Abstract
This paper deals with lattice-valued n-variable functions on a k-element domain, considered as a generalization of lattice-valued Boolean functions. We investigate invariance groups of these functions, i.e., the group of such permutations that leaves the considered function invariant. We show that the invariance groups of lattice-valued functions depend only on the cuts of the function. Furthermore, we construct such lattice-valued Boolean function (and its generalization), the cuts of which represent all representable invariance groups.
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Acknowledgments
E. K. Horváth research was supported by NFSR of Hungary (OTKA), Grant number K 115518. Research of the second and the third authors is partially supported by Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 174013. Research of all authors is partially supported by the Provincial Secretariat for Science and Technological Development, Autonomous Province of Vojvodina, Grant “Ordered structures and applications”.
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Communicated by A. Di Nola.
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Horváth, E.K., Šešelja, B. & Tepavčević, A. Cut approach to invariance groups of lattice-valued functions. Soft Comput 21, 853–859 (2017). https://doi.org/10.1007/s00500-016-2084-3
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DOI: https://doi.org/10.1007/s00500-016-2084-3