A rough set, an extension of a crisp set, is a mathematical tool to understand and model uncertainty without much prior information, additional adjustments or pre-defined membership functions. To manipulate the subjectivity and vagueness of decision-making problems, rough models provide more objective description of given information using upper and lower approximations. In this research paper, we study the absurdity and falsity of existing definition of rough graph. Based on rough relations, we introduce the concepts of rough graphs and rough digraphs and establish certain formulae, lower and upper bounds of color energy of rough graphs. Using D numbers, rough weights and rough entropy weights, we develop rough D-TOPSIS method which incorporates the capability to analyze uncertain and vague information without additional assumptions. We study the importance of rough information for the evaluation of water requirement in agricultural farming, investment analysis in organic and inorganic farming systems and illegal communication networks.

粗集（是脆集的扩展）是一种数学工具，无需太多先验信息，其他调整或预定义的隶属函数即可理解和建模不确定性。为了操纵决策问题的主观性和模糊性，粗糙模型使用上下近似来提供给定信息的更客观描述。在本文中，我们研究了粗糙图现有定义的荒谬性和虚假性。在粗糙关系的基础上，介绍了粗糙图和粗糙图的概念，并建立了粗糙图颜色能量的一定公式，上下界。使用D数，粗略权重和粗略熵权重，我们开发出粗略D-TOPSIS方法，无需额外的假设即可分析不确定和模糊的信息。我们研究了粗略信息对评估农业农业用水需求，有机和无机农业系统中的投资分析以及非法通信网络的重要性。