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Adaptivity is the ability of the system to change its behavior whenever it does not achieve the system requirements. Self-adaptive software systems (SASS) are considered a milestone in software development in many modern complex scientific and engineering fields. Employing self-adaptation into a system can accomplish better functionality or performance; however, it may lead to unexpected system behavior and consequently to uncertainty. The uncertainty that results from using SASS needs to be tackled from different perspectives. The Internet of Things (IoT) that utilizes the attributes of SASS presents great development opportunities. Because IoT is a relatively new domain, it carries a high level of uncertainty. The goal of this work is to highlight more details about self-adaptivity in software systems, describe all possible sources of uncertainty, and illustrate its effect on the ability of the system to fulfill its objectives. We provide a survey of state-of-the-art approaches coping with uncertainty in SASS and discuss their performance. We classify the different sources of uncertainty based on their location and nature in SASS. Moreover, we present IoT as a case study to define uncertainty at different layers of the IoT stack. We use this case study to identify the sources of uncertainty, categorize the sources according to IoT stack layers, demonstrate the effect of uncertainty on the ability of the system to fulfill its objectives, and discuss the state-of-the-art approaches to mitigate the sources of uncertainty. We conclude with a set of challenges that provide a guide for future study.