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STONE DUALITY FOR R0-ALGEBRAS WITH INTERNAL STATES | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 9، دوره 14، شماره 4، آبان 2017، صفحه 139-161 اصل مقاله (468.58 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3330 | ||
نویسندگان | ||
Hongjun Zhou1؛ Hui-Xian Shi ![]() | ||
1School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, CHINA | ||
2School of Mathematics and Information Science, Shaanxi Normal University | ||
چکیده | ||
$R\sb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s. In this paper, we first establish a Stone duality for the category of MV-skeletons of $R\sb{0}$-algebras and the category of three-valued Stone spaces. Then we extend Flaminio-Montagna internal states to $R\sb{0}$-algebras. Such internal states must be idempotent MV-endomorphisms of $R\sb{0}$-algebras. Lastly we present a Stone duality for the category of MV-skeletons of $R\sb{0}$-algebras with Flaminio-Montagna internal states and the category of three-valued Stone spaces with Zadeh type idempotent continuous endofunctions. These dualities provide a topological viewpoint for better understanding of the algebraic structures of $R\sb{0}$-algebras. | ||
کلیدواژهها | ||
$Rsb{0}$-algebra؛ Nilpotent minimum algebra؛ MV-skeleton؛ internal state؛ Stone duality | ||
مراجع | ||
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