• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2023, Volume: 16, Issue: 34, Pages: 2746-2752

Original Article

An Evaluation of Covariance and Correlation Analysis in Entropy Method

Received Date:04 July 2023, Accepted Date:07 August 2023, Published Date:15 September 2023


Objectives: The main aim of this research is to obtain the criterion weight in Multi-Criteria Decision Making (MCDM) with conflicting criteria, as the relevance and impact of the criterion weight alters the outcome of any decision-making. Methods: This study proposes a modification to the existing Entropy technique using principal component analysis, which is found to be suitable for all dayto- day real-life problems. Findings: A comparative study is done between covariance and correlation analysis to validate the accuracy of the proposed technique. The proposed modification is illustrated with a numerical example. Novelty: The inclusion of the concept of covariance analysis in the principal component analysis is a new approach to the determination of the criterion weight in MCDM.

Keywords: Multi-Criteria Decision Making (MCDM); Entropy; Criterion Weight; Covariance; Correlation; Principal Component Analysis (PCA); CRITIC method


  1. Gao X, Ma Y, Zhou W. Analysis of Software Trustworthiness Based on FAHP-CRITIC Method. Journal of Shanghai Jiaotong University (Science). 2022. Available from: https://doi.org/10.1007/s12204-022-2496-4
  2. Anandan V, Uhra G. A Hybrid Approach integrating AHP and Extended TOPSIS by Tanimoto and Jaccard Distances Measures. International Journal of Pure and Applied Mathematics. 2017;117(6):145–153. Available from: https://www.acadpubl.eu/jsi/2017-117-5-6/articles/6/15.pdf
  3. S JG, S SH, A MG, G G, A V. Road safety assessment and risks prioritization using an integrated SWARA and MARCOS approach under spherical fuzzy environment. Neural Computing and Applications. 2022;35(6):4549–4567. Available from: https://doi.org/10.1007/s00521-022-07929-4
  4. Nedjar NH, Djebbar Y, Djemili L. Application of the analytical hierarchy process for planning the rehabilitation of water distribution networks. Arab Gulf Journal of Scientific Research. 2023. Available from: https://doi.org/10.1108/agjsr-07-2022-0110
  5. Wu RMX, Zhang Z, Yan W, Fan JW, Gou J, Liu B, et al. A comparative analysis of the principal component analysis and entropy weight methods to establish the indexing measurement. PLOS ONE. 2022;17(1):e0262261. Available from: https://doi.org/10.1371/journal.pone.0262261
  6. Chen C, Zhou J, Pan J. Correlation structure regularization via entropy loss function for high-dimension and low-sample-size data. Communications in Statistics - Simulation and Computation. 2021;50(4):993–1008. Available from: https://doi.org/10.1080/03610918.2019.1571607
  7. Silva NF, Santos MD, Gomes CFS, Andrade LPD. An integrated CRITIC and Grey Relational Analysis approach for investment portfolio selection. Decision Analytics Journal. 2023;8:100285. Available from: https://doi.org/10.1016/j.dajour.2023.100285
  8. Şahin M. A comprehensive analysis of weighting and multicriteria methods in the context of sustainable energy. International Journal of Environmental Science and Technology. 2021;18(6):1591–1616. Available from: https://doi.org/10.1007/s13762-020-02922-7
  9. Paradowski B, Shekhovtsov A, Bączkiewicz A, Kizielewicz B, Sałabun W. Similarity Analysis of Methods for Objective Determination of Weights in Multi-Criteria Decision Support Systems. Symmetry. 2021;13(10):1874. Available from: https://doi.org/10.3390/sym13101874
  10. Gewers FL, Ferreira GR, Arruda HFD, Silva FN, Comin CH, Amancio DR, et al. Principal Component Analysis. ACM Computing Surveys. 2022;54(4):1–34. Available from: https://doi.org/10.1145/3447755
  11. González-García N, Nieto-Librero AB, Galindo-Villardón P. CenetBiplot: a new proposal of sparse and orthogonal biplots methods by means of elastic net CSVD. Advances in Data Analysis and Classification. 2023;17(1):5–19. Available from: https://doi.org/10.1007/s11634-021-00468-1
  12. Michel G, Keirns LR, Ahlbrecht CD, Barr BC, DA. Calculating Transfer Entropy from Variance-Covariance Matrices Provides Insight into Allosteric Communication in ERK2. Journal of Chemical Theory and Computation. 2021;17(5):3168–3177. Available from: https://doi.org/10.1021/acs.jctc.1c00004
  13. Ali HS, Chakravorty A, Kalayan J, Visser SPD, Henchman RH. Energy–entropy method using multiscale cell correlation to calculate binding free energies in the SAMPL8 host–guest challenge. Journal of Computer-Aided Molecular Design. 2021;35(8):911–921. Available from: https://doi.org/10.1007/s10822-021-00406-5


© 2023 Thirumalai et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)


Subscribe now for latest articles and news.