Title :
De Morgan bisemilattice of fuzzy truth value
Author :
Kikuchi, Hiroaki ; Takagi, Noboru
Author_Institution :
Dept. of Inf. Media Technol., Tokai Univ., Kanagawa, Japan
Abstract :
A fuzzy (linguistic) truth value is a truth value specified by a fuzzy set over a closed interval [0, 1]. Logical operations, defined according to the extension principle, do not satisfy all identities to be lattice because there are subnormal truth values and non-convex truth values that violate the absorption laws. In 2000, Brzozowski proposed de Morgan bisemilattice, which is generalized algebra of de Morgan lattice in order for applications in multi-valued simulations of digital circuits. This paper studies the algebraic structure of fuzzy truth values from a view point of Brozozowski´s (2000) de Morgan bisemilattice. The main results include a necessary and sufficient condition of a subset of fuzzy truth values to be de Morgan bisemilattice
Keywords :
fuzzy logic; fuzzy set theory; multivalued logic; absorption laws; algebraic structure; closed interval; de Morgan bisemilattice; de Morgan lattice; digital circuit simulation; fuzzy linguistic truth value; fuzzy set; generalized algebra; logical operations; multivalued simulations; nonconvex truth values; subnormal truth values; Absorption; Algebra; Circuit simulation; Digital circuits; Fuzzy logic; Fuzzy sets; Lattices; Sufficient conditions;
Conference_Titel :
Multiple-Valued Logic, 2002. ISMVL 2002. Proceedings 32nd IEEE International Symposium on
Conference_Location :
Boston, MA
Print_ISBN :
0-7695-1462-6
DOI :
10.1109/ISMVL.2002.1011087
