A Review of Ranking Approach to Rank Interval-Valued Trapezoidal Intuitionistic Fuzzy Sets

An Interval-valued trapezoidal intuitionistic fuzzy set (IVTrIFS) is a powerful tool in modeling uncertainty. It is a special type of Intuitionistic Fuzzy Set (IFS) and interval-valued intuitionistic fuzzy set (IVIFS), which has a consecutive domain of real numbers. An IVTrIFSs is distinguished by using three characteristic functions namely membership degree, non-membership degree, and hesitancy degree. Ranking is a challenging task, and every ranking method has its own significance and applicability. Since their inception in 1965, several researchers have proposed various ranking methods by using concepts such as Score and Accuracy, Centroids, Centre of Gravity, Distance/Similarity measures, Value and Ambiguity, etc. yet there is no specific ranking approach that is appropriate for all applications or provides adequate results in all situations. The Centre of Gravity (COG) method is one of the most popular defuzzification techniques of fuzzy mathematics. By utilizing the notion of the COG, one can ascertain the central tendency or representative value of a given fuzzy set. As it is derived by using area and centroids of any geometric representation, this method is particularly useful in fuzzy logic systems, fuzzy control, decision-making processes, and fuzzy data analysis. In this paper, we derive a ranking method for IVTrIFS using the Centre of Gravity.