基于树的最小乘积模糊集代数

The Minimum Product Algebra of Fuzzy Set Based on Tree

给出Σ-代数、Σ-树和Σ-树函数的定义。引入了最小乘积模糊集代数,以此研究了一类特定形式的Σ-树。讨论了线性正规等式下的等价类的封闭性,证明了Σ-运算满足分配律并具有保序性。

The notions of Σ-algebra,Σ-tree and Σ-tree function are given.The minimum product algebras of fuzzy sets are introduced and a specific form of Σ-tree is studied.The closure properties of the equational classes defined by linear regular equations are illustrated,all Σ-operations verify distributivity law and possess order-preserving property are proved.