Abstract:

We gave the new concept of antisoft subinclines, and studied the relationship between antisoft subinclines and the antidual of soft sets and got some equivalent characterizations. Then we discussed some properties of the two operations ‘restricted union’ and ‘or’ on it. Using the antiextension principle, we obtained the properties of their antiimage and inverse image. Finally, we introduced the chain condition of H which consisted of all of the antisoft subinclines and gave a necessary and sufficient condition for H was Artinian or Noetherian.

Key words: antisoft subincline, soft set, antidual, chain condition