Modeling the Uncertainty of a Set of Graphs Using Higher-Order Fuzzy Sets

Livi, Lorenzo; Rizzi, Antonello

doi:10.1007/978-1-4614-3442-9_7

Cited by 2 publications

(1 citation statement)

References 54 publications

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“…In this paper, we elaborate a conceptual data granulation framework over the principles of uncertainty. A preliminary version of the herein exposed ideas appeared in [19]. Here we further elaborate over this preliminary work by providing a more extensive discussion of the framework, offering new experiments that demonstrate the different facets underlying such ideas.…”

Section: Introductionmentioning

confidence: 89%

Data granulation by the principles of uncertainty

Livi¹,

Sadeghian²

2015

Pattern Recognition Letters

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Researches in granular modeling produced a variety of mathematical models, such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets, which are all suitable to characterize the socalled information granules. Modeling of the input data uncertainty is recognized as a crucial aspect in information granulation. Moreover, the uncertainty is a well-studied concept in many mathematical settings, such as those of probability theory, fuzzy set theory, and possibility theory. This fact suggests that an appropriate quantification of the uncertainty expressed by the information granule model could be used to define an invariant property, to be exploited in practical situations of information granulation. In this perspective, we postulate that a procedure of information granulation is effective if the uncertainty conveyed by the synthesized information granule is in a monotonically increasing relation with the uncertainty of the input data. In this paper, we present a data granulation framework that elaborates over the principles of uncertainty introduced by Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is possible to apply such principles regardless of the input data type and the specific mathematical setting adopted for the information granules. The proposed framework is conceived (i) to offer a guideline for the synthesis of information granules and (ii) to build a groundwork to compare and quantitatively judge over different data granulation procedures. To provide a suitable case study, we introduce a new data granulation technique based on the minimum sum of distances, which is designed to generate type-2 fuzzy sets. The automatic membership function elicitation is completely based on the dissimilarity values of the input data, which makes this approach widely applicable. We analyze the procedure by performing different experiments on two distinct data types: feature vectors and labeled graphs. Results show that the uncertainty of the input data is suitably conveyed by the generated type-2 fuzzy set models.

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Section: Introductionmentioning

confidence: 89%

Data granulation by the principles of uncertainty

Livi¹,

Sadeghian²

2015

Pattern Recognition Letters

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Granular computing, computational intelligence, and the analysis of non-geometric input spaces

Livi

Sadeghian

2015

Granul. Comput.

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Data granulation emerged as an important paradigm in modeling and computing with uncertainty, exploiting information granules as the main mathematical constructs involved in the context of granular computing. In this paper, we comment on the importance of data granulation in computational intelligence methods. Toward this aim, we discuss also the peculiar aspects related to the analysis of non-geometric patterns, which have recently attracted considerable attention by researchers. As a conclusion, we elaborate over the fundamental, conceptual problems underlying the process of data granulation, which drive the quest for a sound theory of granular computing.

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Modeling the Uncertainty of a Set of Graphs Using Higher-Order Fuzzy Sets

Cited by 2 publications

References 54 publications

Data granulation by the principles of uncertainty

Data granulation by the principles of uncertainty

Granular computing, computational intelligence, and the analysis of non-geometric input spaces

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