Abstract In this work we introduce and study some concepts relatively to fuzzy σ–algebra such as measure, countably additive, complete measure extension of measure. Moreover, present their basic properties examples them. addition, it is shown that the linear combination a too. Finally, relationships between proposed have been introduced.

One special subalgebra of the algebra of fuzzy truth values is the set of those elements that take only 0 and 1 as values. This subalgebra is in one-to-one correspondence with the subsets of the unit interval, but the operations do not correspond to ordinary union and intersection. The automorphisms of this subalgebra are studied here, resulting in showing that the subobjects corresponding to n...