TY - JOUR
ID - 3330
TI - STONE DUALITY FOR R0-ALGEBRAS WITH INTERNAL STATES
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Zhou, Hongjun
AU - Shi, Hui-Xian
AD - School of Mathematics and Information Science, Shaanxi Normal
University, Xi'an, 710062, CHINA
AD - School of Mathematics and Information Science, Shaanxi Normal University
Y1 - 2017
PY - 2017
VL - 14
IS - 4
SP - 139
EP - 161
KW - $Rsb{0}$-algebra
KW - Nilpotent minimum algebra
KW - MV-skeleton
KW - internal state
KW - Stone duality
DO - 10.22111/ijfs.2017.3330
N2 - $Rsb{0}$-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 $Rsb{0}$-algebras and the category of three-valued Stone spaces.Then we extend Flaminio-Montagna internal states to $Rsb{0}$-algebras.Such internal states must be idempotent MV-endomorphisms of $Rsb{0}$-algebras.Lastly we present a Stone duality for the category of MV-skeletons of $Rsb{0}$-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 $Rsb{0}$-algebras.
UR - http://ijfs.usb.ac.ir/article_3330.html
L1 - http://ijfs.usb.ac.ir/article_3330_f12a0f74c6087b8efa1b0345bf21060c.pdf
ER -