Algorithms for the computation of T-transitive closures
Tóm tắt
We present two weight-driven algorithms for the computation of the T-transitive closure of a symmetric binary fuzzy relation on a finite universe X with cardinality n (or, equivalently, of a symmetric (n/spl times/n)-matrix with elements in [0, 1]), with T a triangular norm. The first algorithm is proven to be valid for any triangular norm T, whereas the second algorithm is shown to be valid when T is either the minimum operator or an Archimedean triangular norm. Furthermore, we investigate how these algorithms can be appropriately adapted to generate the T-transitive closure of nonsymmetric binary fuzzy relations (or matrices) as well.
Từ khóa
#Symmetric matrices #Mathematics #Extraterrestrial measurements #Fuzzy sets #Fuzzy logic #Computer science #Biometrics #Process control #Prototypes #Fuzzy systemsTài liệu tham khảo
klement, 2000, Triangular Norms, 8, 10.1007/978-94-015-9540-7
10.1016/0165-0114(90)90101-B
10.1016/0165-0114(90)90102-C
ling, 1965, representation of associative functions, Publ Math Debrecen, 12, 189
miller, 2000, Algorithms Sequential and Parallel a Unified Approach
smutnásmutna, 1998, a note on noncontinuous <formula><tex>$t$</tex></formula>-norms, Busefal, 76, 19
10.1016/S0020-0255(71)80005-1
de baets, 0, on the existence and construction of <formula> <tex>$t$</tex></formula>-transitive closures, Inform Sci
10.1016/S0165-0114(83)80006-2
10.1016/S0020-0190(97)00113-0
10.1109/TSMC.1974.5409141
10.1016/0165-0114(92)90191-6
10.1007/978-94-017-1648-2
10.1007/978-94-011-2014-2_16
10.1016/0165-0114(88)90126-1
kandel, 1974, fuzzy chains, IEEE Trans Syst Man and Cybern, smc 5, 472