AJOR  Vol.3 No.2 , March 2013
Trapezoidal Approximation of a Fuzzy Number Preserving the Expected Interval and Including the Core
Author(s) B. Asady
ABSTRACT

In this paper, we introduce a method to obtain the nearest trapezoidal approximation of fuzzy numbers so that preserving conditions expect interval and include the core of a fuzzy number.


Cite this paper
B. Asady, "Trapezoidal Approximation of a Fuzzy Number Preserving the Expected Interval and Including the Core," American Journal of Operations Research, Vol. 3 No. 2, 2013, pp. 299-306. doi: 10.4236/ajor.2013.32027.
References
[1]   Ming Ma, A. Kandel and M. Friedman, “A New Approach for defuzzification,” Fuzzy Sets and Systems, Vol. 111, No. 3, 2000, pp. 351-356. doi:10.1016/S0165-0114(98)00176-6

[2]   S. Abbasbandy and M. Amirfakhrian, “The Nearest Approximation of a Fuzzy Quantity in Parametric Form,” Applied Mathematics and Computation, Vol. 172, No. 1, 2006, pp. 624-632. doi:10.1016/j.amc.2005.02.019

[3]   S. Abbasbandy and B. Asady, “The Nearest Trapezoidal Fuzzy Number of a Fuzzy Quantity,” Applied Mathematics and Computation, Vol. 156, No. 2, 2004, pp. 381-386.

[4]   L. Coroianu, “Best Lipschitz Constant of the Trapezoidal Approximation Operator Preserving the Expected Interval,” Fuzzy Sets and Systems, Vol. 165, No. 1, 2011, pp. 81-97. doi:10.1016/j.fss.2010.10.004

[5]   A. I. Ban, “On the Nearest Parametric Approximation of Fuzzy Number—Revisited,” Fuzzy Sets and Systems, Vol. 166, No. 21, 2009, pp. 3027-3047. doi:10.1016/j.fss.2009.05.001

[6]   A. I. Ban, “Triangular and Parametric Approximations of a Fuzzy Number—Inadvertences and Corrections,” Fuzzy Sets and Systems, Vol. 160, No. 1, 2009, pp. 3048-3058. doi:10.1016/j.fss.2009.04.003

[7]   A. I. Ban, “Approximation of Fuzzy Numbers by Trapezoidal Fuzzy Numbers Preserving the Expected Interval,” Fuzzy Sets and Systems, Vol. 159, No. 11, 2008, pp. 1327- 1344. doi:10.1016/j.fss.2007.09.008

[8]   A. I. Ban, L. Coroianu and P. Grzegorzewski, “Trapezoidal Approximation and Aggregation,” Fuzzy Sets and Systems, Vol. 177, No. 1, 2011, pp. 45-59. doi:10.1016/j.fss.2011.02.016

[9]   P. Grzegorzewski, “Nearest Interval Approximation of a Fuzzy Number,” Fuzzy Sets and Systems, Vol. 130, No. 3, 2002, pp. 321-330. doi:10.1016/S0165-0114(02)00098-2

[10]   P. Grzegorzewski, “Trapezoidal Approximations of Fuzzy Numbers Preserving the Expected Interval—Algorithms and Properties,” Fuzzy Sets and Systems, Vol. 159, No. 11, 2008, pp. 1354-1364. doi:10.1016/j.fss.2007.12.001

[11]   P. Grzegorzewski, “Trapezoidal Approximations of Fuzzy Numbers Preserving the Expected Interval—Algorithms and Properties,” Fuzzy Sets and Systems, Vol. 159, No. 11, 2008, pp. 1354-1364. doi:10.1016/j.fss.2007.12.001

[12]   P. Grzegorzewski, “Algorithms for Trapezoidal Approximations of Fuzzy Numbers Preserving the Expected Interval, In: B. Bouchon-Meunier, L. Magdalena, M. OjedaAciego, J.-L. Verdegay, R. R. Yager, Eds., Foundations of Reasoning under Uncertainty, Springer, Berlin, 2010, pp. 85-98. doi:10.1007/978-3-642-10728-3_5

[13]   P. Grzegorzewski and E. Mrówka, “Trapezoidal Approximations of Fuzzy Numbers,” Fuzzy Sets and Systems, Vol. 153, No. 1, 2005, pp. 115-135. doi:10.1016/j.fss.2004.02.015

[14]   P. Grzegorzewski and E. Mrówka, “Trapezoidal Approximations of Fuzzy Numbers—Revisited,” Fuzzy Sets and Systems, Vol. 158, No. 7, 2007, pp. 757-768. doi:10.1016/j.fss.2006.11.015

[15]   P. Grzegorzewski and K. Pasternak-Winiarska, “Weighted Trapezoidal Approximations of Fuzzy Numbers,” In: J. P. Carvalho, D. Dubois, U. Kaymak, J.M. C. Sousa (Eds.), Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, 2009, pp. 1531-1534.

[16]   P. Grzegorzewski and K. Pasternak-Winiarska, “Bi-Symmetrically Weighted Trapezoidal Approximations of Fuzzy Numbers,” In: Proceedings of 9th International Conference on Intelligent Systems Design and Applications ISDA 2009, Pisa, 30 November-2 December 2009, pp. 318-323. doi:10.1109/ISDA.2009.138

[17]   R. R. Yager and D. P. Filev, “SLIDE: A Simple Adaptive Defuzzification Method,” IEEE Transactions on Fuzzy Systems, Vol. 1, No. 1, 1993, pp. 69-78. doi:10.1109/TFUZZ.1993.390286

[18]   C.-T. Yeh, “A Note on Trapezoidal Approximations of Fuzzy Numbers,” Fuzzy Sets and Systems, Vol. 158, No. 7, 2007, pp. 747-754. doi:10.1016/j.fss.2006.11.017

[19]   C.-T. Yeh, “On Improving Trapezoidal and Triangular Approximations of Fuzzy Numbers,” International Journal of Approximate Reasoning, Vol. 48, No. 1, 2008, pp. 297-313. doi:10.1016/j.ijar.2007.09.004

[20]   C.-T. Yeh, “Trapezoidal and Triangular Approximations Preserving the Expected Interval,” Fuzzy Sets and Systems, Vol. 159, No. 11, 2008, pp. 1345-1353. doi:10.1016/j.fss.2007.09.010

[21]   C.-T. Yeh, “Weighted Trapezoidal and Triangular Approximations of Fuzzy Numbers,” Fuzzy Sets and Systems, Vol. 160, No. 21, 2009, pp. 3059-3079. doi:10.1016/j.fss.2009.05.008

[22]   W. Y. Zeng and H. X. Li, “Weighted Triangular Approximation of Fuzzy Numbers,” International Journal of Approximate Reasoning, Vol. 46, No. 1, 2007, pp. 137- 150. doi:10.1016/j.ijar.2006.11.001

[23]   T. Allahviranloo and M. A. Firozja, “Note on ‘Trapezoidal Approximation of Fuzzy Numbers’,” Fuzzy Sets and Systems, Vol. 158, No. 7, 2007, pp. 755-756. doi:10.1016/j.fss.2006.10.017

[24]   S. Bodjanova, “Median Value and Median Interval of a Fuzzy Number,” Information Sciences, Vol. 172, No. 1-2, 2005, pp. 73-89. doi:10.1016/j.ins.2004.07.018

[25]   M. Ma, A. Kandel and M. Friedman, “Correction to ‘A New Approach for defuzzification’,” Fuzzy Sets and Systems, Vol. 128, No. 1, 2002, pp. 133-134. doi:10.1016/S0165-0114(01)00248-2

[26]   D. Dubois and H. Prade, “The Mean Value of a Fuzzy Number,” Fuzzy Sets and Systems, Vol. 24, No. 3, 1987, pp. 279-300. doi:10.1016/0165-0114(87)90028-5

[27]   E. N. Nasibov and S. Peker, “On the Nearest Parametric Approximation of a Fuzzy Number,” Fuzzy Sets and Systems, Vol. 159, No. 11, 2008, pp. 1365-1375. doi:10.1016/j.fss.2007.08.005

[28]   Y.-R. Syau, L.-F. Sugianto and E. S. Lee, “A Class of Semicontinuous Fuzzy Mappings,” Applied Mathematics Letters, Vol. 21, No. 8, 2008, pp. 824-827. doi:10.1016/j.aml.2007.09.005

[29]   D. P. Filev and R. R. Yager, “A Generalized Defuzzification Method via Bad Distribution,” International Journal of Intelligent Systems, Vol. 6, No. 7, 1991, pp. 687-697. doi:10.1002/int.4550060702

[30]   R. Goetschel and W. Voxman, “Elementary Fuzzy Calculus,” Fuzzy Sets and Systems, Vol. 18, No. 1, 1986, pp. 31-43. doi:10.1016/0165-0114(86)90026-6

[31]   D. Dubois and H. Prade, “Operations on Fuzzy Numbers,” International Journal of Systems Science, Vol. 9, No. 6, 1978, pp. 613-626. doi:10.1080/00207727808941724

[32]   S. Heilpern, “The Expected Value of a Fuzzy Number,” Fuzzy Sets and Systems, Vol. 47, No. 1, 1992, pp. 81-86. doi:10.1016/0165-0114(92)90062-9

[33]   B. Asady and M. Zendehnam, “Ranking of Fuzzy Numbers by Minimize Distance,” Applied Mathematical Modeling, Vol. 176, 2006, pp. 2405-2416.

[34]   S. Abbasbandy and B. Asady, “A Note on ‘A New Approach for Defuzzification’,” Fuzzy Sets and Systems, Vol. 128, No. 1, 2002, pp. 131-132. doi:10.1016/S0165-0114(01)00247-0

 
 
Top