Ω-Lattices

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• 作者：Elijah Eghosa Edeghagba^a ; ^{edeghagba.elijah@dmi.uns.ac.rs} ; Branimir &Scaron ; e&scaron ; elja^b ; ^{seselja@dmi.uns.ac.rs} ; Andreja Tepavčević^b ; ^{andreja@dmi.uns.ac.rs}
• 关键词：Fuzzy lattice ; Fuzzy identity ; Fuzzy congruence ; Fuzzy equality ; Complete lattice
• 刊名：Fuzzy Sets and Systems
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：53-69
• 全文大小：389 K
• 卷排序：311

文摘

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.