International Journal of Computational Intelligence Systems

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Volume 9, Issue 1, January 2016, Pages 36 - 56

Interval-Valued Intuitionistic Fuzzy Derivative and Differential Operations

Authors
Hua Zhao
Institute of Sciences, PLA University of Science and Technology, Nanjing, Jiangsu 211101, China
Zeshui Xu*
Business School, Sichuan University, Chengdu, Sichuan 610064, China
Zeqing Yao
Institute of Sciences, PLA University of Science and Technology, Nanjing, Jiangsu 211101, China
*Corresponding author. Tel.: +86 25 84483382. E-mails: xuzeshui@263.net; zhaohua_pla@163.com
Corresponding Author
Zeshui Xu
Received 16 September 2015, Accepted 29 October 2015, Available Online 1 January 2016.
DOI
10.1080/18756891.2016.1144152How to use a DOI?
Keywords
Interval-valued intuitionistic fuzzy set (IVIFS); Interval-valued intuitionistic fuzzy function (IVIFF); Limit; Continuity; Derivative; Differential
Abstract

The interval-valued intuitionistic fuzzy set (IVIFS) generalizes Atanassov’s intuitionistic fuzzy set (A-IFS) with the membership and non-membership degrees being intervals instead of real numbers, so it can contain more information. In this paper, we study the derivatives and differentials under interval-valued intuitionistic fuzzy environment. Firstly, we discuss the four change directions (the addition, subtraction, multiplication and division directions) of the interval- valued intuitionistic fuzzy values (IVIFVs); Secondly, we propose four kinds of limits (the addition, subtraction, multiplication and division limits) for different sequences of IVIFVs, and then we define the concepts of interval-valued intuitionistic fuzzy function (IVIFF) and study the continuities of IVIFFs; Thirdly, we develop two kinds of derivatives (the subtraction and division derivatives) of IVIFFs and give an equivalent condition for the existence of the derivative of an IVIFF. At last, we define the concepts of two kinds of differentials (the subtraction and division differentials) of IVIFFs and discuss the approximate computations of IVIFFs by the developed differentials.

Copyright
© 2016. the authors. Co-published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article under the CC BY-NC licence (http://creativecommons.org/licences/by-nc/4.0/).

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<Previous Article In Issue
Next Article In Issue>
Journal
International Journal of Computational Intelligence Systems
Volume-Issue
9 - 1
Pages
36 - 56
Publication Date
2016/01/01
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
10.1080/18756891.2016.1144152How to use a DOI?
Copyright
© 2016. the authors. Co-published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article under the CC BY-NC licence (http://creativecommons.org/licences/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Hua Zhao
AU  - Zeshui Xu
AU  - Zeqing Yao
PY  - 2016
DA  - 2016/01/01
TI  - Interval-Valued Intuitionistic Fuzzy Derivative and Differential Operations
JO  - International Journal of Computational Intelligence Systems
SP  - 36
EP  - 56
VL  - 9
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.1080/18756891.2016.1144152
DO  - 10.1080/18756891.2016.1144152
ID  - Zhao2016
ER  -