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Advances in Fuzzy Systems
Volume 2011, Article ID 178308, 7 pages
Research Article

Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality

1Department of Mathematics, GITAM Institute of Technology, GITAM University, Visakhapatnam 530045, India
2Department of Applied Mathematics, GITAM Institute of Science, GITAM University, Visakhapatnam 530045, India

Received 14 December 2010; Revised 18 April 2011; Accepted 26 April 2011

Academic Editor: José Luis Verdegay

Copyright © 2011 P. Phani Bushan Rao and N. Ravi Shankar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. However, there is no method which gives a satisfactory result to all situations. Most of the methods proposed so far are nondiscriminating and counterintuitive. This paper proposes a new method for ranking fuzzy numbers based on the Circumcenter of Centroids and uses an index of optimism to reflect the decision maker's optimistic attitude and also an index of modality that represents the neutrality of the decision maker. This method ranks various types of fuzzy numbers which include normal, generalized trapezoidal, and triangular fuzzy numbers along with crisp numbers with the particularity that crisp numbers are to be considered particular cases of fuzzy numbers.