Interpretability of Fuzzy Information Granules

Mencar, Corrado

doi:10.1007/978-3-540-92916-1_5

Cited by 2 publications

(1 citation statement)

References 66 publications

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“…Many mathematical settings have been proposed so far in the related literature, such as intervals-hyperboxes, (higher order) fuzzy sets, rough sets, and shadowed sets [36]. The synthesized IGs can be used for interpretability purposes [26,27] or they can be used as a computational component of a suitable intelligent system [1, 3, 10, 23-25, 32, 33, 35, 50]. In any case, the problem of designing effective and justifiable data granulation procedures (GPs) is of paramount importance [6, 7, 12, 29-31, 40, 42].…”

Section: Introductionmentioning

confidence: 99%

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: 99%

Data granulation by the principles of uncertainty

Livi¹,

Sadeghian²

2015

Pattern Recognition Letters

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Granular computing for relational data classification

Hońko

2013

J Intell Inf Syst

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We propose a novel framework for generating classification rules from relational data. This is a specialized version of the general framework intended for mining relational data and is defined in granular computing theory. In the framework proposed in this paper we define a method for deriving information granules from relational data. Such granules are the basis for generating relational classification rules. In our approach we follow the granular computing idea of switching between different levels of granularity of the universe. Thanks to this a granule-based relational data representation can easily be replaced by another one and thereby adjusted to a given data mining task, e.g. classification. A generalized relational data representation, as defined in the framework, can be treated as the search space for generating rules. On account of this the size of the search space may significantly be limited. Furthermore, our framework, unlike others, unifies not only the way the data and rules to be derived are expressed and specified, but also partially the process of generating rules from the data. Namely, the rules can be directly obtained from the information granules or constructed based on them.

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Interpretability of Fuzzy Information Granules

Cited by 2 publications

References 66 publications

Data granulation by the principles of uncertainty

Data granulation by the principles of uncertainty

Granular computing for relational data classification

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