A New Approach For the Ranking of Fuzzy Sets With Different Heights

 

Pushpinder Singh

 

School of Mathematics and Computer Applications Thapar University, Patiala-147 004 India. pushpindersnl@gmail.com.

 

ABSTRACT

Ranking of fuzzy sets plays an important role in decision making, optimization, forecasting, etc. Fuzzy sets must be ranked before an action is taken by a decision maker. Fuzzy sets with different heights are a generalization of the ordinary fuzzy sets. In this paper, with the help of several counterexamples, it is proved that the ranking method proposed by Lee and Chen (Expert Systems with Applications 34, 2008, 2763-2771) is incorrect. The main aim of this paper is to propose a new approach for the ranking of fuzzy sets with different heights. The main advantage of the proposed approach is that with it the correct ordering of fuzzy sets with different heights, and also the results of the proposed ranking method and the existing ranking method, can be compared.

Keywords: sets, fuzzy sets with different heights, ranking function.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

References

[1] S. Abbasbandy and T. Hajjari, "A new approach for ranking of trapezoidal fuzzy numbers", Computers and Mathematics with Applications, 57, 413-419, 2009.         [ Links ]

[2] B. Assady, "The revised method of ranking LR fuzzy number based on deviation degree", Expert Systems with Applications, 37, 5056-5060 2010.         [ Links ]

[3] B. Assady, "Revision of distance minimization method for ranking of fuzzy numbers", Applied Mathematical Modelling, 35, 1306-1313, 2011        [ Links ]

[4] L.M. Campos and A. Gonzalez, "A subjective approach for ranking fuzzy numbers", Fuzzy Sets and Systems, 29, 145-153, 1989.         [ Links ]

[5] S. J. Chen and S. M. Chen, "Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers", Applied Intelligence, 26, 1-11, 2007.         [ Links ]

[6] 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, 36, 6833-6842, 2009.         [ Links ]

[7] S. M. Chen et al., "Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights", Expert Systems with Applications, 39, 6320-6334, 2012        [ Links ]

[8] C.C. Chen and H.C. Tang, "Ranking nonnormal p-norm trapezoidal fuzzy numbers with integral value", Computers and Mathematics with Applications, 56, 2340-2346, 2008.         [ Links ]

[9] S.M. Chen and C.H. Wang, "Fuzzy risk analysis based on ranking fuzzy numbers using α^– cuts, belief features and signal/noise ratios", Expert Systems with Applications, 36, 5576-5581, 2009.         [ Links ]

[10] C.H. Cheng, "A new approach for ranking fuzzy numbers by distance method", Fuzzy Sets and Systems, 95, 307-317, 1998.         [ Links ]

[11] 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, 43, 111-117, 2002.         [ Links ]

[12] Y. Deng and Q. Liu, "A TOPSIS-based centroid-index ranking method of fuzzy numbers and its applications in decision making", Cybernetics and Systems, 36, 581-595, 2005.         [ Links ]

[13] R. Ezzati et al. , "An approach for ranking of fuzzy numbers", Expert Systems with Applications, 39, 690-695, 2012.         [ Links ]

[14] R. Jain, "Decision-making in the presence of fuzzy variables", IEEE Transactions on Systems Man and Cybernetics, 6, 698-703, 1976.         [ Links ]

[15] H.C. Kwang and J.H. Lee, "A method for ranking fuzzy numbers and its application to decision making", IEEE Transactions on Fuzzy Systems, 7, 677-685, 1999.         [ Links ]

[16] W.E. Lee and S.M. Chen, "Fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations", Expert Systems with Applications, 34, 2763-2771, 2008.         [ Links ]

[17] T. S. Liou and M. J. Wang, "Ranking fuzzy numbers with integral value", Fuzzy Sets and Systems, 50, 247-255, 1992.         [ Links ]

[18] M. Modarres and S. Sadi-Nezhad, "Ranking fuzzy numbers by preference ratio", Fuzzy Sets and Systems, 118, 429-436, 2001.         [ Links ]

[19] N. Ramli and D. Mohamad, "A comparative analysis of centroid methods in ranking fuzzy numbers", European Journal of Scientific Research, 28, 492-501, 2009.         [ Links ]

[20] H. Rommelfanger, "A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values", Fuzzy Sets and Systems, 158, 1892-1904, 2007.         [ Links ]

[21] X. Wang and E.E. Kerre, "Reasonable properties for the ordering of fuzzy quantities (I)", Fuzzy Sets and Systems, 118, 375-385, 2001.         [ Links ]

[22] 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, 55, 2033-2042, 2008.         [ Links ]

[23] R.R. Yager, "A procedure for ordering fuzzy subsets of the unit interval", Information Sciences 24, 143-161, 1981.         [ Links ]

[24] L.A. Zadeh, "Fuzzy sets", Information and Control, 8, 338-353 1965.         [ Links ]