Abstract
This paper introduces an extension of the Sugeno integral over generalized semi-quantales. We prove that our generalized Sugeno integral is a scale invariant compatible aggregation function. Moreover, we show that the generalized Sugeno integral provides a one-to-one correspondence between the set of capacities and the set of aggregation functions, which additionally are quantale module homomorphisms.
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14 October 2022
In the original version of the chapter, the following belated corrections have been incorporated: The affiliation “Facultad de Ingeniería, Universidad Andrés Bello, Valparaíso, Chile” of author “Milan Stehlik” has been included in the Chapter 9 (Sugeno Integral over Generalized Semi-quantales). The correction chapter and the book have been updated with the change.
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Acknowledgements
Jan Paseka was supported by the Czech Science Foundation through the project No. 18-06915S. Milan Stehlík was supported by WTZ Project No. HU 11/2016.
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Paseka, J., Solovjovs, S., Stehlík, M. (2022). Sugeno Integral over Generalized Semi-quantales. 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_9
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DOI: https://doi.org/10.1007/978-3-030-81561-5_9
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