Ranking and total ordering on sets of fuzzy numbers
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.
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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.