A Novel Similarity Measure for Generalized Nonlinear Trapezoidal Fuzzy Numbers with Applications to Multi-Attribute Decision Making

Kartik Patra

Authors

Kartik Patra Department of Mathematics, Vivekananda Satavarshiki Mahavidyalaya, Manikpara, West Bengal, India Author https://orcid.org/0000-0002-5312-6841

Keywords:

Similarity Measure, Generalized Trapezoidal Fuzzy Number, Generalized Non Linear Trapezoidal Fuzzy Number, Center of Gravity, COG, Multi-Attribute Decision Making

Abstract

There are several similarity measure techniques for generalized trapezoidal fuzzy numbers. However, no similarity measure technique has yet been proposed for generalized non-linear trapezoidal fuzzy numbers. In the present work, a new similarity measure approach for two generalized non-linear trapezoidal fuzzy numbers is proposed based on distance and center of gravity (COG) measures. Several propositions related to the proposed method are also discussed. Furthermore, a comparative analysis with existing methods is carried out through illustrative examples, demonstrating that the proposed method is applicable to both generalized non-linear and generalized linear trapezoidal fuzzy numbers. Finally, a multi-attribute decision-making problem is considered, and a new algorithm is introduced to identify the best alternative for a decision maker using the proposed similarity measure method.

Downloads

Download data is not yet available.

References

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–356. https://doi.org/10.1016/S0019-9958(65)90241-X

Chen, S. J., & Chen, S. M. (2003). Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. IEEE Transactions on Fuzzy Systems, 11(1), 45–56. https://doi.org/10.1109/TFUZZ.2002.806316

Wei, S. H., & Chen, S. M. (2009). A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. Expert Systems with Applications, 36(1), 589–598. https://doi.org/10.1016/j.eswa.2007.09.033

Xu, Z., Shang, S., Qin, W., & Shu, W. (2010). A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers. Expert Systems with Applications, 37, 1920–1927. https://doi.org/10.1016/j.eswa.2009.07.015

Hejazi, S. R., Doostparast, A., & Hosseini, S. M. (2011). An improved fuzzy risk analysis based on new similarity measures of generalized fuzzy numbers. Expert Systems with Applications, 38, 9179–9185. https://doi.org/10.1016/j.eswa.2011.01.101

Chen, S. M., & Sanguansat, K. (2011). Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers. Expert Systems with Applications, 38(3), 2163–2171. https://doi.org/10.1016/j.eswa.2010.08.002

Patra, K., & Mondal, S. K. (2015). Fuzzy risk analysis using area and height based similarity measure on generalized trapezoidal fuzzy numbers and its application. Applied Soft Computing, 28, 276–284. https://doi.org/10.1016/j.asoc.2014.11.042

Sen, S., Patra, K., & Mondal, S. K. (2016). Fuzzy risk analysis in familial breast cancer using similarity measure of interval-valued fuzzy numbers. Pacific Science Review A: Natural Science and Engineering, 18, 203–221. https://doi.org/10.1016/j.psra.2016.09.014

Chen, S. M., Cheng, S. H., & Lan, T. C. (2016). A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Information Sciences, 343–344, 15–40. https://doi.org/10.1016/j.ins.2016.01.040

Sen, S., Patra, K., & Mondal, S. K. (2021a). A new approach to similarity measure for generalized trapezoidal fuzzy numbers and its application to fuzzy risk analysis. Granular Computing, 6, 705–718. https://doi.org/10.1007/s41066-020-00227-1

Sen, S., Patra, K., & Mondal, S. K. (2021b). Similarity measure of gaussian fuzzy numbers and its application. International Journal of Applied and Computational Mathematics, 7, 96. https://doi.org/10.1007/s40819-021-01040-3

Dutta, P., & Borah, G. (2021). Multicriteria decision making approach using an efficient novel similarity measure for generalized trapezoidal fuzzy numbers. Journal of Ambient Intelligence and Humanized Computing. https://doi.org/10.1007/s12652-021-03347-x

Abbasbandy, S., & Hajjari, T. (2009). A new approach for ranking of trapezoidal fuzzy numbers. Computers and Mathematics with Applications, 57(3), 413–419. https://doi.org/10.1016/j.camwa.2008.10.090

Patra, K., & Mondal, S. K. (2012). Risk analysis in diabetes prediction based on a new approach of ranking of generalized trapezoidal fuzzy numbers. Cybernetics and Systems, 43(8), 623–650. https://doi.org/10.1080/01969722.2012.707572

Chutia, R., & Chutia, B. (2017). A new method of ranking parametric form of fuzzy numbers using value and ambiguity. Applied Soft Computing, 52, 1154–1168. https://doi.org/10.1016/j.asoc.2016.09.013

Chutia, R. (2017). Ranking of fuzzy numbers by using value and angle in the epsilon-deviation degree method. Applied Soft Computing, 60, 706–721. https://doi.org/10.1016/j.asoc.2017.07.025

Patra, K. (2022). An improved ranking method for multi attributes decision making problem based on interval valued intuitionistic fuzzy values. Cybernetics and Systems. https://doi.org/10.1080/01969722.2022.2069078

Li, D. F. (2010). Topsis-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets. IEEE Transactions on Fuzzy Systems, 18(2), 299–311. https://doi.org/10.1109/TFUZZ.2010.2041009

Chen, S. M., Yang, M. W., Yang, S. W., Sheu, T. W., & Liau, C. J. (2012). Multicriteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets. Expert Systems with Applications, 39(15), 12085–12091. https://doi.org/10.1016/j.eswa.2012.04.021

Mishra, A. R., Chandel, A., & Motwani, D. (2020). Extended mabac method based on divergence measures for multi-criteria assessment of programming language with interval-valued intuitionistic fuzzy sets. Granular Computing, 5(1), 97–117. https://doi.org/10.1007/s41066-018-0130-5

Chen, S. M., & Han, W. H. (2019). Multiattribute decision making based on nonlinear programming methodology, particle swarm optimization techniques and interval-valued intuitionistic fuzzy values. Information Sciences, 471, 252–268. https://doi.org/10.1016/j.ins.2018.08.021