Volume 5, Issue 3, June 2012, Pages 519 - 529
Entropy, Similarity Measure, Inclusion Measure of Intuitionistic Fuzzy Sets and Their Relationships
Authors
Qiansheng Zhang, Hongyan Xing, Lihua Wu
Corresponding Author
Qiansheng Zhang
Received 8 September 2011, Accepted 9 April 2012, Available Online 1 June 2012.
- DOI
- 10.1080/18756891.2012.696917How to use a DOI?
- Keywords
- Intuitionistic fuzzy set, Entropy, Similarity measure, Distance measure, Inclusion measure
- Abstract
In the present paper, we introduce a new axiomatic definition of the inclusion measure for intuitionistic fuzzy sets (IFSs, for short). The close relationships among entropy, similarity measure, and inclusion measure of IFSs are then discussed in detail. Also, we obtain some important theorems by which the entropy, similarity measure and inclusion measure of IFSs can be transformed into each other based on their axiomatic definitions. Moreover, some formulae for calculating the entropy, similarity measure and inclusion measure of IFSs are put forward. Finally, we compare the proposed new entropy, similarity and distance measures with the existing ones.
- Copyright
- © 2017, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Qiansheng Zhang AU - Hongyan Xing AU - Lihua Wu PY - 2012 DA - 2012/06/01 TI - Entropy, Similarity Measure, Inclusion Measure of Intuitionistic Fuzzy Sets and Their Relationships JO - International Journal of Computational Intelligence Systems SP - 519 EP - 529 VL - 5 IS - 3 SN - 1875-6883 UR - https://doi.org/10.1080/18756891.2012.696917 DO - 10.1080/18756891.2012.696917 ID - Zhang2012 ER -