A Multiple Attribute Decision Making Approach Based on New Similarity Measures of Interval-valued Hesitant Fuzzy Sets
- https://doi.org/10.2991/ijcis.11.1.2How to use a DOI?
- 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
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.
- © 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 -