Journal of Statistical Theory and Applications

In Press, Corrected Proof, Available Online: 18 January 2021

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

Authors
M. Khalaj1, ORCID, F. Khalaj2, *, ORCID
1 Department of Industrial Engineering, Robat Karim Branch, Islamic Azad University, Tehran, Iran
2 Department of Mathematics and statistics, Robat Karim Branch, Islamic Azad University, Tehran, Iran
*Corresponding author. Email: khalaj82@gmail.com
Corresponding Author
F. Khalaj
Received 19 May 2020, Accepted 4 January 2021, Available Online 18 January 2021.
DOI
https://doi.org/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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Journal
Journal of Statistical Theory and Applications
Publication Date
2021/01
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.d.210111.002How to use a DOI?
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/).

Cite this article

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