Limit properties and derivative operations in the metric space of intuitionistic fuzzy numbers
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- 作者：Zhenghai Ai ; Zeshui Xu ; Qian Lei
- 关键词：Intuitionistic fuzzy set ; Intuitionistic fuzzy calculus ; Metric space ; Intuitionistic fuzzy infinitesimal ; Intuitionistic fuzzy functions
- 刊名：Fuzzy Optimization and Decision Making
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：16
- 期：1
- 页码：71-87
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematical Logic and Foundations; Probability Theory and Stochastic Processes; Optimization; Calculus of Variations and Optimal Control; Optimization; Artificial Intelligence (incl. Robotics); Opera
- 出版者：Springer US
- ISSN：1573-2908
- 卷排序：16
文摘
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.