On the nearest parametric approximation of a fuzzy number - Revisited

The problem of finding the nearest parametric approximation of a fuzzy number with respect to the average Euclidean distance is completely solved. Properties of translation invariance, scale invariance, additivity, preservation of expected value, value and ambiguity of this new approximation operator are studied and an algorithm for computing it is provided.

[1]  Przemyslaw Grzegorzewski,et al.  Metrics and orders in space of fuzzy numbers , 1998, Fuzzy Sets Syst..

[2]  Saeid Abbasbandy,et al.  The nearest trapezoidal fuzzy number to a fuzzy quantity , 2004, Appl. Math. Comput..

[3]  D. Dubois,et al.  Operations on fuzzy numbers , 1978 .

[4]  Semyon Malamud,et al.  Some complements to the Jensen and Chebyshev inequalities and a problem of W. Walter , 2001 .

[5]  Chi-Tsuen Yeh.  A note on trapezoidal approximations of fuzzy numbers , 2007, Fuzzy Sets Syst..

[6]  Przemyslaw Grzegorzewski,et al.  Nearest interval approximation of a fuzzy number , 2002, Fuzzy Sets Syst..

[7]  Chi-Tsuen Yeh.  Trapezoidal and triangular approximations preserving the expected interval , 2008, Fuzzy Sets Syst..

[8]  Chi-Tsuen Yeh,et al.  On improving trapezoidal and triangular approximations of fuzzy numbers , 2008, Int. J. Approx. Reason..

[9]  Sinem Peker,et al.  On the nearest parametric approximation of a fuzzy number , 2008, Fuzzy Sets Syst..

[10]  Stefan Chanas,et al.  On the interval approximation of a fuzzy number , 2001, Fuzzy Sets Syst..

[11]  Przemyslaw Grzegorzewski.  Trapezoidal approximations of fuzzy numbers preserving the expected interval - Algorithms and properties , 2008, Fuzzy Sets Syst..

[12]  Adrian I. Ban,et al.  Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval , 2008, Fuzzy Sets Syst..

[13]  Adrian I. Ban.  Triangular and parametric approximations of fuzzy numbers - inadvertences and corrections , 2009, Fuzzy Sets Syst..

[14]  M. Amparo Vila,et al.  On a canonical representation of fuzzy numbers , 1998, Fuzzy Sets Syst..

[15]  Saeid Abbasbandy,et al.  The nearest trapezoidal form of a generalized left right fuzzy number , 2006, Int. J. Approx. Reason..