The Laplacian Energy of Hesitancy Fuzzy Graphs in Decision-Making Problems

Decision-making (DM) is a process in which several persons concurrently engage, examine the problems, evaluate potential alternatives, and select an appropriate option to the problem. Technique for determining order preference by similarity to the ideal solution (TOPSIS) is an established DM process. The objective of this report happens to broaden the approach of TOPSIS to solve the DM issues designed with Hesitancy fuzzy data, in which evaluation evidence given by the experts on possible solutions is presents as Hesitancy fuzzy decision matrices, each of which is defined by Hesitancy fuzzy numbers. Findings: we represent analytical results, such as designing a satellite communication network and assessing reservoir operation methods, to demonstrate that our suggested thoughts may be used in DM. Aim: We studied a new testing method for the artificial communication system to give proof of the future construction of satellite earth stations. We aim to identify the best one from the different testing places. We are also finding the best operation schemes in the reservoir. In this article, we present the concepts of Laplacian energy (LE) in Hesitancy fuzzy graphs (HFGs), the weight function of LE of HFGs, and the TOPSIS method technique is used to produce the hesitancy fuzzy weighted-average (HFWA). Also, consider practical examples to illustrate the applicability of the finest design of satellite communication systems and also evaluation of reservoir schemes.