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https://open.uns.ac.rs/handle/123456789/20605
Title: | Representation theory for complete L-lattices | Authors: | Edeghagba Elijah Eghosa Šešelja Branimir Tepavčević Andreja |
Issue Date: | 2019 | Journal: | Journal of Multiple Valued Logic and Soft Computing | Abstract: | © 2019 Old City Publishing, Inc. In the framework of L-valued (fuzzy) sets, where L is a complete lattice, we introduce complete L-lattices, based on L-structures investigated by the authors. An L-poset is a set equipped with an L-valued equality E and an L-valued transitive relation R, which is antisymmetric with respect to E. A complete L-lattice is an L-poset in which every subset has a so called pseudo-supremum and a pseudo-infimum. Several properties concerning special elements of these L-structures are investigated. Among our main results, we prove that an L-poset is a complete L-lattice if and only if particular quotient substructures with respect to the L-valued equality are classical complete lattices. As another important result obtained by using closure systems, we present a Representation theorem dealing with a general construction of L-posets and Lcomplete lattices. | URI: | https://open.uns.ac.rs/handle/123456789/20605 | ISSN: | 1542-3980 |
Appears in Collections: | PMF Publikacije/Publications |
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