Everyday usage of online Internet services and the recent rise of the Internet of Things (IoT) cause the collection of a massive amount of data, including personal and sensitive information. Anonymization enables providers to share their datasets and preserve the privacy of individuals at the same time. It is a valuable tool for preserving individuals' privacy in social network datasets and IoT environments. Researchers recently focused on developing a universal and robust anonymization method to keep privacy and preserve almost all data utility. Many various anonymization methods have been developed; however, none meet the requirements perfectly. The application-oriented anonymization has been recently discussed only for relational datasets. This paper introduces the framework for application-oriented anonymization for social network datasets and IoT environments. In our framework, it is not necessary to preserve all data utility but only the data utility specified by the data recipient. While requesting the anonymized social network data, the data receiver can specify the metrics that should be kept as close to the original graph as possible. While requesting anonymized data from the cloud in an IoT environment, the data receiver can prioritize attributes. It enables the data recipient to customize the anonymized data and the data provider to control the computing over their dataset. Moreover, we discuss the vulnerability of application-oriented anonymization to composition attacks.