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Soft Computing

01-01-2010 | Original Paper

Triangular approximations of fuzzy numbers using α-weighted valuations

Authors: S. Abbasbandy, E. Ahmady, N. Ahmady

Published in: Soft Computing | Issue 1/2010

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Abstract

In this paper, a fuzzy triangular approximation using α-weighted valuations is introduced and the nearest approximation by the minimization technique is obtained, such that the computational complexity is less than that in Abbasbandy and Amirfakhrian 2006. Moreover, we investigate some reasonable properties of the α-weighted triangular approximation.

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Literature
Abbasbandy S, Amirfakhrian M (2006) The nearest approximation of a fuzzy quantity in parametric form. Appl Math Comput 172:624–632MATHCrossRefMathSciNet
Allahviranloo T, Adabitabar Firozja M (2007) Note on “Trapezodial approximation of fuzzy numbers”. Fuzzy Sets Syst 158:755–756MATHCrossRefMathSciNet
Ban A (2008) Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval. Fuzzy Sets Syst 159:1327–1344CrossRefMathSciNet
Detyniecki M, Yager R (2000) Ranking fuzzy numbers using α-weighted valuations. Internat J Uncert Fuzziness Knowl Based Syst 8:573–591MATHCrossRefMathSciNet
Filev DP, Yager RR (1991) A generalized defuzzification method via Bad distribution. Int J Intell Syst 6:687–697MATHCrossRef
Grzegorzewski P (2003) Approximation of a fuzzy number preserving entropy-like nonspcifity. Oper Res Decis 4:49–59MathSciNet
Kandel A (1986) Fuzzy mathematical techniques with application. Addison-Wesley, New York
Yager RR (1999) On ranking fuzzy numbers using valuations. Int J Intell Syst 14:1249–1268MATHCrossRef
Yager RR, Filev DP (1998) On the instantiation of possibility distributions. Technical report MII-1817, Machine Intelligence Institute, Iona College, New Rochelle
Metadata
Title
Triangular approximations of fuzzy numbers using α-weighted valuations
Authors
S. Abbasbandy
E. Ahmady
N. Ahmady
Publication date
01-01-2010
Publisher
Springer-Verlag
Published in
Soft Computing / Issue 1/2010
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-008-0390-0

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