Abstract
A new similarity measure has been proposed in this paper for generalized trapezoidal fuzzy numbers (GTrFNs). Here, the proposed similarity measure has been devised based on exponent distance, area, perimeter and height of a GTrFN. Most of the researchers described the similarity measure between two GTrFNs whose components belong to [0, 1] only. But the components of GTrFNs should be any real numbers belonged to R. For this reason, in this paper a similarity measure technique has been framed newly on GTrFN whose components are any real number which is the most important consideration here. Depending on the proposed method of similarity measure, some essential properties have been illustrated in this paper. Also, this method has been compared with some existing techniques of similarity measure taking twenty five different sets of GTrFNs. Henceforth, it is obtained that our proposed technique is better than other existing techniques. Finally, the proposed similarity measure has been applied in fuzzy risk analysis in a production system which has been described with numerical illustration.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bai SM, Chen SM (2008a) Automatically constructing grade membership functions of fuzzy rules for students’ evaluation. Expert Syst Appl 35(3):1408–1414
Bai SM, Chen SM (2008b) Automatically constructing concept maps based on fuzzy rules for adapting learning systems. Expert Syst Appl 35(1–2):41–49
Chen SM (1996) New methods for subjective mental workload assessment and fuzzy risk analysis. Cybern Syst 27(5):449–472
Chen SJ (2006) New Similarity measure of generalized fuzzy numbers based on geometric mean averaging operator. In: Proceedings of IEEE international conference on fuzzy systems, Fuzz-IEEE, Vancouver, Canada
Chen SJ, Chen SM (2001) A new method to measure the similarity between fuzzy numbers. In: Proceedings of the \(10\)th IEEE international conference on fuzzy systems, Melbourne, Australia. pp 208–214
Chen SJ, Chen SM (2003) Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. IEEE Trans Fuzzy Syst 11(1):45–56
Chen SJ, Chen SM (2007) Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. Appl Intell 26(1):1–11
Chen SM, Chen SW (2014) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy logical relationships. IEEE Trans Cybern 45(3):391–403
Chen SM, Chu HP, Sheu TW (2012) TAIEX forecasting using fuzzy time series and automatically generated weights of multiple factors. IEEE Trans Syst Man Cybern Part A Syst Hum 42(6):1485–1495
Chen SM, Manalu GMT, Pan JS, Liu H-C (2013) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and particle swarm optimization techniques. IEEE Trans Cybern 43(3):1102–1117
Chen SM, Cheng SH, Lan TC (2016) A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf Sci 343:15–40
Ejegwa PA (2018) Distance and similarity measures for Pythagorean fuzzy sets. Granul Comput. https://doi.org/10.1007/s41066-018-00149-z
Hejazi SR, Doostparast A, Hosseini SM (2011) An improve d fuzzy risk analysis based on new similarity measures of generalized fuzzy numbers. Expert Syst Appl 38:9179–9185
Hsieh CH, Chen SH (1999) Similarity of generalized fuzzy numbers with graded mean integration representation. In: Proceedings of 8th international fuzzy systems association world congress (vol. 2), Taipei, Taiwan, Republic of China. pp 551–555
Kaur A, Kumar A, Appadoo SS (2019) A note on approaches to interval intuitionistic trapezoidal fuzzy multiple attribute decision makingwith incomplete weight information. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-018-0581-5
Khorshidi HA, Nikfalazar S (2016) A improved similarity measure of generalized trapezoidal fuzzy numbers and its application to fuzzy risk analysis. Appl Soft Comput J 52:478–486
Li J, Huang GH, Zeng G, Maqsood I, Huang Y (2007) An integrated fuzzy stochastic modeling approach for risk assessment of groundwater contamination. J Environ Manag 82(2):173–188
Liang R, Wang JQ (2019) A linguistic intuitionistic cloud decision support model with sentiment analysis for product selection in E-commerce. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-019-00606-0
Liu W, Li L (2019) Emergency decision-making combining cumulative prospect theory and group decision-making. Granul Comput 4:39–52
Manna S, Basu TM, Mondal SK (2019) Trapezoidal interval type-2 fuzzy soft stochastic set and its application in stochastic multi-criteria decision-making. Granul Comput 4:585–599
Mishra AR, Singh RK, Motwani D (2019) Multi-criteria assessment of cellular mobile telephone service providers using intuitionistic fuzzy WASPAS method with similarity measures. Granul Comput 4:511–529
Patra K, Mondal SK (2012) Risk analysis in diabetes prediction based on a new approach of ranking of generalized trapezoidal fuzzy numbers. Cybern Syst Int J 43(8):623–650
Patra K, Mondal SK (2015) Fuzzy risk analysis using area and height based similarity measure on generalized trapezoidal fuzzy numbers and its application. Appl Soft Comput J 28:276–284
Schmucker KJ (1984) Fuzzy sets, natural language computations and risk analysis. Computer Science Press, Rockville
Singh S, Shreevastava S, Som T, Jain P (2019) Intuitionistic fuzzy quantifier and its application in feature selection. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-018-00603-9
Subasic P, Hirota K (1998) Similarity rules and gradual rules for analogical and interpolative reasoning with imprecise data. Fuzzy Sets Syst 96(1):53–75
Tang TC, Chi LC (2005) Predicting multilateral trade credit risks: comparisons of logic and fuzzy logic models using ROC curve analysis. Expert Syst Appl 31(2):309–319
Wei SH, Chen SM (2009) A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. Expert Syst Appl 36(1):589–598
Xie J, Zeng W, Li J, Yin Q (2019) Similarity measures of generalized trapezoidal fuzzy numbers for fault diagnosis. Soft Comput 23:1999–2014
Xu Z, Shang S, Quin W, Shu W (2010) A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers. Expert Syst Appl 37:1920–1927
Yong D, Wenkang S, Feng D, Qi L (2004) A new similarity measure of generalized fuzzy numbers and its application to pattern recognition. Pattern Recognit Lett 25:875–883
Yoshida Y (2019) Dynamic risk-sensitive fuzzy asset management with coherent risk measures derived from decision makers utility. Granul Comput. https://doi.org/10.1007/s41066-019-00196-0
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
Zuo X, Wang L, Yuo Y (2013) A new similarity measure of generalized trapezoidal fuzzy numbers and its application on rotor fault diagnosis. Math Probl Eng 7:291–300
Acknowledgements
The authors are very thankful to the editors and anonymous reviewers for providing very thoughtful comments which have led to an improved version of this paper. This work is supported by the University Grant Commission (UGC), New Delhi, India, through NET JRF FELLOWSHIP (ROLL NO: 423143/DOE: 20-12-2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Sen, S., Patra, K. & Mondal, S.K. A new approach to similarity measure for generalized trapezoidal fuzzy numbers and its application to fuzzy risk analysis. Granul. Comput. 6, 705–718 (2021). https://doi.org/10.1007/s41066-020-00227-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41066-020-00227-1