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Erschienen in:
2018 | Supplement | Buchkapitel
Convolution on Bounded Lattices
verfasst von : Laura De Miguel, Humberto Bustince, Bernard De Baets
Erschienen in: Advances in Fuzzy Logic and Technology 2017
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Abstract
The union and intersection of two membership degrees of type-2 fuzzy sets are defined using a generalization of the mathematical operation of convolution. In the literature, it has been deeply studied when these convolution operations constitute a bounded distributive lattice. In this paper, we generalize the union and intersection convolution operations by replacing the functions from [0, 1] to itself with functions from a bounded lattice \(\mathbb {L}_1\) to a frame \(\mathbb {L}_2\), a particular type of bounded lattice. Similarly to some previous studies in the literature, we analyze when these new convolution operations constitute a bounded distributive lattice.