|Authors:||Eghosa Edeghagba, Elijah
|Title:||Ω-Lattices||Journal:||Fuzzy Sets and Systems||Volume:||311||First page:||53||Last page:||69||Issue Date:||15-Mar-2017||Rank:||M21a||ISSN:||0165-0114||DOI:||10.1016/j.fss.2016.10.011||Abstract:||
In the framework of Ω-sets, where Ω is a complete lattice, we introduce Ω-lattices, both as algebraic and as order structures. An Ω-poset is an Ω-set equipped with an Ω-valued order which is antisymmetric with respect to the corresponding Ω-valued equality. Using a cut technique, we prove that the quotient cut-substructures can be naturally ordered. Introducing notions of pseudo-infimum and pseudo-supremum, we obtain a definition of an Ω-lattice as an ordering structure. An Ω-lattice as an algebra is a bi-groupoid equipped with an Ω-valued equality, fulfilling particular lattice-theoretic formulas. On an Ω-lattice we introduce an Ω-valued order, and we prove that particular quotient substructures are classical lattices. Assuming Axiom of Choice, we prove that the two approaches are equivalent.
|Keywords:||Complete lattice | Fuzzy congruence | Fuzzy equality | Fuzzy identity | Fuzzy lattice||Publisher:||Elsevier||Project:||Development of methods of computation and information processing: theory and applications|
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