Abstract:

Firstly, the definition of singlepoint coannihilator operator was given in the BLalgebras, then some properties of singlepoint co-annihilator operator were studied. Secondly, some properties of multiplepoint co-annihilator operator were discussed, and the necessary and sufficient conditions were given for a subset being an image of multiplepoint co-annihilator operator in the BLalgebras. Finally, some properties of multiplepoint co-annihilator operator’s image of BLhomomorphism were discussed, and the necessary and sufficient conditions were given when coannihilator operator’s image of BL-homomorphism and its inverse image of BL-homomorphism are the images of multiple point co-annihilator operator.

Key words: fuzzy logic, BL-algebra, single-point co-annihilator operator, multiple-point co-annihilator operator, BL-homomorphism