Interval-Valued Intuitionistic Fuzzy Cosine Similarity Measures for Real World Problem Solving
(1) * Sangeetha Palanisamy Mail (Bharathiar University, India)
(2) Jayaraman Periyasamy Mail (Bharathiar University, India)
*corresponding author

Abstract


Similarity measures (SMs) are fundamental in various applications, including identifying patterns within medical data and aiding pattern recognition (PR) by quantifying the likeness between different patterns. Moreover, they play a crucial role in real-world problems such as Multiple Criteria Decision Making (MCDM), where decision-makers assess and compare alternatives based on multiple criteria simultaneously. Moreover, Cosine similarity is a measurement that quantifies the similarity between two or more objects. This study presents a comprehensive exploration of Interval-Valued Intuitionistic Fuzzy Cosine Similarity Measures (IV IF CSMs) as a novel technique for assessing the degree of association between objects in realworld applications. By extending traditional cosine similarity measures (CSM) to interval-valued intuitionistic fuzzy sets (IV IFS), the proposed IV IF CSMs offer an effective framework for handling uncertainty, ambiguity, and imprecision in decision-making processes. The research demonstrates the practical utility of IV IF CSMs in addressing complex issues in PR, medical diagnosis (MD), and MCDM. In contrast to established methods like Singh’s, Xu’s, and Luo’s measures, our approach consistently generates higher similarity values, encompassing both membership (MF) and non-membership (NMF) with interval values.


Keywords


Measures; Similarity Measure; Cosine Similarity Measure; Fuzzy Set; Pattern Recognition; MCDM; Medical Diagnosis

   

DOI

https://doi.org/10.31763/ijrcs.v4i2.1251 		      

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References


[1] H. Kamaci, “Complex linear Diophantine fuzzy sets and their cosine similarity measures with applications,†Complex & Intelligent Systems, vol. 8, no. 3, pp. 1281-1305, 2022, https://doi.org/10.1007/s40747-021-00573-w.

[2] L. A. Zadeh, “Fuzzy sets,†Information and control, vol. 8, no. 3, pp. 338-353, 1965, https://doi.org/10.1016/S0019-9958(65)90241-X.

[3] Atanassov K T, “Intuitionistic fuzzy sets,†Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986, https://doi.org/10.1016/S0165-0114(86)80034-3.

[4] L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning—I,†Information sciences, vol. 8, no. 3, pp. 199-249, 1975, https://doi.org/10.1016/0020-0255(75)900365.

[5] K. T. Atanassov, “Interval valued intuitionistic fuzzy sets,†Fuzzy Sets Systems, vol. 31, no. 3, pp. 343-349, 1989, https://doi.org/10.1007/978-3-030-32090-4.

[6] B. Gohain, R. Chutia, and P. Dutta, “A distance measure for optimistic viewpoint of the information in interval-valued intuitionistic fuzzy sets and its applications,†Engineering Applications of Artificial Intelligence, vol. 119, no. 1, 2023, https://doi.org/10.1016/j.engappai.2022.105747.

[7] H. Garg, M. Olgun, E. Turkarslan, M. ¨Unver, “A Choquet Integral Based Cosine Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and an Application to Pattern Recognition,†Lobachevskii Journal of Mathematics, vol. 43, no. 9, pp. 2444-2452, 2022, https://doi.org/10.1134/S1995080222120113.

[8] S. Hendiani, and G. Walther, “TOPSISort-L: An extended likelihood-based interval-valued intuitionistic fuzzy TOPSIS-sort method and its application to multi-criteria group decision-making,†Expert Systems with Applications, vol. 233, 2023, https://doi.org/10.1016/j.eswa.2023.121005.

[9] R. Yao, and H. Guo, “A multiattribute group decision-making method based on a new aggregation operator and the means and variances of interval-valued intuitionistic fuzzy values,†Scientific Reports, vol. 12, no. 1, 2022, https://doi.org/10.1038/s41598-022-27103-z.

[10] Y. Zahraoui, M. Akherraz, and A. Ma’arif, “A comparative study of nonlinear control schemes for induction motor operation improvement,†International Journal of Robotics and Control Systems, vol. 2, no. 1, pp. 1-17, 2022, https://doi.org/10.31763/ijrcs.v2i1.521.

[11] Y. Liu, and W, Jiang, “A new distance measure of interval-valued intuitionistic fuzzy sets and its application in decision making,†Soft Computing, vol. 24, pp. 6987-7003, 2020, https://doi.org/10.1007/s00500-019-04332-5.

[12] Mishra A R, Chandel A, & Motwani D, “Extended MABAC method based on divergence measures for multi-criteria assessment of programming language with interval-valued intuitionistic fuzzy sets,†Granular Computing, vol. 5, pp. 97-117, 2020, https://doi.org/10.1007/s41066-018-0130-5.

[13] K. Guo, and H. Xu, “A unified framework for knowledge measure with application: From fuzzy sets through interval-valued intuitionistic fuzzy sets,â€Applied Soft Computing, vol. 109, 2021, https://doi.org/10.1016/j.asoc.2021.107539.

[14] S. Fang, P. Zhou, H. Dinc¸er, and S. Yuksel, “Assessment of safety management system on energy investment risk using house of quality based on hybrid stochastic interval-valued intuitionistic fuzzy decision making approach,†Safety Science, vol. 141, no. 15, 2021, https://doi.org/10.1016/j.ssci.2021.105333.

[15] S. Li, J. Yang, G. Wang, and T. Xu, “Multi-granularity distance measure for interval-valued intuitionistic fuzzy concepts,†Information Sciences, vol. 570, pp. 599-622, 2021, https://doi.org/10.1016/j.ins.2021.05.003.

[16] M. Afzali, and K. Suresh, “Comparative analysis of various similarity measures for finding similarity of two documents,†International Journal of Database Theory and Application, vol. 10, no. 2, pp. 23-30, 2017, http://dx.doi.org/10.14257/ijdta.2017.10.2.02.

[17] W. H. Gomaa, and A. A. Fahmy, “A survey of text similarity approaches,†International journal of Computer Applications, vol. 68, no. 13, pp. 13-18, 2013, https://doi.org/10.5120/11638-7118.

[18] A. Bhattacharya, “On a measure of divergence of two multinominal populations Sankhya,†Indian Journal of Statistics, vol. 7, pp. 401-406, 1946, https://www.jstor.org/stable/25047882.

[19] G. Salton, and M. J. McGill, “Introduction to modern information retrieval,†McGraw-Hill Book Company, New York, 1983, https://cir.nii.ac.jp/crid/1574231873785747328.

[20] W. Guo, L. Bi, B. Hu, and S. Dai, “Cosine similarity measure of complex fuzzy sets and robustness of complex fuzzy connectives,†Mathematical Problems in Engineering, vol. 2020, 2020, https://doi.org/10.1155/2020/6716819.

[21] J. Ye, “Cosine similarity measures for intuitionistic fuzzy sets and their applications,†Mathematical and computer modelling, vol. 53, no.1-2, pp. 91-97, 2011, https://doi.org/10.1016/j.mcm.2010.07.022.

[22] P. Singh, “A new method on measure of similarity between interval-valued intuitionistic fuzzy sets for pattern recognition,†Journal of Applied & computational mathematics, vol. 1, no.1, pp. 1-5, 2012, http://dx.doi.org/10.4172/2168-9679.1000101.

[23] J. Ye, “Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision making,†International Journal of General Systems, vol. 42, no. 8, pp. 883-891, 2013, https://doi.org/10.1080/03081079.2013.816696.

[24] D. Liu, X. Chen,and D. Peng, “Interval-valued intuitionistic fuzzy ordered weighted cosine similarity measure and its application in investment decision-making,†Complexity, 2017, https://doi.org/10.1155/2017/1891923.

[25] Harish G, “An improved cosine similarity measure for intuitionistic fuzzy sets and their applications to decision-making process,†Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, pp. 1578-1594, 2018, http://dx.doi.org/10.15672/HJMS.2017.510.

[26] P. Purwono, A. Ma’arif, W. Rahmaniar, H. I. K. Fathurrahman, A. Z. K. Frisky, and Q. M. U. Haq, “Understanding of convolutional neural network (cnn): A review,†International Journal of Robotics and Control Systems, vol. 2, no. 4, pp. 739-748, 2022, http://dx.doi.org/10.31763/ijrcs.v2i4.888.

[27] P. Rathnasabapathy, and D. Palanisami, “A theoretical development of improved cosine similarity measure for interval valued intuitionistic fuzzy sets and its applications,†Journal of Ambient Intelligence and Humanized Computing, vol. 14, pp. 16575-16587, 2023, https://doi.org/10.1007/s12652-022-04019-0.

[28] J. S. Saputro, H. Maghfiroh, F. Adriyanto, M. R. Darmawan, M. H. Ibrahim, and S. Pramono, “Energy Monitoring and control of automatic transfer switch between grid and solar panel for home system,†International Journal of Robotics and Control Systems, vol. 3, no. 1, pp. 59-73, 2023, https://doi.org/10.31763/ijrcs.v3i1.843.

[29] R. Verma, and J. M. Merigo, “A new decision making method using interval-valued intuitionistic fuzzy cosine similarity measure based on the weighted reduced intuitionistic fuzzy sets,†Informatica, vol. 31, no. 2, pp. 399-433, 2020, https://doi.org/10.15388/20-INFOR405.

[30] R. Zhang, Z. Xu, and X. Gou, “ELECTRE II method based on the cosine similarity to evaluate the performance of financial logistics enterprises under double hierarchy hesitant fuzzy linguistic environment,†Fuzzy Optimization and Decision Making, vol. 22, no. 1, pp. 23-49, 2023, https://doi.org/10.1007/s10700-022-09382-3.

[31] S. Singh, and A. H. Ganie, “Applications of picture fuzzy similarity measures in pattern recognition, clustering, and MADM,†Expert Systems with Applications, vol. 168, 2021, https://doi.org/10.1016/j.eswa.2020.114264.

[32] B. Noorulden, and A. Ma’arif, “NB theory with bargaining problem: a new theory,†International Journal of Robot and Control Systems, vol. 2, no. 3, pp. 606-609, 2022, http://dx.doi.org/10.31763/ijrcs.v2i3.798.

[33] J. S. Chai, G. Selvachandran, F. Smarandache, V. C. Gerogiannis, L. H. Son, Q. T. Bui, and B. Vo, “New similarity measures for single-valued neutrosophic sets with applications in pattern recognition and medical diagnosis problems,†Complex & Intelligent Systems, vol. 7, pp. 703-723, 2021, https://doi.org/10.1007/s40747-020-00220-w.

[34] N. X. Thao, and S. Y. Chou, “Novel similarity measures, entropy of intuitionistic fuzzy sets and their application in software quality evaluation,†Soft Computing, vol. 26, pp. 2009-2020, 2022, https://doi.org/10.1007/s00500-021-06373-1.

[35] A. R. Mishra, A. Chandel, and P. Saeidi, “Low-carbon tourism strategy evaluation and selection using interval-valued intuitionistic fuzzy additive ratio assessment approach based on similarity measures,†Environment, Development and Sustainability, vol. 24, no. 5, pp. 7236-7282, 2022, https://doi.org/10.1007/s10668-021-01746-w.

[36] W. H. Lee, J. H. Tsai, and L. C. Lee, “A new multiple criteria decision making approach based on intuitionistic fuzzy sets, the weighted similarity measure, and the extended TOPSIS method,†Journal of Internet Technology, vol. 22, no. 3, pp. 645-656, 2021, https://jit.ndhu.edu.tw/article/view/2521.

[37] H. Garg, and D. Rani, “Novel similarity measure based on the transformed right-angled triangles between intuitionistic fuzzy sets and its applications,†Cognitive Computation, vol. 13, no. 1, pp. 447-465, 2021, https://doi.org/10.1007/s12559-020-09809-2.

[38] E. Salajegheh, S. Mojalal, and A. M. Ghahfarokhi, “Treatment of Bone Marrow Cancer Based on Model Predictive Control,†International Journal of Robotics and Control Systems, vol. 1, no. 4, pp. 463-476, 2021, https://doi.org/10.31763/ijrcs.v1i4.481.

[39] A. Singh, and S. Kumar, “A novel dice similarity measure for IFSs and its applications in pattern and face recognition,†Expert Systems with Applications, vol. 149, 2020, https://doi.org/10.1016/j.eswa.2020.113245.

[40] Y. Donyatalab, F. K. Gundogdu, F. Farid, S. A. S. Shishavan, E. Farrokhizadeh, and C. Kahraman, “Novel spherical fuzzy distance and similarity measures and their applications to medical diagnosis,†Expert Systems with Applications, vol. 191, pp. 116330, 2022, https://doi.org/10.1016/j.eswa.2021.116330.

[41] A. Mousavi, A. H. Sadeghi, A. M. Ghahfarokhi, F. Beheshtinejad, and M. M. Masouleh, “Improving the Recognition Percentage of the Identity Check System by Applying the SVM Method on the Face Image Using Special Faces,†International Journal of Robotics and Control Systems, vol. 3, no. 2, pp. 221-232, 2023, https://doi.org/10.31763/ijrcs.v3i2.939.

[42] A. Mousavi, H. Arefanjazi, M. Sadeghi, A. M. Ghahfarokhi, F. Beheshtinejad and M. M. Masouleh, “Comparison of feature extraction with PCA and LTP methods and investigating the effect of dimensionality reduction in the bat algorithm for face recognition,†International Journal of Robotics and Control Systems, vol. 3, no. 3, pp. 501-509, 2023, http://dx.doi.org/10.31763/ijrcs.v3i3.1057.

[43] J. K. Gunn, H. A. Khorshidi, and U. Aickelin, “Similarity measure for aggregated fuzzy numbers from interval-valued data,†Soft Computing Letters, vol. 2, pp. 100002, 2020, https://doi.org/10.1016/j.socl.2020.100002.

[44] K. Ullah, T. Mahmood, and N. Jan, “Similarity measures for T-spherical fuzzy sets with applications in pattern recognition,†Symmetry, vol. 10, no. 6, pp. 1-14, 2018, https://doi.org/10.3390/sym10060193.

[45] P. Wang, J. Wang, G. Wei, and C. Wei, “Similarity measures of q-rung orthopair fuzzy sets based on cosine function and their applications,†Mathematics, vol. 7, no. 4, pp. 1-23, 2019, https://doi.org/10.3390/math7040340.

[46] S. Singh, and A. H. Ganie, “Applications of picture fuzzy similarity measures in pattern recognition, clustering, and MADM,†Expert Systems with Applications, vol. 168, 2021, https://doi.org/10.1016/j.eswa.2020.114264.

[47] M. Luo, and J. liang, “A novel similarity measure for interval-valued intuitionistic fuzzy sets and its applications,†Symmetry, vol. 10, no. 10, pp. 1-13, 2018, https://doi.org/10.3390/sym10100441.

[48] J. Dhivya, and B. Sridevi, “A novel similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers with applications to pattern recognition and medical diagnosis,†Applied Mathematics-A Journal of Chinese Universities, vol. 34, pp. 229-252, 2019, https://doi.org/10.1007/s11766-019-3708-x.

[49] C. Wei, P. Wang, Y. Zang, “Entropy, similarity measure of interval valued intuitionistic fuzzy sets and their applications,†Information Sciences, vol. 181, no. 19, pp. 4273–4286, 2011, https://doi.org/10.1016/j.ins.2011.06.001.

[50] Z. S. Xu, and J. Chen, “An overview of distance and similarity measures of intuitionistic fuzzy sets,†International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 16, no. 4, pp. 529-555, 2008, https://doi.org/10.1142/S0218488508005406.

[51] P. Liu, K. Zhang, P. Wang, and F. Wang, “A clustering-and maximum consensus-based model for social network large-scale group decision making with linguistic distribution,†Information Sciences, vol. 602, pp. 269-297, 2022, https://doi.org/10.1016/j.ins.2022.04.038.

[52] S. Wang, J. Wu, F. Chiclana, Q. Sun and E. Herrera-Viedma, “Two-Stage Feedback Mechanism With Different Power Structures for Consensus in Large-Scale Group Decision Making,†in IEEE Transactions on Fuzzy Systems, vol. 30, no. 10, pp. 4177-4189, 2022, https://doi.org/10.1109/TFUZZ.2022.3144536.


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