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Selecting the most suitable renewable energy technology among feasible alternatives considering conflicting criteria is a Multiple Criteria Decision Making (MCDM) problem. One of the essential stages in the methods used to solve such problems is determining the appropriate weight of each criterion to be considered. The Shannon Entropy method is a frequently used MCDM method to calculate the criteria weights, however it is not suitable to solve problems for which uncertainty in the input data exists. This paper presents a new extended Shannon Entropy method: the Integrated Constrained Fuzzy Shannon Entropy (IC-FSE) method, by which criteria weights are obtained from uncertain input data. To show the applicability of IC-FSE, an illustrative example for the selection of a renewable energy technology in the mining industry is presented, in which three alternative renewable energy technologies, onshore wind, solar photovoltaic and concentrated solar power, were evaluated with respect to technical, social, economic and environmental categories. The results show that IC-FSE can effectively provide appropriate fuzzy solutions for weighting the sustainability criteria for renewable energy technologies. The superiority of this method is showcased by demonstrating that IC-FSE results are more robust than those obtained using other existing methods. The methodology presented can be applied broadly in the renewable energy sector to ensure better informed decision making processes. Highlights• A new criteria weighting method for imprecise quantitative data is described.• The method is used to weight renewable energy technologies' sustainability criteria.• The normalisation procedure proposed is shown to reduce uncertainty.• The method yields more appropriate results than existing methods.• The method yields objective criteria weights, minimising the risk of information loss.

The ability of the Analytical Hierarchy Process (AHP) when applied to the choice problem in the context of group decision making under uncertainty has been often criticised. AHP is not able to fully capture the various opinions and the uncertainty associated with the lack of information. This work develops an integrated constrained fuzzy stochastic analytic hierarchy process (IC-FSAHP) method in order to deal with the aforementioned drawbacks. IC-FSAHP combines two existing fuzzy AHP (FAHP) methods and further extends its applicability by implementing stochastic simulations. A case study has been conducted in order to assess the ability of IC-FSAHP; the results showed that IC-FSAHP is able to capture the uncertainty and multiple DMs' opinions. This paper also discusses the effect that the number of DMs has in enhancing rank discrimination. Besides, the possibility of the occurrence of rank reversal because of the use of IC-FSAHP has been analysed. The results showed that the ranking of alternatives was preserved throughout the changes in the number of alternatives, however, rank reversal occurred in the case of changes in judgements scales. By comparing the U-uncertainty in fuzzy global priorities obtained using IC-FSAHP to that obtained using an existing FSAHP method, we show that our method is capable of minimising the risk of losing important knowledge during the computations. We also discuss how IC-FSAHP can decrease the uncertainty and increase the reliability of the decisions by means of robust computations.

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