Reasonable properties for the ordering of fuzzy quantities (I)

This work aims at the discussion of reasonable properties for the ordering of fuzzy quantities. In the fuzzy literature more than 35 indices exist for the comparison of fuzzy quantities. To grasp this amalgam of indices we split them up into three classes (with linguistic approaches excluded). In this paper we briefly introduce the ordering indices in the first and second class. Based on these indices some ways to formulate the ranking orders among fuzzy quantities are suggested. Then we propose some axioms which serve as the reasonable properties to figure out the rationality of an ordering procedure. Finally, we check all the ordering indices in the first and second class to see whether the proposed axioms are fulfilled or not. (C) 2001 Elsevier Science B.V. All rights reserved.