软 d-代数中几类算子的性质

摘要

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)췍(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 d-algebra (F ,A)is a soft d-algebra over X .Finally,we proved that the extended intersection (F ,A )∩E (G,B )of two d-idealistic (resp.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 .%将软集的思想应用到 d-代数上,研究软 d-代数中的限制交、限制并、扩张交、扩张并、“AND”以及子集算子等重要运算,并讨论可理想化软 d-代数,得到一些重要性质。证明了：软 d-代数(F ,A)在其子集 B 上的限制(F B ,B )仍是 X 上的软 d-代数；两个软 d-代数(F ,A)和(G,B )的限制交(F ,A)∩R (G,B )和扩张并(F ,A)췍(G,B )仍是 X 上的软 d-代数；两个软d-代数(F ,A)和(G,A)的“AND”交(F ,A)∧(G,A)也是 X 上的一个软 d-代数；软 d-代数(F ,A)的同态像(f (F ),A )也是 X 上的一个软 d-代数；两个 d-理想化(或 d #-理想化,或d *-理想化)软 d-代数(F ,A )和(G,B )的扩张交(F ,A )∩E (G,B )是 X 上的 d-理想化(或 d #-理想化,或 d *-理想化)软 d-代数。