Approximations of Fuzzy Numbers by General Trapezoidal Fuzzy Numbers - Innovative Management in Information and Production - page 370

5 Conclusions

In this paper, we propose two more general approximations of fuzzy numbers,
named general f-trapezoidal approximation and general f-triangular approximation.
In practices, you can see situation of shape of the given fuzzy number. Then, pick
out a suitable function f = f ( x ) , which must be decreasing and left continuous such

that f ( 0 )= 1and f ( 1 )= 0, and pick out a weighted function λ = λ ( t ) (in general,

you can simply choose 1 ). Consequently, apply the proposed Algorithm 4 to

compute its general f-trapezoidal approximation and/or f-triangular approximation.

λ ( t )=

References

S. Abbasbandy, B. Asady, The nearest trapezoidal fuzzy number to a fuzzy quantity. Appl. Math.
Comput. 156 , 381-386 (2004)
S. Abbasbandy, T. Hajjari, Weighted trapezoidal approximation preserving cores of a fuzzy
number, Comput. Math. Appl. 59 , 3066-3077 (2010)
A.I. Ban, Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected
interval. Fuzzy Set. Syst. 159 , 1327-1344 (2008)
A.I. Ban, On the nearest parametric approximation of a fuzzy number-revisited. Fuzzy Set. Syst.
160 , 3027-3047 (2009)
A.I. Ban, A. Brandas, L. Coroianu, C. Negrutiu, O. Nica, Approximations of fuzzy numbers
by trapezoidal fuzzy numbers preserving the value and ambiguity. Comput. Math. Appl. 61 ,
1379-1401 (2011)
S. Bodjanova, Median value and median interval of a fuzzy number. Inform. Sci. 172 , 73-89 (2005)
D. Dubois, H. Prade, Operations on fuzzy number. Int. J. Syst. Sci. 9 , 613-626 (1978)
P. Grzegorzewski, Nearest interval approximation of a fuzzy number. Fuzzy Set. Syst. 130 ,
321-330 (2002)
P. Grzegorzewski, E. Mrowka, Trapezoidal approximations of fuzzy numbers. Fuzzy Set. Syst.
153 , 115-135 (2005)
P. Grzegorzewski, Trapezoidal approximations of fuzzy numbers preserving the expected interval -
algorithms and properties. Fuzzy Set. Syst. 159 , 1354-1364 (2008)
M. Ma, A. Kandel, M. Friedman, A new approach for defuzzification. Fuzzy Set. Syst. 111 ,
351-356 (2000)
E.N. Nasibov, S. Peker, On the nearest parametric approximation of a fuzzy number. Fuzzy Set.
Syst. 159 , 1365-1375 (2008)