Rankings and Total Orderings on Sets of Generalized Fuzzy Numbers

Ranking and ordering generalized fuzzy numbers are hot topics in decision making under uncertainty. By extension principle, addition and multiplication of generalized fuzzy numbers are presented for establishing goodness criteria. This paper initially proposes four criteria for judging the goodness of a given ranking or total ordering defined on a set of generalized fuzzy numbers and then discusses the methods of rankings and total orderings which satisfy these goodness criteria. Besides, the cardinality of the set of all generalized fuzzy numbers is, for the first time, determined.