Novel decision making approach for sustainable renewable energy resources with cloud fuzzy numbers

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.