Decision making approaches depending on the assessments of individual decision makers produce inaccurate results due to the existence of multiple uncertainties. To model intrapersonal uncertainty, interpersonal uncertainty and randomness in decision making assessments, this research study proposes a novel approach by integrating linear and non-linear type of fuzzy numbers with cloud model theory using novel technique of computing entropy of these fuzzy numbers. A novel mathematical model known as cloud fuzzy numbers is introduced using the concepts of fuzzy numbers and cloud theory. The self-evaluated relative weights of experts are computed using a non-linear optimization method which is based on maximum deviation method and Lagrange multipliers of cloud fuzzy numbers. The new cloud fuzzy numbers are then combined with CODAS (combinative distance based assessment) approach that is based on the largest Euclidean and Taxicab distances for the selection of suitable criteria. Firstly, the linguistics evaluations are converted into the fuzzy numbers and then cloud fuzzy numbers using formulae of expectation and entropy ensuring that the obtained interval cloud values follows a normal distribution. Secondly, the cloud fuzzy weighted arithmetic averaging operator is used to aggregate cloud fuzzy numbers using the self-evaluated fuzzy weights Thirdly, the assessment score is determined to rank the alternatives by computing the distance between normalized weighted matrix and the negative ideal solution. Finally, a case study is discussed for the selection of best renewable energy resource in Turkey to elaborate the significance of the proposed research. The convergence and accuracy of the proposed model is proved with certain mathematical and theoretical results.

中文翻译：

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基于云模糊数字的可持续可再生能源资源的新决策方法


由于存在多种不确定性，依赖于个人决策者评估的决策方法会产生不准确的结果。为了模拟决策评估中的人际不确定性、人际不确定性和随机性，本研究提出了一种新颖的方法，通过使用计算这些模糊数熵的新技术，将线性和非线性类型的模糊数与云模型理论相结合。使用模糊数和云理论的概念引入了一种称为云模糊数的新型数学模型。专家的自我评估相对权重是使用非线性优化方法计算的，该方法基于最大偏差法和云模糊数的拉格朗日乘数。然后将新的云模糊数与基于最大欧几里得和出租车距离的 CODAS（基于组合距离的评估）方法相结合，以选择合适的标准。首先，将语言学评估转换为模糊数，然后使用期望和熵公式将云模糊数转换为云模糊数，确保获得的区间云值服从正态分布。其次，使用云模糊加权算术平均运算符，使用自评估的模糊权重聚合云模糊数 第三，通过计算归一化加权矩阵与负理想解之间的距离来确定评估分数以对备选方案进行排名。最后，讨论了选择土耳其最佳可再生能源资源的案例研究，以详细说明拟议研究的重要性。所提模型的收敛性和准确性用一定的数学和理论结果得到了证明。