Abstract
Bodjanova, Kalina and Král’ recently introduced a construction method, called paving, which enables to define a new associative, commutative and increasing operation from a given one and a discrete representable partial operation. As a matter of fact, not every discrete t-norm is representable, i.e. it can not always be generated by some additive generator, and this also holds for t-conorms and uninorms. Inspired by this fact and the method of paving, we construct some new associative, commutative and increasing operations on the unit interval from a t-norm on the unit interval and a discrete t-norm, t-superconorm, t-conorm or uninorm. Because of the duality between t-norms and t-conorms, we also define some operations from a t-conorm and a discrete t-norm, t-subnorm, t-conorm or uninorm.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China No. 61573211. The author Wenwen Zong is supported by the China Scholarship Council under Grant No. 201606220121. The author Yong Su is supported by the China Scholarship Council under Grant No. 201506220039.
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Zong, W., Su, Y., Liu, HW., De Baets, B. (2018). On the Construction of Associative, Commutative and Increasing Operations by Paving. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_24
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DOI: https://doi.org/10.1007/978-3-319-59306-7_24
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