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A New Approach For Ranking Of Generalized Trapezoidal Fuzzy Numbers
Abstract:Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (2009) 6833-6842) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The main advantage of the proposed approach is that the proposed approach provide the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets and Systems 118 (2001) 375-385).
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082927Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2568
 L. A. Zadeh Fuzzy Sets, Information and Control, vol. 8, 1965, pp. 338-353.
 R. Jain, Decision-making in the presence of fuzzy variables, IEEE Transactions on Systems, Man and Cybernetics, vol. 6, 1976, pp.698- 703
 R. R. Yager, A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, vol. 24, 1981, pp. 143-161.
 A. Kaufmann and M. M. Gupta, Fuzzy mathemaical models in engineering and managment science, Elseiver Science Publishers, Amsterdam, Netherlands, 1988.
 L. M Campos and A. MGonzalez, A subjective approach for ranking fuzzy numbers, Fuzzy Sets and Systems, vol. 29, 1989, pp.145-153.
 T. S. Liou, T.S and M. J. Wang, Ranking fuzzy numbers with integral value, Fuzzy Sets and Systems, vol. 50, 1992, pp.247-255.
 C. H. Cheng, A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems, vol. 95, 1998, pp. 307-317.
 H. C. Kwang and J. H. Lee, A method for ranking fuzzy numbers and its application to decision making, IEEE Transaction on Fuzzy Systems, vol. 7, 1999, pp. 677-685.
 M. Modarres and S. Sadi-Nezhad, Ranking fuzzy numbers by preference ratio, Fuzzy Sets and Systems, vol. 118, 2001, pp. 429-436.
 T. C. Chu and C. T. Tsao, Ranking fuzzy numbers with an area between the centroid point and original point, Computers and Mathematics with Applications, vol. 43, 2002, pp. 111-117.
 Y. Deng and Q. Liu, A TOPSIS-based centroid-index ranking method of fuzzy numbers and its applications in decision making, Cybernatics and Systems, vol. 36, 2005, pp. 581-595.
 C. Liang, J. Wu and J. Zhang, Ranking indices and rules for fuzzy numbers based on gravity center point, Paper presented at the 6th world Congress on Intelligent Control and Automation, Dalian, China, 2006, pp.21-23.
 Y. J. Wang and H. S.Lee, The revised method of ranking fuzzy numbers with an area between the centroid and original points, Computers and Mathematics with Applications, vol. 55, 2008, pp.2033-2042.
 S. j. Chen and S. M. Chen, Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers, Applied Intelligence, vol. 26, 2007, pp. 1-11.
 S. Abbasbandy and T. Hajjari, A new approach for ranking of trapezoidal fuzzy numbers, Computers and Mathematics with Applications, vol. 57, 2009, pp. 413-419.
 S. M Chen and J. H. Chen, Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads, Expert Systems with Applications, vol. 36, 2009. pp. 6833-6842.
 D. Dubois and H. Prade, Fuzzy Sets and Systems, Theory and Applications, Academic Press, New York, 1980.
 X. Wang and E. E. Kerre, Reasonable properties for the ordering of fuzzy quantities (I), Fuzzy Sets and Systems, vol. 118, 2001, pp.375-385.