Abstract
In general, expert rules expressed by imprecise (fuzzy) words of natural language like “small” lead to imprecise (fuzzy) control recommendations. If we want to design an automatic controller, we need, based on these fuzzy recommendations, to generate a single control value. A procedure for such generation is known as defuzzification. The most widely used defuzzification procedure is centroid defuzzification, in which, as the desired control value, we use one of the coordinates of the center of mass (“centroid”) of an appropriate 2-D set. A natural question is: what is the meaning of the second coordinate of this center of mass? In this paper, we show that this second coordinate describes the overall measure of fuzziness of the resulting recommendation.
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Acknowledgements
This work was supported in part 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).
The authors are thankful to all the participants of the World Congress of the International Fuzzy Systems Association and the Annual Conference of the North American Fuzzy Information Processing Society IFSA/NAFIPS’2019 (Lafayette, Louisiana, June 18–21, 2019) for valuable discussions.
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Figueroa García, J.C., Servin, C., Kreinovich, V. (2022). Centroids Beyond Defuzzification. 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_35
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DOI: https://doi.org/10.1007/978-3-030-81561-5_35
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