Similarity Measure Based on the Belief Function Theory: Application in a Decision-Making Process

Authors

M. Khalaj^1, , F. Khalaj^{2, *,}

¹Department of Industrial Engineering, Robat Karim Branch, Islamic Azad University, Tehran, Iran

²Department of Mathematics and statistics, Robat Karim Branch, Islamic Azad University, Tehran, Iran

^*Corresponding author. Email: khalaj82@gmail.com

DOI

10.2991/jsta.d.210111.002How to use a DOI?

Keywords

Belief function theory; Belief set; Similarity measure; Decision-making

Abstract

This study considers a new aspect of the belief function theory to define a belief set, which is characterized by truth, uncertainty and falsity belief degrees as a 3D vector representation. Then, based on the implication of a belief set, one of the similarity measures (i.e., Cosine, Jaccard and Dice) between two belief sets is defined. Furthermore, the weighted similarity measure of these different species between each alternative and ideal alternative is presented in order to rank alternatives and determine the best one. Finally, a comparison between similarity measures and an application of a new method based on similarity measures between two belief sets in the decision-making process is calculated to show the capability and validity of the proposed method.

Copyright

© 2021 The Authors. Published by Atlantis Press B.V.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - M. Khalaj
AU  - F. Khalaj
PY  - 2021
DA  - 2021/01/18
TI  - Similarity Measure Based on the Belief Function Theory: Application in a Decision-Making Process
JO  - Journal of Statistical Theory and Applications
SP  - 1
EP  - 10
VL  - 20
IS  - 1
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.210111.002
DO  - 10.2991/jsta.d.210111.002
ID  - Khalaj2021
ER  -