The MacNeille Completions for Residuated S-Posets

• Autoři: ZHANG Xia; PASEKA Jan
• Rok publikování: 2021
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: International Journal of Theoretical Physics
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://doi.org/10.1007/s10773-019-04046-2
• Doi: http://dx.doi.org/10.1007/s10773-019-04046-2
• Klíčová slova: Residuated poset; S-semigroup; Residuated S-poset; Order-embedding; Subhomomorphism; Lattice-valued sup-lattice; Sup-algebra; Quantale; Q-module; Q-algebra; S-semigroup quantale; Injective object; Injective hull
• Popis: In this paper, we continue the study of injectivity for fuzzy-like structures. We extend the results of Zhang and Paseka for S-semigroups to the setting of residuated S-posets. It turns out that every residuated S-poset over a quantale S embeds into its MacNeille completion as its E?-injective hull. In particular, if S is a commutative quantale, then the injectives in the category of residuated S-posets with subhomomorphisms are precisely the quantale algebras introduced by Solovyov. Quantale algebras provide a convenient universally algebraic framework for developing lattice-valued analogues of fuzzification.

Související projekty

• Nové přístupy k agregačním operátorům v analýze a zpracování dat