反集合环

Antimanifold Ring

利用下截集的概念，将集环的定义推广到反集环。在反集环中定义了“∨，∧，－ ”运算，进而讨论了（－Ａ （Ｘ），∨，∧，－ ）具有的性质，并指出它是软代数但不是布尔代数。最后。

Applying a conception on lower cut set, the definition of set ring is extented to an antimanifold ring. Herein, an operation of calculating “∨,∧,-” is defined in the antimanifold. Consequently, the nature embodied by (\%\-A(X),∨,∧,-\%) is discussed. Again, it is pointed out what mentioned above is characterized by soft algebra, not by Boolean algebra. Finally, the paper discusses respectively the relationship between the antimanifold ring and fuzzy set and pairing set or nonpairing set.