Limit properties and derivative operations in the metric space of intuitionistic fuzzy numbers

被引：19

作者：

Ai, Zhenghai ^{[1
]}

Xu, Zeshui ^{[2
,3
]}

Lei, Qian ^{[4
]}

机构：

[1] Leshan Normal Univ, Dept Math & Informat Sci, Leshan 614000, Sichuan, Peoples R China

[2] Sichuan Univ, Sch Business, Chengdu 610064, Sichuan, Peoples R China

[3] Collaborat Innovat Ctr Social Safety Sci & Techno, Nanjing 210007, Jiangsu, Peoples R China

[4] PLA Univ Sci & Technol, Coll Sci, Nanjing 210007, Jiangsu, Peoples R China

来源：

FUZZY OPTIMIZATION AND DECISION MAKING | 2017年 / 16卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Intuitionistic fuzzy set; Intuitionistic fuzzy calculus; Metric space; Intuitionistic fuzzy infinitesimal; Intuitionistic fuzzy functions; CONSISTENCY;

D O I：

10.1007/s10700-016-9239-7

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Intuitionistic fuzzy numbers (IFNs) are a useful tool to depict the uncertain information in real life. Based on IFNs, the intuitionistic fuzzy calculus (IFC) has been put forward recently. To further develop the IFC theory, in this paper, we investigate the limit properties of IFCs, and study the intuitionistic fuzzy infinitesimals and their orders. We also discuss the continuity, the derivatives and the differentials of intuitionistic fuzzy functions in detail, and reveal their relationships. Additionally, we define the metric space of the IFNs, based on which, a series of desirable results are obtained. These results are similar to the ones in the classical calculus.

引用

页码：71 / 87

页数：17

共 23 条

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[2]

[Anonymous], 1997, The Ordered Weighted Averaging Operation: Theory, Methodology and Applications

[3]

[Anonymous], 2014, STUDIES FUZZINESS SO

[4]

[Anonymous], 2008, Fuzzy sets and their extensions: Representation, aggregation and models