Abstract:

We applied the soft idea to d-algebras to investigate some important operations such as restricted intersection, restricted union, extended intersection, extended union, “AND”, and subset operations of soft d-algebras and the idealistic soft d-algebras, and gave some important properties of them. First of all, we proved that the restriction (F|_B,B) of (F,A) on its subset B is a soft d-algebra over X; the restricted intersection (F,A)∩_R(G,B)and extended union (F,A)(G,B) of two soft dalgebras (F,A) and (G,B) are soft d-algebras over X; the “AND” (F,A)∧(G,A) of two soft d-algebras (F,A) and (G,B) is a soft d-algebra over X. Second, we proved that the homomorphism image (f(F),A) of soft dalgebra (F,A) is a sft dalgebra over X. Finally, we proved that the extended intersection(F,A)∩_E(G,B) of two didealistic (r
esp. d^#-idealistic and d^*-idealistic) soft d-algebras (F,A) and (G,B) over X is a d-idealistic (resp. d^#-idealistic and d^*-idealistic) soft d-algebra over X.

Key words: soft d-algebra, extended intersection, restricted intersection, extended union, restricted union, idealistic soft d-algebras, homomorphism