International Journal of Computational Intelligence Systems

Volume 11, Issue 1, January 2018, Pages 15 - 32

A Multiple Attribute Decision Making Approach Based on New Similarity Measures of Interval-valued Hesitant Fuzzy Sets

Authors
Yi Liu1, 2, 3, *, liuyiyl@126.com, Jun Liu3, J.liu@ulster.ac.uk, Zhiyong Hong4, hongmr@163.com
1 Data Recovery Key Lab of Sichuan Province, Neijiang Normal University, Neijiang 641000, Sichuan, P.R. China
2 School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641000, Sichuan, P.R. China
3 School of Computing and Mathematics, Ulster University, Jordanstown Campus, Northern Ireland BT 37 0TR, UK
4 School of Computer Science, Wuyi University, Jiangmen 529020, Guangdong, P.R. China
Corresponding Author
Received 15 June 2017, Accepted 14 September 2017, Available Online 1 January 2018.
DOI
https://doi.org/10.2991/ijcis.11.1.2How to use a DOI?
Keywords
Interval-valued hesitant fuzzy set, II-type interval-valued hesitant fuzzy distance, interval-valued hesitant fuzzy Lp distance, relative similarity measure, multiple attribute decision making
Abstract

Hesitant fuzzy sets, as an extension of fuzzy sets to deal with uncertainty, have attracted much attention since its introduction, in both theory and application aspects. The present work is focused on the interval-valued hesitant fuzzy sets (IVHFSs) to manage additional uncertainty. Now that distance and similarity as a kind of information measures are essential and important numerical indexes in fuzzy set theory and all their extensions, the present work aims at investigating distance and similarity measures in the IVHFSs and then employing them into multiple attribute decision making application. To begin with, II-type generalized interval-valued hesitant fuzzy distance is firstly introduced in the IVHFS, along with its properties and its relationships with the traditional Hamming-Distance and the Euclidean distance. Afterwards, another interval-valued hesitant fuzzy Lp distance based on Lp metric is proposed and its relationship with the Hausdorff distance is discussed. In addition, different from most of similarity measures with dependent on the corresponding distances, a new similarity measure based on set-theoretic approach for IVHFSs is introduced and its properties are discussed; especially, a relative similarity measure is proposed based on the positive ideal IVHFS and the negative ideal IVHFS. Finally, we describe how the IVHFS and its relative similarity measure can be applied to multiple attribute decision making. A numerical example is then provided to illustrate the effectiveness of the proposed method.

Copyright
© 2018, 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/).

Download article (PDF)
View full text (HTML)

Journal
International Journal of Computational Intelligence Systems
Volume-Issue
11 - 1
Pages
15 - 32
Publication Date
2018/01
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
https://doi.org/10.2991/ijcis.11.1.2How to use a DOI?
Copyright
© 2018, 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

TY  - JOUR
AU  - Yi Liu
AU  - Jun Liu
AU  - Zhiyong Hong
PY  - 2018
DA  - 2018/01
TI  - A Multiple Attribute Decision Making Approach Based on New Similarity Measures of Interval-valued Hesitant Fuzzy Sets
JO  - International Journal of Computational Intelligence Systems
SP  - 15
EP  - 32
VL  - 11
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.11.1.2
DO  - https://doi.org/10.2991/ijcis.11.1.2
ID  - Liu2018
ER  -