International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 74165, 19 pages

Equivalence class in the set of fuzzy numbers and its application in decision-making problems

Geetanjali Panda, Motilal Panigrahi, and Sudarsan Nanda

Department of Mathematics, Indian Institute of Technology, West Bengal Kharagpur-721302, India

Received 4 November 2005; Revised 20 June 2006; Accepted 22 June 2006

Copyright © 2006 Geetanjali Panda et al. 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.


An equivalence relation is defined in the set of fuzzy numbers. In a particular equivalence class, arithmetic operations of fuzzy numbers are introduced. A fuzzy matrix with respect to a particular class and its associated crisp matrices are also introduced. The concept of equivalence class is applied in fuzzy decision-making problems and justified through a numerical example.