Extended-order algebras as a generalization of posets

Demonstratio mathematica

article

Sergey A. Solovyov¹ 

[1] Department of Mathematics, University of Latvia;Institute of Mathematics and Computer Science, University of Latvia

关键词: categorical equivalence;    completion of a poset;    (co)product of objects;    coseparator;    d-algebra;    epimorphism;    extended-order algebra;    extended-relation algebra;    free object;    Hilbert algebra;    implicative algebra;    initial morphism;    poset;    pre-ordered set;    quantale;    rough set;    ∨-semilattice;   

DOI  :  10.1515/dema-2013-0321

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

Motivated by the recent study of several researchers on extended-order algebras , introduced by C. Guido and P. Toto as a possible common framework for the majority of algebraic structures used inmany-valued mathematics, the paper focuses on the properties of homomorphisms of the new structures, considering extended-order algebras as a generalization of partially ordered sets. The manuscript also introduces the notion of extended-relation algebra providing a new framework for developing the theory of rough sets.

【 授权许可】

CC BY