n-Dimensional overlap functions

One of the most common techniques to find the adequate weights in ordered weighted averaging (OWA) operators is based on the orness concept, where the weights are determined by maximizing the entropy (variation) for a fixed orness value. But such an entropy represents a dispersion measure for nominal variables, while weights in an OWA operator are essentially ordinal rather than nominal. Hence, in this paper, we propose a novel way to determine OWA weights based upon ordinal dispersion measures instead of an standard entropy measure. From this approach, we find an explicit formula for the weights, and we illustrate differences by means some multicriteria decision‐making examples.

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“…An aggregation operator is usually defined as a real function

A : {[0, 1]}^{n} goodbreakinfix\to [0, 1]

, such that for

n

items in

[0, 1]

, yields an aggregation value in the same interval and fulfilling the following conditions:…”

Section: Preliminariesmentioning

confidence: 99%

A novel ordered weighted averaging weight determination based on ordinal dispersion

et al. 2019

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“…In this section, we recall some concepts and properties of bivariate and n-dimensional overlap and grouping functions, which were initially proposed in [2,19] , and that where extended to the ndimensional case in [13].…”

Section: Preliminariesmentioning

confidence: 99%

“…In [13], previous ideas presented for two sets or classes were extended into a more general case. Sometimes, an object may belong to more than two classes, and thus it could be interesting to measure the degree of overlap of this object with respect to the classification system given by the available classes.…”

Section: N-dimensional Overlap Functionsmentioning

confidence: 99%

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Fuzzy Community detection based on grouping and overlapping functions

Gómez¹,

Rodríguez²,

Montero³

et al. 2015

Advances in Intelligent Systems Research

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One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measure the quality of a fuzzy community detection output based on n-dimensional grouping and overlapping functions that generalize the classical modularity for crisp community detection problems and also for crisp overlapping community detection problems.

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“…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.…”

Section: Introductionmentioning

confidence: 99%