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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. 323-335.
ISBN 978-3-319-47556-1

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Official URL: https://link.springer.com/chapter/10.1007/978-3-319-47557-8_19

## 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 |
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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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