## 1 Introduction  
Recent developments in medicine have resulted in better diagnostic methods and increased number or improved efficacy of treatments, further resulting in improved quality of care at the cost of more expensive and complex healthcare. In order to deal with this complexity and anticipate the increased demand for care, many hospitals and healthcare providers standardize care processes by using clinical guidelines and protocols [1]. Such an approach has many benefits [2, 3], such as reduced hospital complication rates without an increased length of stay [4] and reduced treatment costs [5]. [PERSON] and [PERSON] [6] define a _clinical guideline_ as \"systematically developed statements to assist practitioners and patient decisions about appropriate health care for specific circumstances\". Clinical guidelines are designed based on the best available evidence and can be seen as a set of rules that do not need to be strictly followed since individual patient variation may necessitate deviation from such guidelines. In order to make clinical guidelines more operational, many hospitals develop more specific clinical protocols for specific, more standardized care processes in which limited variation in care is known to exist. _Clinical protocols_ provide \"a comprehensive set of rigid criteria outlining the management steps for a single clinical condition or aspects of organization\" [7]. Hospitalscan have many of such clinical protocols implemented in daily practice [8], e.g., clinical protocols for detoxification [9], or the glucose management or weaning protocols as used in many intensive care units (ICUs) [10]. The effect of applying clinical protocols in daily practice, in general, is measured during intervention case studies [11; 12]. In such studies, a situation is assessed before and after the introduction of the protocol. Moreover, compliance with the protocol is measured and reported as evidence that the observed outcome change was indeed caused by following the protocol. In this context, by _compliance_, we mean \"the degree to which the behavior of the executors of the clinical protocol corresponds to the behavior described in the clinical protocol\" [13]. In the literature (and in this paper), the terms _adherence_, _compliance_ and _conformance_ are used interchangeably [14; 15; 16]. In the medical domain, however, the term adherence is sometimes preferred (e.g., patient adherence) because compliance has a negative connotation [17; 18]. Measurement of compliance is not a part of the routine in daily practice, however. Therefore, it is difficult to quantify the effectiveness of a clinical protocol on a daily basis. One of the difficulties with automatically measuring compliance is that not every activity is recorded in the hospital information system. Information about some performed activities, e.g., whether a certain test was performed, if not entered manually or automatically, nevertheless could be deduced from the presence of specific patients' results' in the system. Another difficulty is that a widely accepted definition of compliance or compliance metrics is lacking. Two commonly used compliance metrics are (1) the percentage of protocol executions with all activities compliant and (2) the percentage of compliant activities (over all patients) for a given protocol [11; 12]. In those approaches, it is assumed that a single activity within the protocol can be either compliant with the clinical protocol or not compliant. However, when discussing with healthcare providers, especially more experienced doctors and nurses, one can notice that compliance is not a binary state. For instance, some thresholds are too strict for specific patients who require a different treatment strategy. Therefore, we want to capture this additional flexibility while calculating compliance levels. In this paper, we address the issue of compliance measurement in more detail and propose new measures for (fuzzy) compliance with a clinical protocol and their interpretations.