Validation of methods for ranking fuzzy numbers in decision making

The concept of ranking fuzzy numbers has attracted significant attention recently due to its successful use in decision making problems. This concept allows decision makers to appropriately exercise their subjective judgment under situations that are vague, imprecise, ambiguous and uncertain in nature. The literature on ranking fuzzy numbers describes the validation of ranking methods as the most important aspect of the application of these methods. This is due to the fact that the validation confirms the suitability of the associated methods for ranking fuzzy numbers and decision making purposes. In this paper, a comprehensive review on validation techniques for methods of ranking fuzzy numbers is presented. These techniques are associated with properties of ranking fuzzy quantities as well as consistency and efficiency evaluation of ranking operations. The techniques are described in detail and discussed in the context of many established and more recent works in the field.