Chain and Substitution Rules of Intuitionistic Fuzzy Calculus

被引：18

作者：

Lei, Qian ^{[1
]}

Xu, Zeshui ^{[1
,2
]}

机构：

[1] PLA Univ Sci & Technol, Coll Sci, Nanjing 211101, Jiangsu, Peoples R China

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

来源：

IEEE TRANSACTIONS ON FUZZY SYSTEMS | 2016年 / 24卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Chain rule of derivatives; form invariance of differentials; intuitionistic fuzzy calculus; substitution rules of integrals; OPERATIONS; OPERATORS;

D O I：

10.1109/TFUZZ.2015.2450832

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The intuitionistic fuzzy set, originally given by Atanassov, can be considered as a set that consists of intuitionistic fuzzy numbers (IFNs), each of which is described by amembership degree, a nonmembership degree, and a hesitancy degree. Recently, the calculus of IFNs has been proposed, and the derivatives, differentials, indefinite integrals, and definite integrals with respect to IFNs have also been developed in previous research studies. In this paper, some novel results of intuitionistic fuzzy calculus are derived, which include mainly the chain rule of derivatives, the form invariance of differentials, and the substitution rules for indefinite integrals and definite integrals in intuitionistic fuzzy environment.

引用

页码：519 / 529

页数：11

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