Derivation and Comparative Study on Centroid Ranking Value of TrIFN and Apply on Fuzzy Geometric Programming

Ranking fuzzy numbers has become an important process in decision making. Many ranking methods have been proposed thus far and one of the commonly used is centroid of trapezoid. Here we try to derive detail mathematical derivation of centroids of a Trapezoidal Intuitionistic Fuzzy Number along x and y axis. After that we derive the ranking value from two centroid along x and y axis. At the end of the article ranking value on fuzzy geometric programming is used. Here we are dealing with three strong decision making concepts. Intuitionistic trapezoidal fuzzy system is much more decision oriented approach than normal fuzzy number in real life uncertain environment, where we can apply membership and non membership concept for analyzing any real life situation. Ranking value, based on centroid of any Trapezoidal Intuitionistic Fuzzy Number helps for conclusion derivation in quantitative way. We here choose most powerful non linear optimization tool, geometrical programming technique, for generating any decision, using Trapezoidal Intuitionistic Fuzzy Number with centroid ranking approach.