Abstract
We claim and justify that the future of a fuzzy logic is in the interconnection of various well-developed theories. We are focused on a lattice valued analysis that unifies the treatments of atomic elements, sets of atomic elements, functions between sets of atomic elements and their properties. We clarify the relationship between a fuzzy function and its ordinary core. We discuss the property of continuity of a fuzzy function in a lattice valued topology.
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- 1.
Fuzzy equivalence appears in the literature under the names similarity or indistinguishability as well.
- 2.
This notion was introduced in [7].
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Acknowledgments
The support of the two projects is kindly announced: ESF project 2013/0024/1DP/1.1.1.2.0/13/APIA/VIAA/045, European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070).
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Perfilieva, I., Šostak, A. (2015). From Lattice Valued Theories to Lattice Valued Analysis. In: Seising, R., Trillas, E., Kacprzyk, J. (eds) Towards the Future of Fuzzy Logic. Studies in Fuzziness and Soft Computing, vol 325. Springer, Cham. https://doi.org/10.1007/978-3-319-18750-1_9
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DOI: https://doi.org/10.1007/978-3-319-18750-1_9
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