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Symmetric trapezoidal approximations of fuzzy numbers under a general condition

  • Fuzzy systems and their mathematics
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Abstract

The symmetric triangular approximation under a general condition was first proposed by Ban and Coroianu (Ban and Coroianu Soft Comput 20:1249–1261, 2016). Ban and Coroianu completed the calculation and provided a computational formula. However, symmetric trapezoidal approximation cannot be deduced from their conclusions. The aim of this paper is to continue and foster the development of this topic. The calculation for the symmetric trapezoidal approximations of a fuzzy number under a general condition will be completed in this paper. Some applications related with value, expected value and ambiguity, which are important parameters, are given too. Numerical examples are given and the quantitative improvement in approximation is also addressed.

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References

  • Abbasbandy S, Amirfakhrian M (2006a) The nearest approximation of a fuzzy quantity in parametric form. Appl Math Comput 172:624–632

    MathSciNet  Google Scholar 

  • Abbasbandy S, Amirfakhrian M (2006b) The nearest trapezoidal form of a generalized left right fuzzy number. Int J Approx Reason 43:166–178

    Article  MathSciNet  Google Scholar 

  • Abbasbandy S, Asady B (2004) The nearest trapezoidal fuzzy number to a fuzzy quantity. Appl Math Comput 156:381–386

    MathSciNet  Google Scholar 

  • Abbasbandy S, Ahmady E, Ahmady N (2010) Triangular approximations of fuzzy numbers using α-weighted valuations. Soft Comput 14:71–79

    Article  Google Scholar 

  • Allahviranloo T, Firozja MA (2007) Note on trapezoidal approximation of fuzzy numbers. Fuzzy Sets Syst 158:755–756

    Article  MathSciNet  Google Scholar 

  • Ban AI (2008) Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval. Fuzzy Sets Syst 159:1327–1344

    Article  MathSciNet  Google Scholar 

  • Ban AI (2011) Remarks and corrections to the triangular approximations of fuzzy numbers using α-weighted valuations. Soft Comput 15:351–361

    Article  Google Scholar 

  • Ban AI, Coroianu L (2012) Nearest interval, triangular and trapezoidal approximation of a fuzzy number preserving ambiguity. Int J Approx Reason 53:805–836

    Article  MathSciNet  Google Scholar 

  • Ban AI, Coroianu L (2014) Existence, uniqueness and continuity of trapezoidal approximations of fuzzy numbers under a general condition. Fuzzy Sets Syst 257:3–22

    Article  MathSciNet  Google Scholar 

  • Ban AI, Coroianu L (2015) Existence, uniqueness, calculus and properties of triangular approximations of fuzzy numbers under a general condition. Int J Approx Reason 62:1–26

    Article  MathSciNet  Google Scholar 

  • Ban AI, Coroianu L (2016) Symmetric triangular approximations of fuzzy numbers under a general condition and properties. Soft Comput 20:1249–1261

    Article  Google Scholar 

  • Chanas S (2001) On the interval approximation of a fuzzy number. Fuzzy Sets Syst 122:353–356

    Article  MathSciNet  Google Scholar 

  • Coroianu L (2011) Best Lipschitz constant of the trapezoidal approximation operator preserving the expected interval. Fuzzy Sets Syst 165:81–97

    Article  MathSciNet  Google Scholar 

  • Coroianu L (2012) Lipschitz functions and fuzzy number approximations. Fuzzy Sets Syst 200:116–135

    Article  MathSciNet  Google Scholar 

  • Delgado M, Vila MA, Voxman W (1998) On a canonical representation of a fuzzy number. Fuzzy Sets Syst 93:125–135

    Article  MathSciNet  Google Scholar 

  • Diamond P, Kloeden P (1994) Metric spaces of fuzzy sets. Theory and applications. World Scientific, Singapore

    Google Scholar 

  • Dubois D, Prade H (1978) Operations on fuzzy numbers. Int J Syst Sci 9:613–626

    Article  MathSciNet  Google Scholar 

  • Dubois D, Prade H (1987) The mean value of a fuzzy number. Fuzzy Sets Syst 24:279–300

    Article  MathSciNet  Google Scholar 

  • Grzegorzewski P (1998) Metrics and orders in space of fuzzy numbers. Fuzzy Sets Syst 97:83–94

    Article  MathSciNet  Google Scholar 

  • Grzegorzewski P (2002) Nearest interval approximation of a fuzzy number. Fuzzy Sets Syst 130:321–330

    Article  MathSciNet  Google Scholar 

  • Grzegorzewski P (2008) Trapezoidal approximations of fuzzy numbers preserving the expected interval—algorithms and properties. Fuzzy Sets Syst 159:1354–1364

    Article  MathSciNet  Google Scholar 

  • Grzegorzewski P (2008) New algorithms for trapezoidal approximation of fuzzy numbers preserving the expected interval. In: Magdalena L, Ojeda M, Verdegay JL (eds) Proceedings on information processing and management of uncertainty in knowledge-based system conference, Malaga, pp 117–123

  • Grzegorzewski P, Mrówka E (2005) Trapezoidal approximations of fuzzy numbers. Fuzzy Sets Syst 153:115–135

    Article  MathSciNet  Google Scholar 

  • Grzegorzewski P, Mrówka E (2007) Trapezoidal approximations of fuzzy numbers-revisited. Fuzzy Sets Syst 158:757–768

    Article  Google Scholar 

  • Heilpern S (1992) The expected value of a fuzzy number. Fuzzy Sets Syst 47:81–86

    Article  MathSciNet  Google Scholar 

  • Li J, Wang ZX, Yue Q (2012) Triangular approximation preserving the centroid of fuzzy numbers. Int J Comput Math 89:810–821

    Article  MathSciNet  Google Scholar 

  • Ma M, Kandel A, Friedman M (2000) A new approach for defuzzication. Fuzzy Sets Syst 111:351–356

    Article  Google Scholar 

  • Nasibov EN, Peker S (2008) On the nearest parametric approximation of a fuzzy number. Fuzzy Sets Syst 159:1365–1375

    Article  MathSciNet  Google Scholar 

  • Rockafeller RT (1970) Convex analysis. Princeton University Press, Princeton

    Book  Google Scholar 

  • Yeh CT (2007) A note on trapezoidal approximation of fuzzy numbers. Fuzzy Sets Syst 158:747–754

    Article  MathSciNet  Google Scholar 

  • Yeh CT (2008a) On improving trapezoidal and triangular approximations of fuzzy numbers. Int J Approx Reason 48:297–313

    Article  MathSciNet  Google Scholar 

  • Yeh CT (2008b) Trapezoidal and triangular approximations preserving the expected interval. Fuzzy Sets Syst 159:1345–1353

    Article  MathSciNet  Google Scholar 

  • Yeh CT (2009) Weighted trapezoidal and triangular approximations of fuzzy numbers. Fuzzy Sets Syst 160:3059–3079

    Article  MathSciNet  Google Scholar 

  • Yeh CT (2011) Weighted semi-trapezoidal approximations of fuzzy numbers. Fuzzy Sets Syst 165:61–80

    Article  MathSciNet  Google Scholar 

  • Yeh CT (2017) Existence of interval, triangular, and trapezoidal approximations of fuzzy numbers under a general condition. Fuzzy Sets Syst 310:1–13

    Article  MathSciNet  Google Scholar 

  • Zeng W, Li H (2007) Weighted triangular approximation of fuzzy numbers. Int J Approx Reason 46:137–150

    Article  MathSciNet  Google Scholar 

Download references

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  1. Department of Mathematical Sciences, National Chengchi University, 64, Sec.2, ZhiNan Rd., Wenshan District, Taipei City, 11605, Taiwan

    Hsin-Ting Lin

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  1. Hsin-Ting Lin
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Lin, HT. Symmetric trapezoidal approximations of fuzzy numbers under a general condition. Soft Comput 28, 119–133 (2024). https://doi.org/10.1007/s00500-023-09104-w

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