基于一类完备格诱导的直觉模糊集的多元扩展运算

Multivariate extension operations of intuitionistic fuzzy sets induced by a complete lattice

基于一种二元序完备格引入了直觉模糊集的截集的概念,给出了直觉模糊集的加、减和乘法等算术运算,获得了这种截集的算术运算性质,并通过实例说明这些包含关系可以严格成立.此外,在完备格诱导的直觉模糊集的截集基础上,得到了直觉模糊集的多元扩展原理,进而讨论了多元扩展运算的2个基本性质.

The concept of cut set of intuitionistic fuzzy set is introduced based on the complete lattice of a kind of binary order. The arithmetic operations of intuitionistic fuzzy sets such as addition, subtraction and multiplication are given, some properties of the arithmetic operation of the cut sets are obtained. An example shows that the strict inclusion relations of the cut sets are possible to sure. In addition, on the basis of the cut sets induced by a complete lattice, the multivariate extension principle of intuitionistic fuzzy sets is gained, and then the two basic properties of the multivariate extension operation are discussed.