期刊
KNOWLEDGE-BASED SYSTEMS
卷 76, 期 -, 页码 1-16出版社
ELSEVIER
DOI: 10.1016/j.knosys.2014.11.019
关键词
Intuitionistic fuzzy numbers; Intuitionistic fuzzy calculus; Newton-Leibniz formula; Intuitionistic fuzzy set; Intultionistic fuzzy functions
资金
- National Natural Science Foundation of China [61273209]
The intuitionistic fuzzy set (A-IFS) introduced by Atanassov (1986) is a generalization of fuzzy set (Zadeh, 1965). The basic elements of an A-IFS are intuitionistic fuzzy numbers (IFNs) (Xu and Yager, 2006), each of which is described by a membership degree, a non-membership degree and a hesitancy degree. The IFN is an effective tool in expressing fuzzy information of things. Based on IFNs and their basic operations, the paper first defines the indefinite integral and antiderivative of intuitionistic fuzzy functions (IFFs), and then gives the concept of definite integral of IFFs. Finally, the paper deduces the Newton-Leibniz formula (the fundamental theorem of calculus) in Atanassov's intuitionistic fuzzy environment, and studies some basic properties of intuitionistic fuzzy calculus. Finally, this paper presents an aggregation method, which is based on the definite integral of IFFs, to deal with intuitionistic fuzzy information, and analyzes some basic properties of the method. (C) 2014 Elsevier B.V. All rights reserved.
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