Overlap functions,10.1016/j.na.2009.08.033,Nonlinear Analysis-theory Methods & Applications,H. Bustince,J. Fernandez,R. Mesiar,J. Montero,R. Orduna

Overlap functions   (Citations: 2)
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In this paper we address a key issue in scenario classification, where classifying concepts show a natural overlapping. In fact, overlapping needs to be evaluated whenever classes are not crisp, in order to be able to check if a certain classification structure fits reality and still can be useful for our declared decision making purposes. In this paper we address an object recognition problem, where the best classification with respect to background is the one with less overlapping between the class object and the class background. In particular, in this paper we present the basic properties that must be fulfilled by overlap functions, associated to the degree of overlapping between two classes. In order to define these overlap functions we take as reference properties like migrativity, homogeneity of order 1 and homogeneity of order 2. Hence we define overlap functions, proposing a construction method and analyzing the conditions ensuring that t-norms are overlap functions. In addition, we present a characterization of migrative and strict overlap functions by means of automorphisms.
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    • ...its membership function will be a mapping μpp : R + → [0, 1]...
    • ...When the ranking among the fuzzy numbers of the image is clear, in the sense that there not exist too many overlap (see [1]) between the membership functions of the fuzzy numbers, the algorithm produce betters results than those situations in which the overlapping is high...

    Edwing de Jesus Zarrazolaet al. A hierarchical segmentation for image processing

    • ...It would be the case, for example, when we consider the aggregation of several measures obtained by different experts: a well known problem in remote sensing is to chose an adequate distance in order to compare opinions from different experts (the analysis of ignorance and overlap measures will be extremely pertinent here, see [2], [3])...

    Daniel Gómezet al. A Structural Approach to Image Segmentation

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