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Extended-order algebras as a generalization of posets

Solovyov S. A.

Demonstratio Mathematica

2011

Vol. 44, nr 3

589-614

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 in many 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.