International Journal of Approximate Reasoning
The variety generated by the truth value algebra of type-2 fuzzy sets
Fuzzy Sets and Systems
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A fuzzy (linguistic)truth value is a truth value speci?ed by a fuzzy set over a closed interval [0; 1] Logical operations, de?ned 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 algebraic structure of fuzzy truth values from a view point of Brozozowski's de Morgan bisemilattice. The main results include a necessary and suf?cient condition of subset of fuzzy truth values to be de Morgan bisemilattice.