Abstract
Empirical studies have shown that in many practical problems, out of all symmetric membership functions, special distending functions work best, and out of all hedge operations and negation operations, fractional linear ones work the best. In this paper, we show that these empirical successes can be explained by natural invariance requirements.
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Acknowledgements
This work was supported in part by the grant TUDFO/47138-1/2019-ITM from the Ministry of Technology and Innovation, Hungary, and by the US National Science Foundation grants 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science) and HRD-1242122 (Cyber-ShARE Center of Excellence).
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Urenda, J.C., Csiszár, O., Csiszár, G., Dombi, J., Eigner, G., Kreinovich, V. (2022). Natural Invariance Explains Empirical Success of Specific Membership Functions, Hedge Operations, and Negation Operations. In: Bede, B., Ceberio, M., De Cock, M., Kreinovich, V. (eds) Fuzzy Information Processing 2020. NAFIPS 2020. Advances in Intelligent Systems and Computing, vol 1337. Springer, Cham. https://doi.org/10.1007/978-3-030-81561-5_41
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DOI: https://doi.org/10.1007/978-3-030-81561-5_41
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