Abstract
Relations appear in many fields of mathematics and computer science. In classical mathematics these relations are usually crisp, i.e. two objects are related or they are not. However, many relations in real-world applications are intrinsically fuzzy, i.e. objects can be related to each other to a certain degree.
With each fuzzy relation, different kinds of fuzzy relational images can be associated, all with a very practical interpretation in a wide range of application areas. In this paper we will explicite the formal link between well known direct and inverse images of fuzzy sets under fuzzy relations on one hand, and different kinds of compositions of fuzzy relations on the other. Continuing from this point of view we are also able to define a new scale of so-called double images. The wide applicability in mathematics and computer science of all these fuzzy relational images is illustrated with several examples.
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Nachtegael, M., De Cock, M., Van der Weken, D., Kerre, E.E. (2002). Fuzzy Relational Images in Computer Science. In: de Swart, H.C.M. (eds) Relational Methods in Computer Science. RelMiCS 2001. Lecture Notes in Computer Science, vol 2561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36280-0_10
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DOI: https://doi.org/10.1007/3-540-36280-0_10
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