直觉折线模糊数空间的完备可分性和逼近性  

Complete separability and approximation of the intuitionistic polygonal fuzzy number space

作　　者：李丹 王贵君[2] LI Dan;WANG Guijun(School of Science and Technology,University of Sanya,Sanya 572000,Hainan Province,China;School of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]三亚学院理工学院,海南三亚572000 [2]天津师范大学数学科学学院,天津300387

出　　处：《浙江大学学报（理学版）》2022年第5期532-539,共8页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(61374009)。

摘　　要：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。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.

关 键 词：直觉模糊数 折线模糊数 直觉折线模糊数 逼近性 

分 类 号：O159[理学—数学]