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Ω-Lattices
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DOI：10.1016/j.fss.2016.10.011.png)
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Abstract
En 中文
In the framework of Omega-sets, where Omega is a complete lattice, we introduce Omega-lattices, both as algebraic and as order structures. An Omega-poset is an Omega-set equipped with an Omega-valued order which is antisymmetric with respect to the corresponding Omega-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 Omega-lattice as an ordering structure. An Omega-lattice as an algebra is a bi-groupoid equipped with an Omega-valued equality, fulfilling particular lattice-theoretic formulas. On an Omega-lattice we introduce an Omega-valued order, and we prove that particular quotient substructures are classical lattices. Assuming Axiom of Choice, we prove that the two approaches are equivalent. (C) 2016 Elsevier B.V. All rights reserved.
Keywords:
Fuzzy lattice
Fuzzy identity
Fuzzy congruence
Fuzzy equality
Complete lattice
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