A Fuzzy Measure Similarity Between Sets of Linguistic Summaries

In this paper, we consider the problem of evaluating the similarity of two sets of linguistic summaries of sensor data. Huge amounts of available data cause a dramatic need for summarization. In continuous monitoring, it is useful to compare one time interval of data with another, for example, to detect anomalies or to predict the onset of a change from a normal state. Assuming that summaries capture the essence of the data, it is sufficient to compare only those summaries, i.e., they are descriptive features for recognition. In previous work, we developed a similarity measure between two individual summaries and proved that the associated dissimilarity is a metric. Additionally, we proposed some basic methods to combine these similarities into an aggregate value. Here, we develop a novel parameter free method, which is based on fuzzy measures and integrals, to fuse individual similarities that will produce a closeness measurement between sets of summaries. We provide a case study from the eldercare domain where the goal is to compare different nighttime patterns for change detection. The reasons for studying linguistic summaries for eldercare are twofold: First, linguistic summaries are the natural communication tool for health care providers in a decision support system, and second, due to the extremely large volume of raw data, these summaries create compact features for an automated reasoning for detection and prediction of health changes as part of the decision support system.