Possibilistic Similarity Measures

The concept of similarity plays an essential role in a wide range of application fields like pattern recognition, reasoning, data, and knowledge mining. Nevertheless, the formulation of a valid and general-purpose definition of the similarity concept cannot be easily and simply expressed by a formula and remains a challenging issue. An important concern is that often similarity judgments are based on partial matching and a consideration of the whole structure of the compared objects is missing. Nevertheless, and despite these criticisms, the fundamental place that similarity holds in different theories of perception, knowledge representation, decision-making, and reasoning cannot be denied. Generally speaking, similarity allows assessing how two objects are alike, classifying patterns into different classes, inferring knowledge in order to “categorize” objects into a higher semantic level (classes, categories, etc.), helping a decision-maker to deal with a new encountered situation by comparing it with similar previously encountered ones, etc. From an engineering point of view, several similarity measures have been proposed in order to mathematically express and measure the similarity. All these measures are derived from a set of assumptions, are tied to particular applications, and are strongly related to different forms of knowledge representation and the available information.