直觉折线模糊数空间的完备可分性和逼近性

折线模糊数可借助一组实数的有序表示确定模糊信息，不仅可以实现一般模糊数之间的近似线性运算，而且克服了基于Zadeh扩展原理的模糊数四则运算复杂问题。基于直觉模糊数和折线模糊数，提出了直觉折线模糊数的概念。通过引入距离公式，证明了直觉折线模糊数可构建完备可分的度量空间，给出了直觉折线模糊数的逼近定理。进一步用实例验证了直觉折线模糊数对直觉模糊数具有逼近性。

Complete separability and approximation of the intuitionistic polygonal fuzzy number space.

The polygonal fuzzy number can determine fuzzy information by means of the ordered representation of a group of real numbers. It can not only approximately realize the linear operations among general fuzzy numbers, but also get rid of the complexity of the arithmetic operations of fuzzy numbers based on Zadeh's extension principle. In this paper, the concept of the intuitionistic polygonal fuzzy number is first proposed based on the characteristics of the intuitionistic fuzzy number and polygonal fuzzy number, and its distance formula is introduced. Secondly, it is proved that intuitionistic polygonal fuzzy numbers constitute a complete separable metric space through the distance formula, and the approximation theorem is obtained. Finally, we verify by an example that the intuitionistic polygonal fuzzy number can approximate to an intuitionistic fuzzy number.