rifqi, M., Bothorel, S.: Towards general measures of comparison of objects. Fuzzy Sets Syst. 84(2), 143–153 (1996)
Bouchon-Meunier, B., Rifqi, M., Marsala, C.: Interpolative reasoning based on graduality. In: Proceedings of the IEEE International Conference on Fuzzy Systems, FUZZ-IEEE’2000, pp. 483–487. San Antonio, USA (2000)
Chatterjee, N., Campbell, J.A.: Knowledge interpolation: a simple approach to rapid symbolic reasoning. Comput. Artif. Intell. 17(6), 517–551 (1998)
Detyniecki, M., Marsala, C., Rifqi, M.: Double-linear fuzzy interpolation method. In: Proceedings of the IEEE International Conference on Fuzzy Systems, FUZZ-IEEE’2011, pp. 455–462. IEEE, Taipei, ROC (2011)
Jenei, S.: Interpolation and extrapolation of fuzzy quantities revisited-an axiomatic approach. Soft. Comput. 5(3), 179–193 (2001)
Kóczy, L.T., Hirota, K.: Rule interpolation in approximate reasoning based fuzzy control. In: IFSA’91, pp. 89–92. Brussels, Belgium (1991)
Kóczy, L.T., Hirota, K.: Interpolative reasoning with insufficient evidence in sparse fuzzy rule bases. Inf. Sci. 71(1–2), 169–201 (1993)
Perfilieva, I., Dubois, D., Prade, H., Esteva, F., Godó, L., Hodakova, P.: Interpolation of fuzzy data: analytical approach and overview. Fuzzy Sets Syst. 192, 134–158 (2012)
Ughetto, L., Dubois, D., Prade, H.: Implicative and conjunctive fuzzy rules: a tool for reasoning from knowledge and examples. In: Proceeding of the Sixteenth National Conference on AI (AAAI’99), pp. 214–219. Orlando, Fl, USA (1999)
Wu, Z.Q., Masaharu, M., Shi, Y.: An improvement to Kóczy and Hirota’s interpolative reasoning in sparse fuzzy rule bases. Int. J. Approx. Reason. 15(3), 185–201 (1996)
Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern. 3, 28–44 (1973)
Zadeh, L.A.: A theory of approximate reasoning. Mach. Intell. 9, 149–194 (1979)
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Detyniecki, M. (2021). Interpolative Reasoning: Valid, Specificity-Gradual and Similarity-Based. In: Lesot, MJ., Marsala, C. (eds) Fuzzy Approaches for Soft Computing and Approximate Reasoning: Theories and Applications. Studies in Fuzziness and Soft Computing, vol 394. Springer, Cham. https://doi.org/10.1007/978-3-030-54341-9_4
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