Realisation of the diverse advantages of green computing will lead to restructuring internet technology firms for incorporating sustainability. Green computing aims to design, manufacture and dispose of computing technologies and devices without much of impact on environment. Cloud computing is a green computing technology with the concept of sharing services over a network for maximising the effectiveness of resources. These resources are shared by multiple users all over the world, thus maximising the computing power and reducing environmental damages with less usage of energy, less carbon emissions and reduced e-waste. Hosting on the cloud is more environment friendly and it results in less of a carbon footprint. Inadequate authentication in cloud facilities can cause security threats and data stealing. Biometric authentication is a promising solution which provides safer user authentication for cloud services. Finger vein recognition is a competent biometrics possessing a superior level of security and stronger robustness against spoofing than other biometrics of modern era. In this paper, a fuzzy set theory-based image classification is proposed for finger vein images for securing cloud services against unauthorised access. Performance of the proposed method is evaluated in terms of recall and precision rates. Copyright © 2018 Inderscience Enterprises Ltd.