Abstract
In this paper, inspired by the Zadeh approach to the fuzzy connectives in fuzzy set theory and by some applications, we introduce and study set-based extended functions on different universes. After presenting some results for set-based extended functions on a general universe, we focus our investigation on set-based extended functions on some particular universes, including lattices and (bounded) chains. A special attention is devoted to characterization of set-based extended aggregation functions on the unit interval [0, 1].
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Acknowledgement
R. Mesiar and A. Šeliga kindly acknowledge the support of the grant VEGA 1/0006/19, and A. Kolesárová is grateful for the support of the grant VEGA 1/0614/18. All these three authors also acknowledge the support of the project of Science and Technology Assistance Agency under the contract No. APVV–18–0052. D. Gómez and J. Montero kindly acknowledge the support of the projects TIN205-66471-P (Government of Spain), S2013/ICE-2845 (State of Madrid) and Complutense University research group GR3/14-910149. Moreover, the authors thank M. Botur for inspirative personal discussion.
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Mesiar, R., Kolesárová, A., Šeliga, A., Montero, J., Gómez, D. (2019). Set-Based Extended Functions. In: Torra, V., Narukawa, Y., Pasi, G., Viviani, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2019. Lecture Notes in Computer Science(), vol 11676. Springer, Cham. https://doi.org/10.1007/978-3-030-26773-5_4
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