# Outlier Recognition via Linguistic Aggregation of Graph Databases
## 1 Introduction  
In collecting and processing information, there appear some uncertainties, mostly incomplete or imprecise data. Sources of uncertainty are usually measurements, probabilistic (stochastic uncertainty), lack of credibility, and linguistic descriptions (natural language uncertainty). To take care about such data, that, although strange, may contain valuable and exceptional information, one can consider them to be outliers. An \"outlier\" or \"exception\" (also: deviation, anomaly, aberration, etc.) means an observation that is rare, special, unique, unexampled, or infrequent. These terms mean that properties of interest possessed by outlying objects, are specific to recipients considering/processing them. Outliers are especially noticeable as highlighted or unusual observations on a background of numerous phenomena/objects similar one to another, typical, or ordinary. Unrecognized outliers in data exploration and mining, may decrease reliability of analysis, increase data imprecision and noise. In other words, outlying objects may distort or blur the final gists or meaning of collections analyzed. On the contrary, appropriately recognized outliers can bring unique information on change of activities and congestion in networks or intrusions into them, illegal use of debit/credit cards, serious damages of production lines, rapid changes of patients' health status and parameters of medical devices, etc. The literature enumerates various definitions of outliers, mostly subjective, intuitive, and dependent on different numerical characteristic showing \"how much\" considered objects are atypical for analyzed databases or sets. For example, the definition of outlier by [PERSON], the most frequently quoted, is [1] \"An outlier is an observation which deviates so much from the other observations as to arouse suspiciions that it was generated by a different mechanism\". Additionally, in [1], an outlier is defined as: \"any object \(x\) in thespace \(\mathcal{X}\), which has some abnormal, unusual characteristics in comparison to other objects from \(\mathcal{X}^{\prime\prime}\). Next, in [2], the authors say that outliers are \"noise points outside the set which determine clusters\", or, alternatively, as \"points outside the clusters but separated from the noise\". Next, according to [3,4], \"a point \(p\) in a data set is an outlier with respect to parameters \(k\) and \(\lambda\), if no more than \(k\) points in the data set are at a distance \(\lambda\) or less from \(p\)\", with \(k\in\mathbb{N},\lambda\in\mathbb{R}\). The \(\lambda\) parameter can be interpreted in terms of relations between objects in \(\{x_{1},\ldots,x_{N}\}\), \(N\in\mathbb{N}\), not only as a metric, distance, a semantic connection (e.g., similarity as a binary fuzzy relation), etc. Moreover, another definition for outliers are worth mentioning from [5, 6, 7], and global and local outliers proposed in [8, 9, 10]. Interesting applications and techniques as far as approaches mixing outliers detection with clustering methods are proposed in [11,12]. Outliers in data streams (series or linear structures) are considered in [13]. Recognition of outliers is also the subject of consideration in [3,14,15] and many other. The most important idea on the above literature review, is that it does not provide one objective or axiomatic definition of an outlier at all. This is the specificity of this domain of research: outliers can be defined in different manners, with different characteristics and parameters, and in specific relations to particular problems, issues, datasets, etc. Thus, in this contribution, we focus on outliers defined in terms of linguistic quantification and fuzzy sets [16, 17, 18, 19], since no publications on outliers handled this way can be found. Recognizing outliers via fuzzy quantification and linguistic information can be useful when numerical information and traditional quantitative terms are inaccessible for a given set of objects.