A valid and advanced method for ranking the fuzzy numbers

Abstract

With no doubt, ranking the fuzzy numbers are extremely effective and useful in different scientific fields such as Artificial Intelligence, Economics, Engineering and decision-making units and etc. The fuzzy quantities must be ranked before their engagement in the cycle of the applied functionalities. In this article,We offer a valid and advanced method for ranking the fuzzy numbers based on the Distance Measure Meter. In addition to the Distance Measure, we define a particular condition of the generalized fuzzy numbers. Having discussed some examples in this regard, we touch upon the advantages of this new method.

Keywords

• Fuzzy numbers,ranking method,distance measure

References

1. [1] Wang X, Kerre E E (2001) Reasonable properties for the ordering of fuzzy quantities I. Fuzzy Sets Syst. 118, 375–385.
2. [2] Singh P (2015) Distance and similarity measures for multiple-attribute decision making with dual hesitantfuzzy sets. J Comput Appl Math, 1–16.
3. [3] Wang T, Lu Z, Li F (2002) Bidirectional approximate reasoning based on weighted similarity measures fvague sets. J Comput Eng Sci 24, 96–100.
4. [4] Tran L, Duckstein L (2002) Comparison of fuzzy numbers using a fuzzy distance measure. Fuzzy Sets Syst.130(3), 331–341.
5. [5] Chakraborty C, Chakraborty D (2006) A theoretical development on fuzzy distance measure for fuzzy numbers. Math. Comput. Model. 43, 254–261.
6. [6] Guha D, Chakraborty D (2010) A new approach to fuzzy distance measure and similarity measure between two generalized fuzzy numbers. Appl. Soft Comput. 10, 90–99
7. [7] Chu T, Tsao C (2002) Ranking fuzzy numbers with an area between the centroid point and original point, Comput. Math. Appl. 43, 11- 117.
8. [8] Chen S H (1985) Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems. 17, 113- 129.

9. [9] Abbasbandy S, Asady B (2006) Ranking of fuzzy numbers by sign distance., Information Science. 176, 2405 - 2416.
10. [10] Abbasbandy S, Hajjari T (2009) A new approach for ranking of trapezoidal fuzzy numbers.,Computer and Mathematics with Appl. 57, 413 - 419.
11. [11] Asady B, Zendehnam A (2007) Ranking fuzzy numbers by distance minimization, Appl. Math Model. 31, 2589 - 2598.
12. [12] Nasibov E N (2007) Fuzzy least squares regression model based of weighted distance between fuzzy numbers, Automatic Control and Computer. Science. 41, 10 – 17.
13. [13] Grzegorzewski P (2002) Nearest interval approximation of a fuzzy number, Fuzzy Sets and Systems. 130, 321 - 330.
14. [14] Zimmermann H j (1991) Fuzzy sets theory and its applications, Kluwer Academic Press, Dordrecht.
15. [15] Saneifard R, Allahviranloo T, Hosseinzadeh F, Mikaeilvand N (2007) Euclidean ranking DMUs with fuzzy data in DEA, Applied Mathematical Sciences. 60, 2989 -2998.
16. [16] Saneifard R (2009) A method for defuzzification by weighted distance, International Journal of Industrial Mathematics. 3, 209 - 217.9
17. [17] Saneifard R (2009) Ranking L-R fuzzy numbers with weighted averaging based on levels, International Journal of Industrial Mathematics. 2, 163 - 173.
18. [18] Wang ML,Wang H F, Lung L C (2005) Ranking fuzzy numbers based on lexicographic screening procedure, International Journal of Information Technology and decision making. 4, 663 – 678.
19. [19] Zadeh L A (1965) Fuzzy sets, Information and Control, 8, 338–353.
20. [20] Saneifard R, Saneifard R. (2011) An Approximation Approach to Fuzzy Numbers by Continuous Parametric Interval, Aust. J. Basic & Appl. Sci, 3, 505-515.
21. [21] Eslamipoor R, Hosseini nasab H, Sepehriar A (2015) An improved ranking method for generalized fuzzy numbers based on euclidian distance concept. Afrika Matematika, 26 (7-8), 1291-1297.
22. [22] Chen J, Huang X, and Tang J. (2017) Distance Measure For Higher Order Dual Hesitant Fuzzy Sets. Computational and Applied Mathematics, 1-23.
23. [23] Saneifard R, Another Method for Defuzzification Based on Signal/Noise Ratios and its Applications in Comparing DMUs.. Communications on Advanced Computational Science with Applications. Volume 2015, No. 1 (2015), 32-36.
24. [24] Ahmadian A, Senu N, Salahshour S, Suleiman M. (2016) Nearest interval-valued approximation of interval-valued fuzzy numbers. Malaysian Journal of Mathematical Sciences 10(S), 325–336.