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Sanz, José Antonio and Galar, Mikel and Mesiar, Radko and Bustince, H. and Fernandez, Javier and Montero, Javier (2017) Construction of Capacities from Overlap Indexes. In Fuzzy Sets, Rough Sets, Multisets and Clustering. Studies in Computational Intelligence (671). Springer, Cham, pp. 323335. ISBN 9783319475561

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Official URL: https://link.springer.com/chapter/10.1007/9783319475578_19
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Abstract
In many problems, it is crucial to find a relation between groups of data. Such relation can be expressed, for instance, in terms of an appropriate fuzzy measure or capacity([10, 21]) which reflects the way the different data are connected to each other [20]. In this chapter, taking into account this fact and following the developments in [8],we introduce a method to build capacities ([20, 21]) directly from the data (inputs) of a given problem. In order to do so, we make use of the notions of overlap function and overlap index ([5, 12, 13, 7, 4, 14, 16]) for constructing capacities which reflect how different data are related to each other.
This paper is organized as follows: after providing some preliminaries, we analyse, in Section 3, some properties of overlap functions and indexes. In Sections 4 we discuss a method for constructing capacities from overlap functions and overlap indexes. Finally, we present some conclusions and references.
Item Type:  Book Section 

Uncontrolled Keywords:  Overlap functio; Capacity; Fuzzy measure 
Subjects:  Sciences > Mathematics > Logic, Symbolic and mathematical 
ID Code:  44856 
Deposited On:  28 Sep 2017 08:09 
Last Modified:  14 Jan 2018 00:01 
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