A Novel Technique for Criteria Weighting in Multi-Criteria Decision-Making: Tanimoto Contrast Approach (TCA)

Year 2025, Volume: 12 Issue: 2, 445 - 478, 30.06.2025

Furkan Fahri Altıntaş

https://doi.org/10.54287/gujsa.1673755

Abstract

This study introduces the Tanimoto Contrast Approach (TCA), a novel objective method for determining criterion weights in Multi-Criteria Decision-Making (MCDM) problems. Built on the internal–external dispersion logic of the CRITIC method, TCA replaces Pearson correlation with Tanimoto similarity to capture both linear and non-linear relationships, enabling a more comprehensive evaluation of inter-criterion contrasts and similarities. The method was tested using the 2024 Global Innovation Index data from selected seven countries. Sensitivity analysis revealed that TCA maintains ranking stability under varying conditions, while comparative analysis showed strong correlation with ENTROPY, SVP, and MEREC methods, confirming its reliability and credibility. In addition, simulation analysis based on ten different decision matrix scenarios demonstrated that TCA produces high average variance and consistent, homogeneous weight distributions evidence of its robustness and stability. TCA’s advantages include distribution free applicability, insensitivity to zero or negative values, scale independence, and effectiveness with large datasets. Moreover, its comparative performance against widely used objective weighting methods such as ENTROPY, CRITIC, SD, SVP, MEREC, and LOPCOW has been thoroughly discussed. In conclusion, TCA offers contrast-based, decision-maker-independent weighting framework that generates meaningful, balanced, and sensitive results. Its integration into MCDM applications provides a valuable contribution to the advancement of objective weighting techniques.

Keywords

Tanimoto Similarity , Tanimoto Contrast , MCDM , Criteria Weight

References

• Ahmad, N., Ibrahim, M. A., Sayed, S. R., Shah, S. A., Tahir, M. H., & Zou, Y. (2025). Data mining and machine learning based search for optimal materials for perovskite and organic solar cells. Solar Energy, 267, 105-113. https://doi.org/10.1016/j.solener.2024.113223
• Anastasiu, D. C., & Karypis, G. (2017). Efficient identification of Tanimoto nearest neighbors. Int J Data Sci Anal, 4, 153–172. https://doi.org/10.1007/s41060-017-0064-z
• Ayçin, E. (2019). Çok Kriterli Karar Verme. Ankara: Nobel Yayın.
• Aydemir, M. F. (2025). Evaluation of foreign direct investment attractiveness of BRICS-T countries: The critic-lopcow based aras approach. Politik Ekonomik Kuram, 9(1), 372-392. https://doi.org/10.30586/pek.1613421
• Bajusz, D., Rácz, A., & Héberger, K. (2015). Why is Tanimoto index an appropriate choice for fingerprint-based similarity calculations? Journal of Cheminformatics, 7(20), 1-13. https://doi.org/10.1186/s13321-015-0069-3
• Baldi, P., & Benz, R. W. (2008). BLASTing small molecules—statistics and extreme statistics of chemical similarity scores. BIOINFORMATICS, 24, 357-365. https://doi.org/10.1093/bioinformatics/btn187
• Baş, F. (2021). Çok Kriterli Karar Verme Yöntemlerinde Kriter Ağırlıklarının Belirlenmesi. Ankara: Nobel Bilimsel.
• Baydaş, M., Elma, O. E., & Stević, Ž. (2024). Proposal of an innovative MCDA evaluation methodology: knowledge discovery through rank reversal, standard deviation, and relationship with stock return. Financial Innovation, 10(4), 1-35. https://doi.org/10.1186/s40854-023-00526-x
• Bero, S. A., Muda, A. K., Choo, Y. H., Muda, N. A., & Pratama, S. F. (2018). Similarity measure for molecular structure: A brief review. IOP Conf. Series: Journal of Physics: Conf. Series(892), 1-9. https://doi.org/10.1088/1742-6596/892/1/012015
• Bircan, H. (2020). Çok Kriterleri Karar Verme Problemlerinde Kriter Ağırlıklandırma Yöntemleri. Ankara: Nobel Akademik.
• Chung, N. C., Miasojedow, B., Startek, M., & Gambin, A. (2019). Jaccard/Tanimoto similarity test and estimation methods for biological presence-absence data. BMC Bioinformatics, 20(15), 1-11. https://doi.org/10.1186/s12859-019-3118-5
• Demir, G., & Arslan, R. (2022). Sensitivity analysis in multi-criteria decision-making problems. Ankara Hacı Bayram Veli Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 24(3), 1025-1056.
• Demir, G., Özyalçın, A. T., & Bircan, H. (2021). Çok kriterli karar verme yöntemleri ve ÇKKV yazılımı ile problem çözümü. Ankara: Nobel.
• Dhara, A., Kaur, G., Kishan, P. M., Majumder, A., & Yadav, R. (2022). An efficient decision support system for selecting very light business jet using critic-topsis method. Aircraft Engineering and Aerospace Technology, 94(3), 458-472. https://doi.org/10.1108/AEAT-04-2021-013
• Diakoulaki, D., Mavrotas, G., & Papayannakis , L. (1995). Determining objective weights in multiple criteria problems: The critic method. Computers & Operations Research, 22(7), 763-770.
• Dinçer, S. E. (2019). Çok Kriterli Karar Alma. Ankara: Gece Akademi.
• Dokmanic, I., Parhizkar, R., Ranieri, J., & Vetterli, M. (2015). Euclidean distance matrices: Essential theory, algorithms, and applications. IEEE Signal Processing Magazine, 32(6), 12-30. https://doi.org/10.1109/MSP.2015.2398954
• Durdu, D. (2025). Evaluating financial performance with spc-lopcow-marcos hybrid methodology: A Case study for firms listed in BIST sustainability index. Knowledge and Decision Systems with Applications, 1, 92-111. http://www.doi.org/10.59543/kadsa.v1i.13879
• Ecer, F. (2020). Çok Kriterli Karar Verme. Ankara: Seçkin Yayıncılık.
• Ecer, F., & Pamucar, D. (2022). A novel lopcow-dobi multi-criteria sustainability performance assessment methodology: An application in developing country banking sector. Omega, 1-35. https://doi.org/10.1016/j.omega.2022.102690
• Eligüzel, İ. M., & Eligüzel, N. (2024). Evaluation of sustainable transportation in 25 European countries using gra and entropy mabac. Journal of Transportation and Logistics, 9(2), 245-259. https://doi.org/10.26650/JTL.2024.1437521
• Feldmann, C. W., Sieg, J., & Mathea, M. (2025). Analysis of uncertainty of neural fingerprint-based models. Faraday Discussions, 256, 551-567. http://dx.doi.org/10.1039/D4FD00095A
• Feldmann, C., & Bajorath, J. (2022). Calculation of exact Shapley values for support vector machines with Tanimoto kernel enables model interpretation. iScience, 25, 1-13. https://doi.org/10.1016/j.isci.2022.105023
• Iglesias, F., & Kastner, W. (2013). Analysis of similarity measures in times series clustering for the discovery of building energy patterns. Energies, 6, 579-597. https://doi.org/10.3390/en6020579
• Kalaycı, Ş. (2014). SPSS Uygulamalı Çok Değişkenli İstatistik Teknikleri. Ankara: Anı Yayın Dağıtım.
• Karagöz, Y. (2014). SPSS 21.1 Uygulamalı İstatistik Tıp, Eczacılık, DişHekimliği ve Sağlık Bilimleri İçin. Ankara: Nobel Akademik Yayıncılık.
• Keleş, N. (2023). Uygulamalarla Klasik ve Güncel Karar Verme Yöntemleri. Ankara: Nobel Bilimsel.
• Keshavarz-Ghorabaee, M., Amiri, M., Zavadskas, E. K., Turskis, Z., & Antucheviciene, J. (2021). Determination of objective weights using a new method based on the removal effects of criteria (MEREC). Symmetry, 13(525), 1-21. https://doi.org/10.3390/sym13040525
• Kilmen, S. (2015). Eğitim Araştırmacıları için SPSS uygulamalı istatistik. Ankara: Edge Akademi.
• Kryszkiewicz , M. (2013). Using non-zero dimensions for the cosine and tanimoto similarity search among real valued vectors. Fundamenta Informaticae, 127(1-4), 307-323. https://doi.org/10.3233/FI-2013-911
• Kryszkiewicz, M. (2021). Determining Tanimoto Similarity Neighborhoods of Real-Valued Vectors by Means of the Triangle Inequality and Bounds on Lengths. In: S. C. Ramanna (Eds.), Rough Sets. IJCRS Lecture Notes in Computer Science (pp. 8–34). Singapore Springer.
• Lasek, P., & Mei, Z. (2019). Clustering and visualization of a high-dimensional diabetes dataset. Procedia Computer Science, 159, 2179–2188. https://doi.org/10.1016/j.procs.2019.09.392
• Lipkus, A. H. (1999). A proof of the triangle inequality for the tanimoto distance. Journal of Mathematical Chemistry, 26, 263–265. https://doi.org/10.1023/A:1019154432472
• Ma, C., Wang, L., & Xie, X.-Q. (2011). GPU accelerated chemical similarity calculation for compound library comparison. Journal of Chemical Information and Modeling, 51(7), 1521–1527. https://doi.org/10.1021/ci1004948
• Mana, S. C., & Sasipraba, T. (2021). Research on cosine similarity and pearson correlation based. International Conference on Mathematical Sciences(1770), 1-7. https://doi.org/10.1088/1742-6596/1770/1/012014
• Mellor, C. L., Marchese, R. L., Robinson, Benigni, R., Ebbrell, D., Enoch, S. J., . . . Cronin, M. (2019). Molecular fingerprint derived similarity measures for toxicological read across: Recommendations for optimal use. Regulatory Toxicology and Pharmacology, 101, 121-134.
• Mohebbi, A., Ebrahimi, M., Askari, F. S., Shaddel, R., Mirarab, A., & Oladnabi, M. (2022). QSAR modeling of a ligand-based pharmacophore derived from hepatitis B virus surface antigen ınhibitors. ACTA MICROBIOLOGICA BULGARICA, 38(3), 197-206.
• Momena, A. F., Gazi, K. H., Rahaman, M., Sobczak, A., Salahshour, S., Mondal, S. P., & Ghosh, A. (2024). Ranking and challenges of supply chain companies using MCDM methodology. Logistics, 8, 1-32. https://doi.org/10.3390/logistics8030087
• Mukhametzyanov, I. Z. (2021). Specific character of objective methods for determining weights of criteria in mcdm problems: Entropy, critic, sd. decision making. Applications in Management and Engineering, 4(2), 76-105.
• Mulia, I., Kusuma, W. A., & Afendi, F. M. (2018). Algorithm for predicting compound protein ınteraction using tanimoto similarity and klekota-roth fingerprint. TELKOMNIKA, 16(4), 1785-1792. https://doi.org/10.12928/TELKOMNIKA.v16i4.5916
• Nasser, A. A., Alkhulaidi, A., Ali, M. N., Hankal, M., & Al-olofe, M. (2019). A study on the ımpact of multiple methods of the data normalization on the result of saw, wed and topsis ordering in healthcare multi-attributte decision making systems based on ew, entropy, critic and svp weighting approaches. Indian Journal of Science and Technology, 12(4), 1-21. https://doi.org/10.17485/ijst/2019/v12i4/140756
• Nowatzky, Y., Russo, F. F., Lisec, J., Kister, A., Reinert, K., Muth, T., & Benner, P. (2025). FIORA: Local neighborhood-based prediction of compound mass spectra from single fragmentation events. Nature Communications, 16, 1-17. https://doi.org/10.1038/s41467-025-57422-
• Özdamar, K. (2018). Eğitim, Sağlık ve Sosyal Bilimler için SPSS Uygulamalı Temel İstatistik. Bursa: Nisan Yayınevi.
• Öztel, A., & Alp, İ. (2020). Çok Kriterli Karar Verme Seçiminde Yeni Bir Yaklaşım. İstanbul: Kriter Yayıncılık.
• Paulose, R., Jegatheesan, K., & Balakrishnan, G. S. (2018). A big data approach with artificial neural network and molecular similarity for chemical data mining and endocrine disruption prediction. Indian Journal of Pharmacology, 50(4), 169-176. https://doi.org/10.4103/ijp.IJP_304_17
• Podani, J. (2000). Introduction to the exploration of multivariate biological data. Leiden: Backhuys Publishers.
• Popović, G., Pucar, D., & Smarandache, F. (2022). MEREC-COBRA approach in e-commerce development strategy selection. Journal of Process Management and New Technologies, 10(3-4), 66-74.
• Sankara, R. A., Durga , B. S., Sobha , R. T., Raju , S. B., & Narahari , S. G. (2011). Study of Diversity and Similarity of Large Chemical Databases Using Tanimoto Measure. In: K. R. Venugopal & L. M. Patnaik (Eds.). Communications in Computer and Information Science (pp. 1-12. https://doi.org/10.1007/978-3-642-22786-8_5
• Sehgal, K., Kaur, H., Kaur, S., Singh, S., Channi, H. K., & Stević, Ž. (2025). Cost-Effective optimization of hybrid renewable energy system for micro, small, and medium enterprises: A decision-making framework integrating merec and marcos. Opportunities and Challenges in Sustainability, 4(1), 17-32. https://doi.org/10.56578/ocs040102
• Selvi, C., & Sivasankar, E. (2018). A Novel Singularity Based Improved Tanimoto Similarity Measure for Effective Recommendation Using Collaborative Filtering. In: Proceedings of the 8th International Conference on Cloud Computing, Data Science & Engineering (Confluence) (NODIA, 2018)., (pp. 256-262).
• Shan, R., Zhang, R., Gao, Y., Wang, W., Zhu, W., Xin, L., . . . Cui, P. (2025). Evaluating ionic liquid toxicity with machine learning and structural similarity methods. Green Chemical Engineering, 6, 249–262. https://doi.org/10.1016/j.gce.2024.08.008
• Sharma, A., & Lal, S. P. (2011). Tanimoto based similarity measure for ıntrusion detection system. Journal of Information Security, 2, 195-201. https://doi.org/10.4236/jis.2011.24019
• Sleem, A., Mostafa, N., & Elhenawy, I. (2023). Neutrosophic critic mcdm methodology for ranking factors and needs of customers in product's target demographic in virtual reality metaverse. Neutrosophic Systems with Applications, 2, 55-66. https://doi.org/10.61356/j.nswa.2023.10
• Surendran, A., Zsigmond, K., López-Pérez, K., & Miranda-Quintana, R. A. (2025). Is Tanimoto a metric? bioRxiv, 1-12. https://doi.org/10.1101/2025.02.18.638904
• Tayalı, H. A., & Timor, M. (2017). Ranking with Statistical variance procedure based analytic hierarchy process. Acta Infologica, 1(1), 31-38.
• Thakkar, J. J. (2021). Multi criteria decision making. Springer Singapore.
• Thiel, P., Sach-Peltason, L., Ottmann, C., & Kohlbacher, O. (2014). Blocked inverted indices for exact clustering of large chemical spaces. Chem. Inf. Model, 54(9), 2395–2401.
• Todeschini , R., Ballabio , D., Consonni, V., Mauri, A., & Pavan, M. (2007). CAIMAN (Classification And Influence Matrix Analysis): A new approach to the classification based on leverage-scaled functions. Chemometrics and Intelligent Laboratory Systems, 87(1), 3-17. https://doi.org/10.1016/j.chemolab.2005.11.001
• Uludağ, A. S., & Doğan, H. (2021). Üretim Yönetiminde Çok Kriterli Karar Verme. Ankara: Nobel.
• Ulutaş, A., & Topal, A. (2020). Bütünleştirilmiş Çok Kriterli Karar Verme Yöntemlerinin Üretim Sektörü Uygulamaları. Ankara: Akademisyen Kitapevi.
• Vivek, M. B., Manju, N., & Vijay, M. B. (2018). Machine Learning Based Food Recipe Recommendation System. In: Guru, D. S., Vasudev, T., Chethan, H. K., & Kumar, Y.S, In: Proceedings of International Conference on Cognition and Recognition (SINGAPORE 2018), (pp. 11-19).
• Wang, C.-N., Nguyen, N.-A.-T., & Dang, T.-T. (2023). Sustainable evaluation of major third-party logistics providers: a framework of an mcdm-based entropy objective weighting method. Mathematics, 11, 1-27. https://doi.org/10.3390/math11194203
• Xu, H., Zeng, W., Zeng, X., & Yen, G. (2019). An evolutionary algorithm based on minkowski distance for many objective optimization. IEEE Transactions on Cybernetics, 49(11), 3968-3979. https://doi.org/10.1109/TCYB.2018.2856208
• Yasin, Y., Riaz, M., & Alsager, K. (2025). Synergy of machine learning and the einstein choquet integral with lopcowand fuzzy measures for sustainable solid waste management. AIMS Mathematics, 10(1), 460–498. https://doi.org/10.3934/math.2025022
• Yazdi, A. K., Tan, Y., Birau, R., Frank, D., & Pamučar, D. (2025). Sustainable solutions: using mcdm to choose the best location for green energy projects. International Journal of Energy Sector Management, 19(1), 146-180. https://doi.org/10.1108/IJESM-01-2024-0005
• Ying, C. Z., Leong, C. H., Alvin, L. W., & Yang, C. J. (2021). Improving the Workflow of Chemical Structure Elucidation with Morgan Fingerprints and the Tanimoto Coefficient. In: Guo, H, Ren, H & Kim, N (Eds.). IRC-SET 2020 (pp. 13-24). Singapore Springer.
• Yoon, D., & Lee, H. (2025). In silico discovery of novel compounds for fak activation using virtual screening, AI based prediction, and molecular dynamics. Computational Biology and Chemistry, 117, https://doi.org/10.1016/j.compbiolchem.2025.108420
• Yoshizawa, T., Ishida, S., Sato, T., Ohta, M., Honma, T., & Terayama, K. (2025). A data-driven generative strategy to avoid reward hacking in multi-objective molecular design. Nature Communications, 16, 1-12. https://doi.org/10.1038/s41467-025-57582-3
• Zahrotun, L. (2016). Comparison jaccard similarity, cosine similarity and combined both of the data clustering with shared nearest neighbor method. Computer Engineering and Applications, 5(1), 11-18.
• Zainudin, S., & Nurjana, N. R. (2018). Comparison of similarity method to improve retrieval performance for chemical data. Jurnal Teknologi Maklumat dan Multimedia Asia-Pasifik, 7(1), 91-98. https://doi.org/10.17576/apjitm-2018-0701-08.
• Zardari, N. H., Ahmed, K., Shirazi, S. M., & Yusop, Z. B. (2014). Weighting Methods and their Effects on Multi Criteria Decision Making Model Outcomes in Water Resources Management. Springer Nature.
• Zhang, B., Vogt, M., Maggiora, G. M., & Bajorath, J. (2015). Design of chemical space networks using a Tanimoto similarity variant based upon maximum common substructures. J Comput Aided Mol Des, 29, 937–950. https://doi.org/10.1007/s10822-015-9872-1
• Zhang, X., Wang, C., Li, E., & Xu, C. (2014). Assessment model of ecoenvironmental vulnerability based on improved entropy weight method. Scientific World Journal, 2014, 1-7. http://dx.doi.org/10.1155/2014/797814