An Evaluation of Covariance and Correlation Analysis in Entropy Method

K Thirumalai; G Uthra; V Anandan

doi:10.17485/IJST/v16i34.1651

Article

An Evaluation of Covariance and Correlation Analysis in Entropy Method

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i34.1651

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

Original Article

An Evaluation of Covariance and Correlation Analysis in Entropy Method

K Thirumalai^1*, G Uthra², V Anandan³

¹Research Scholar, University of Madras & Department of Mathematics, Saveetha Engineering College, Chennai
²PG & Research Department of Mathematics, Pachaiyappa’s College, Chennai
³Department of Mathematics, Saveetha Engineering College, Chennai, India

*Corresponding Author
Email: [email protected]

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

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

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

References

Torbacki W. A Hybrid MCDM Model Combining DANP and PROMETHEE II Methods for the Assessment of Cybersecurity in Industry 4.0. Sustainability. 2021;13(16):8833. Available from: https://doi.org/10.3390/su13168833
Mukhametzyanov I. Specific character of objective methods for determining weights of criteria in MCDM problems: Entropy, CRITIC and SD. Decision Making: Applications in Management and Engineering. 2021. Available from: https://doi.org/10.31181/dmame210402076i
Demircan BG, Yetilmezsoy K. A Hybrid Fuzzy AHP-TOPSIS Approach for Implementation of Smart Sustainable Waste Management Strategies. Sustainability. 2023;15(8):6526. Available from: https://doi.org/10.3390/su15086526
Krishnan AR, Kasim MM, Hamid R. An Alternate Unsupervised Technique Based on Distance Correlation and Shannon Entropy to Estimate λ0-Fuzzy Measure. Symmetry. 2020;12(10):1708. Available from: https://doi.org/10.3390/sym12101708
Yang N, Lv T, Cui H. A Study on the Coupling and Coordination Relationship of Science and Technology Innovation, Higher Education, and Clean Energy Based on the Entropy Weight and Gray Correlation Analysis Method. International Journal of Energy Research. 2023;2023:1–19. Available from: https://doi.org/10.1155/2023/9122778
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
Navitha K, Rao BM, Sandhya R. Assessment of Groundwater Potential Zone using Multi-criteria Decision-making Technique: A Case Study in the South-western Part of Yadadri Bhuvanagiri District, Telangana, India. Journal of the Geological Society of India. 2023;99(4):539–544. Available from: https://doi.org/10.1007/s12594-023-2342-9
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
B SK, JV, Jacob J. Optimal thermochemical material selection for a hybrid thermal energy storage system for low temperature applications using multi criteria optimization technique. Materials Science for Energy Technologies. 2022;5:452–472. Available from: https://doi.org/10.1016/j.mset.2022.10.005
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
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
Kırda K, Aytekin A. Assessing industrialized countries’ environmental sustainability performances using an integrated multi-criteria model and software. Environment, Development and Sustainability. 2023. Available from: https://doi.org/10.1007/s10668-023-03349-z
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
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
Li H, Lin Y, Wang Y, Liu J, Liang S, Guo S, et al. Multi-Criteria Analysis of a People-Oriented Urban Pedestrian Road System Using an Integrated Fuzzy AHP and DEA Approach: A Case Study in Harbin, China. Symmetry. 2021;13(11):2214. Available from: https://doi.org/10.3390/sym13112214
Luyen LA, Thanh NV. Logistics Service Provider Evaluation and Selection: Hybrid SERVQUAL–FAHP–TOPSIS Model. Processes. 2022;10(5):1024. Available from: https://doi.org/10.3390/pr10051024
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
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
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
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
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
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
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

Copyright

© 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)