Department of Mathematics

### Inside this content area:

Ranking Fuzzy Numbers by their Left and Right Wingspans

Zhenyuan Wang

### Description

Ranking fuzzy numbers is an essential component of decision making with fuzzy data. Some common methods of ranking fuzzy numbers in literature, such as being based on the centroid, violate the intuition and, therefore, are not reasonable. A ranking method based the wingspans of fuzzy numbers is now proposed.

### References

[1] 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.
[2] D. Dubois and H. Prade, Ranking fuzzy numbers in the setting of possibility theory, Information Sciences 30, 183-224, 1983.
[3] Y. J. Wang and H. S. Lee, The revised method of ranking fuzzy numbers with an area between the centroid point and original point, Computers and Mathematics with Applications 55, 2033-2042, 2008.
[4] Y.-M. Wang, J.-B. Yang, D.-L. Xu, and K. S. Chin, On the centroid of fuzzy numbers, Fuzzy Sets and Systems, 157, 919-926, 2006.

MATH 8370

### Requirements

By using the knowledge on fuzzy numbers and decision making, discuss why some existing ranking methods are not reasonable. Introduce a new method of ranking fuzzy numbers based on the left and right wingspans. Show the unambiguity of the definition for the ranking index involving the core and wingspans of a fuzzy number. Complete a paper that can be submitted to some international academic conference.