Trapezoidal Approximation of Fuzzy Numbers Based on Sample Data

1. Abbasbandy, S., Asady, B.: The nearest approximation of a fuzzy quantity in parametric form. Applied Mathematics and Computation 172, 624–632 (2006)

   Article  MATH  MathSciNet  Google Scholar 

2. Abbasbandy, S., Amirfakhrian, M.: The nearest trapezoidal form of a generalized LR fuzzy number. International Journal of Approximate Reasoning 43, 166–178 (2006)

   Article  MATH  MathSciNet  Google Scholar 

3. Ban, A.: Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval. Fuzzy Sets and Systems 159, 1327–1344 (2008)

   Article  MATH  MathSciNet  Google Scholar 

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

   Article  MATH  MathSciNet  Google Scholar 

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

   Article  MATH  MathSciNet  Google Scholar 

6. Grzegorzewski, P.: Trapezoidal approximations of fuzzy numbers preserving the expected interval - algorithms and properties. Fuzzy Sets and Systems 159, 1354–1364 (2008)

   MATH  MathSciNet  Google Scholar 

7. Grzegorzewski, P.: New algorithms for trapezoidal approximation of fuzzy numbers preserving the expected interval. In: Magdalena, L., Ojeda-Aciego, M., Verdegay, J.L. (eds.) Proceedings of the Twelfth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2008, Spain, Torremolinos, Málaga, pp. 117–123 (2008)

   Google Scholar 

8. Grzegorzewski, P.: Algorithms for trapezoidal approximations of fuzzy numbers preserving the expected interval. In: Bouchon-Meunier, B., Magdalena, L., Ojeda-Aciego, M., Verdegay, J.-L., Yager, R.R. (eds.) Foundations of Reasoning under Uncertainty, pp. 85–98. Springer, Heidelberg (2010)

   Chapter  Google Scholar 

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

   Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

11. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

12. Pedrycz, W.: Why triangular membership functions? Fuzzy Sets and Systems 64, 21–30 (1994)

    Article  MathSciNet  Google Scholar 

13. Yeh, C.T.: Trapezoidal and triangular approximations preserving the expected interval. Fuzzy Sets and Systems 159, 1345–1353 (2008)

    Article  MATH  MathSciNet  Google Scholar 

Download references