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Department of Mathematics
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Ranking and total ordering on sets of fuzzy numbers

Advisor

Zhenyuan Wang

Description

Using the knowledge on relations and fuzzy sets, give a theoretical description of rankings and total orderings on sets consisting of fuzzy numbers. A view point of reference systems may be adopted. Some criteria for the goodness of ranking and total orderings are introduced. Sufficient examples are cited to illustrate the results.

References

[1] D. Dubois and H. Prade, Ranking fuzzy numbers in the setting of possibility theory, Information Sciences 30, 183-224, 1983.
[2] W. Wang and Z. Wang, Total ordering defined on the set of all fuzzy numbers, submitted to international journal of Fuzzy Sets and Systems.
[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] Z. Wang, R. Yang, and K. S. Leung, Nonlinear integrals and Their Applications in Data Mining, World Scientific, Singapore, 2010.
[5] Z. Wang and L. Zhang-Westman, The cardinality of the set of all fuzzy numbers, Proc. IFSA2013. 1045-1049.
[6] L. Zhang-Westman and Z. Wang, Ranking fuzzy numbers by their left and right wingspans, IFSA2013, 1039-1044.

Prerequisites

MATH 8370

Requirements

Give the theoretical definitions of rankings and total orderings and discuss the relation between them to clean up the confusion in literature. Develop the criteria for the goodness of rankings and total ordering defined on various sets of fuzzy numbers. Some examples should be used to illustrate these results. A research paper on this topic should be completed and be submitted to some international academic conference or journal in time.