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An improved fuzzy risk analysis by using a new similarity measure with center of gravity and area of trapezoidal fuzzy numbers

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Abstract

This paper is to develop a new similarity measure of generalized trapezoidal fuzzy numbers (GTFNs). Firstly, a new method to calculate the center of gravity (COG) of GTFNs is put forward. Then, based on the drawbacks of existing similarity measures, a new similarity measure is proposed by using the COGs, areas, heights and geometric distances of GTFNs. Some properties of the proposed similarity measure are investigated. Moreover, with 32 different sets of GTFNs, we make a comparison between the proposed similarity measure and the existing similarity measures. Furthermore, two fuzzy risk analysis problems are analyzed by utilizing the new similarity measure and the results indicate that it is effective to deal with fuzzy risk analysis problems.

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References

  • Chen SH (1985) Operations on fuzzy numbers with function principal. Tamkang J Manag Sci 6:13–25

    MATH  Google Scholar 

  • Chen SM (1996) New methods for subjective mental workload assessment and fuzzy risk analysis. Cybern Syst 27:449–472

    MATH  Google Scholar 

  • Chen SJ, Chen SM (2000) A new simple center-of-gravity method for handling the fuzzy ranking and the defuzzification problems. In: Proceedings of the eighth national conference on fuzzy theory and its applications, Taipei, Taiwan

  • Chen SJ, Chen SM (2003) Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. IEEE Trans Fuzzy Syst 11:45–56

    Google Scholar 

  • Chen SJ, Chen SM (2007) Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. Appl Intell 26(1):1–11

    Google Scholar 

  • Chen SM, Wang CY (2013) Fuzzy decision making systems based on interval type-2 fuzzy sets. Inf Sci 242:1–21

    MathSciNet  MATH  Google Scholar 

  • Chen HY, Zhou LG (2012) A relative entropy approach to group decision making with interval reciprocal relations based on COWA operator. Group Decis Negot 21:585–599

    Google Scholar 

  • Chen SM, Cheng SH, Lin TE (2015) Group decision making systems using group recommendations based on interval fuzzy preference relations and consistency matrices. Inf Sci 298:555–567

    MathSciNet  MATH  Google Scholar 

  • Chen SM, Cheng SH, Tsai WH (2016) Multiple attribute group decision making based on interval-valued intuitionistic fuzzy aggregation operators and transformation techniques of interval-valued intuitionistic fuzzy values. Inf Sci s367–368:418–442

    MATH  Google Scholar 

  • Cheng SH, Chen SM, 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 343–344:15–40

    MathSciNet  MATH  Google Scholar 

  • Chu TC (2002) Ranking fuzzy numbers with an area between the centroid point and original point. Comput Math Appl 43(1–2):111–117

    MathSciNet  MATH  Google Scholar 

  • Dong YC, Li CC, Chiclana F, Herrera-Viedma E (2016) Average-case consistency measurement and analysis of interval-valued reciprocal preference relations. Knowl Based Syst 114:108–117

    Google Scholar 

  • Gere J, Gere JM, Goodno BJ (2012) Mechanics of materials. Nelson Education

  • Gong ZW, Li LS, Zhou FX, Yao TX (2009) Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations. Comput Ind Eng 57(4):1187–1193

    Google Scholar 

  • Gong ZW, Li LS, Forrest J, Zhao Y (2011) The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity. Expert Syst Appl 38:4394–4402

    Google Scholar 

  • Gong ZW, Li Y, Yao TX (2012) Uncertain fuzzy preference relations and their applications. Springer, Berlin

    Google Scholar 

  • Gong ZW, Xu XX, Li LS, Xu C (2015a) Consensus modeling with nonlinear utility and cost constrains: a case study. Knowl Based Syst 88:210–222

    Google Scholar 

  • Gong ZW, Xu XX, Li LS, Xu C (2015b) On consensus models with utility preference relations and limited budget. Appl Soft Comput 35:840–849

    Google Scholar 

  • Gong ZW, Xu XX, Zhang HH, AytunOzturk U, Viedma EH, Xu C (2015c) The consensus models with interval preference opinions and their economic interpretation. Omega 55:81–90

    Google Scholar 

  • Gong ZW, Zhang HH, Forrest J, Li LS, Xu XX (2015d) Two consensus models based on minimum cost and maximum return regarding either all individuals or one individual. Eur J Oper Res 240:183–192

    MathSciNet  MATH  Google Scholar 

  • Hejazi SR, Doostparast A, Hosseini SM (2011) An improved fuzzy risk analysis based on new similarity measures of generalized fuzzy numbers. Expert Syst Appl 38:9179–9185

    Google Scholar 

  • Hsieh CH, Chen SH (1999) Similarity of generalized fuzzy numbers with graded mean integration representation. In: Proceedings of the 1999 eighth international fuzzy systems association world congress, vol. 2, Taipei, Taiwan, pp 551–555

  • Khorshidi HA, Nikfalazar S (2017) An improved similarity measure for generalized fuzzy numbers and its application to fuzzy risk analysis. Appl Soft Comput 52:478–486

    Google Scholar 

  • Lee YW, Dahab MF, Bogard I (1995) Nitrate-risk assessment using fuzzy set approach. J Environ Eng 121:245–256

    Google Scholar 

  • 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 82:173–188

    Google Scholar 

  • Ma XY, Wu P, Zhou LG, Chen HY, Zheng T, Ge JQ (2016) Approaches based on interval type-2 fuzzy aggregation operators for multiple attribute group decision making. Int J Fuzzy Syst 18(4):1–19

    MathSciNet  Google Scholar 

  • Mendel JM, Korjani MM (2013) Theoretical aspects of fuzzy set qualitative comparative analysis (fsQCA). Inf Sci 237:137–161

    Google Scholar 

  • Murakami S, Maeda S, Imamura S (1983) Fuzzy decision analysis on the development of centralized regional energy control systems. In: Proceedings of the IFAC symposium on fuzzy information, knowledge representation and decision analysis. Pergamon Press, New York

    Google Scholar 

  • 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 28:276–284

    Google Scholar 

  • Schmucker KJ (1984) Fuzzy sets, natural language computations and risk analysis. Computer Science Press, Rockville

    MATH  Google Scholar 

  • Subašić P, Hirota K (1998) Similarity rules and gradual rules for analogical and interpolative reasoning with imprecise data. Fuzzy Sets Syst 96:53–75

    MathSciNet  Google Scholar 

  • Tang TC, Chi LC (2005) Predicting multilateral trade credit risks: comparisons of logic and fuzzy logic models using ROC curve analysis. Expert Syst Appl 31:309–319

    Google Scholar 

  • Wan SP (2013) Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making. Appl Math Model 37(6):4112–4126

    MathSciNet  MATH  Google Scholar 

  • Wang YM, Elhag T (2006) Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment. Expert Syst Appl 31:309–319

    Google Scholar 

  • Wang YM, Luo Y (2009) Area ranking of fuzzy numbers based on positive and negative ideal points. Comput Math Appl 58(9):1769–1779

    MathSciNet  MATH  Google Scholar 

  • Wang YM, Yang JB, Xu DL, Chin KS (2006) On the centroids of fuzzy numbers. Fuzzy Sets Syst 157(7):919–926

    MathSciNet  MATH  Google Scholar 

  • Wei SH, Chen SM (2009) A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. Expert Syst Appl 36:589–598

    Google Scholar 

  • Wu P, Zhou LG, Zheng T, Chen HY (2017) A fuzzy group decision making and its application based on compatibility with multiplicative trapezoidal fuzzy preference relations. Int J Fuzzy Syst 19(3):683–701

    MathSciNet  Google Scholar 

  • Wu P, Wu Q, Zhou LG, Chen HY, Zhou H (2019) A consensus model for group decision making under trapezoidal fuzzy numbers environment. Neural Comput Appl 31(2):377–394

    Google Scholar 

  • Xu ZS (2007) Intuitionistic preference relations and their application in group decision making. Inf Sci 177(11):2363–2379

    MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Ye J (2012) Multicriteria group decision-making method using vector similarity measures for trapezoidal intuitionistic fuzzy numbers. Group Decis Negot 21(4):519–530

    Google Scholar 

  • Zhang WR (1986) Knowledge representation using linguistic fuzzy relations. Ph.D. dissertation, University of South Carolina

  • Zhou LG, He YD, Chen HY, Liu JP (2014) On compatibility of interval multiplicative preference relations based on the COWGA operator. Int J Uncertain Fuzz Knowl Based Syst 22:407–428

    MathSciNet  MATH  Google Scholar 

  • Zhou LG, Merigó JM, Chen HY, Liu JP (2016) The optimal group continuous logarithm compatibility measure for interval multiplicative preference relations based on the COWGA operator. Inf Sci 328:250–269

    MATH  Google Scholar 

  • Zhou YY, Cheng LH, Zhou LG, Chen HY, Ge JQ (2017) A group decision making approach for trapezoidal fuzzy preference relations with compatibility measure. Soft Comput 21(10):2709–2721

    MATH  Google Scholar 

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Acknowledgements

The authors would like to thank the Editor, Prof. Antonio Di Nola, Managing Editor, Prof. Raffaele Cerulli and the anonymous reviewers for their insightful and constructive comments and suggestions that have led to this improved version of the paper. The work was supported by National Natural Science Foundation of China (Nos. 71771001, 71701001, 71501002, 71871001), The Natural Science Foundation for Distinguished Young Scholars of Anhui Province (No. 1908085J03), Research Funding Project of Academic and technical leaders and reserve candidates in Anhui Province (No. 2018H179).

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, Anhui, China

    Peng Wu, Ligang Zhou, Huayou Chen & Han Zhou

  2. China Institute of Manufacturing Development, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Ligang Zhou

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  1. Peng Wu
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  2. Ligang Zhou
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  3. Huayou Chen
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  4. Han Zhou
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Correspondence to Ligang Zhou.

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Wu, P., Zhou, L., Chen, H. et al. An improved fuzzy risk analysis by using a new similarity measure with center of gravity and area of trapezoidal fuzzy numbers. Soft Comput 24, 3923–3936 (2020). https://doi.org/10.1007/s00500-019-04160-7

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