Mobile Ad-hoc Network (MANET) is mostly decentralized and self-adjustable network system. It is significant to optimize the overall network energy utilization and improve packet sending performance by reducing the errors, generated due to different real-life environmental effects. In this paper, considering atmospheric, environmental change and varying distance for topological change, we try to generate the routing cost. By introducing m-minimum (membership value as m) triangular fuzzy number at interval based cost and energy of the network, we try to handle the uncertain environment. Here we generate both fuzzy minimum spanning tree (FMST) for a given n- nodes network and p-node fuzzy multicast minimum spanning tree (pFMMST), in fuzzy interval based format. Applying the fuzzy credibility distribution we modify the network routing cost and energy utilization for both FMST and pFMMST. Comparing the routing cost and residual energy for FMST and pFMMST of MANET, it is concluded that, pFMMST is better FMST based packet routing approach, with minimum routing cost, optimized total energy utilization and best possible technique to reduce the error which is generated due to the deviation of interval of upper and lower limit data in route cost and residual energy.

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.