International Journal of Computational Intelligence Systems

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Volume 10, Issue 1, 2017, Pages 569 - 592

A theoretical development on the entropy of interval-valued intuitionistic fuzzy soft sets based on the distance measure

Authors
Yaya Liu1, yayaliu@my.swjtu.edu.cn, Junfang Luo1, junfangluo@163.com, Bing Wang2, bwang@my.swjtu.edu.cn, Keyun Qin1, *, keyunqin@263.net
College of Mathematics, Southwest Jiaotong University, Cheng Du, 610000, Sichuan, PR China
College of Information Science and Technology, Southwest Jiaotong University, Cheng Du, 610000, Sichuan, PR China
*Corresponding author.
Corresponding Author
Received 16 May 2016, Accepted 19 December 2016, Available Online 1 January 2017.
DOI
10.2991/ijcis.2017.10.1.39How to use a DOI?
Keywords
interval-valued intuitionistic fuzzy soft set; entropy; similarity measures; inclusion measures; fuzzy equivalences
Abstract

In this work, the axiomatical definition of similarity measure, distance measure and inclusion measure for interval-valued intuitionistic fuzzy soft set (IVIFSSs) are given. An axiomatical definition of entropy measure for IVIFSSs based on distance is firstly proposed, which is consistent with the axiomatical definition of fuzzy entropy of fuzzy sets introduced by De Luca and Termini. By different compositions of aggregation operators and a fuzzy negation operator, we obtain eight general formulae to calculate the distance measures of IVIFSSs based on fuzzy equivalences. Then we discuss the relationships among entropy measures, distance measures, similarity measures and inclusion measures of IVIFSSs. We prove that the presented entropy measures can be transformed into the similarity measures and the inclusion measures of IVIFSSs based on fuzzy equivalences.

Copyright
© 2017, the Authors. Published by Atlantis Press.
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

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Journal
International Journal of Computational Intelligence Systems
Volume-Issue
10 - 1
Pages
569 - 592
Publication Date
2017/01/01
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
10.2991/ijcis.2017.10.1.39How to use a DOI?
Copyright
© 2017, the Authors. Published by Atlantis Press.
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Yaya Liu
AU  - Junfang Luo
AU  - Bing Wang
AU  - Keyun Qin
PY  - 2017
DA  - 2017/01/01
TI  - A theoretical development on the entropy of interval-valued intuitionistic fuzzy soft sets based on the distance measure
JO  - International Journal of Computational Intelligence Systems
SP  - 569
EP  - 592
VL  - 10
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.2017.10.1.39
DO  - 10.2991/ijcis.2017.10.1.39
ID  - Liu2017
ER  -