Abstract
T-operators were defined on [0, 1] by Mas et al. in 1999. In 2001, Calvo et al. introduced the notion of nullnorms, also on [0, 1]. Both of these operations were defined as generalizations of t-norms and t-conorms. As Mas et al. in 2002 pointed out, t-operators and nullnorms coincide on [0, 1]. Afterwards, only nullnorms were studied and later generalized as operations on bounded lattices. Our intention is to introduce also t-operators as operations on bounded lattices. We will show that, on bounded lattices, nullnorms and t-operators need not coincide. We will explore conditions under which one of these operations is necessarily the other one, and conditions under which they differ.
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Acknowledgements
The work of Martin Kalina has been supported from the Science and Technology Assistance Agency under contract No. APVV-14-0013, and from the VEGA grant agency, grant No. 2/0069/16.
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Bodjanova, S., Kalina, M. (2018). Nullnorms and T-Operators on Bounded Lattices: Coincidence and Differences. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_14
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DOI: https://doi.org/10.1007/978-3-319-91473-2_14
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