Distinguishability quantification of fuzzy sets

Mencar, Corrado; Castellano, Giovanna; Fanelli, Anna Maria

doi:10.1016/j.ins.2006.04.008

Cited by 45 publications

(28 citation statements)

References 20 publications

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“…2) Rule refinement: once the Gaussians are obtained, rules are then generated. These rules undergo an optimization process which consists of merging the membership functions (fuzzy sets) using the Jaccard's similarity measure for type-2 FS's which is based on the analysis provided in [31]. Those exceeding a threshold are merged using an adapted formula for fusing univariate Gaussians like:…”

Section: B Rule Base Optimizationmentioning

confidence: 99%

GT2FC: An Online Growing Interval Type-2 Self-Learning Fuzzy Classifier

Bouchachia

Vanaret

2014

IEEE Trans. Fuzzy Syst.

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Abstract-In the present paper we propose a Growing Type-2 Fuzzy Classifier (GT2FC) for online rule learning from real-time data streams. While in batch rule learning the training data are assumed to be drawn from a stationary distribution, in online rule learning data can dynamically change over time becoming potentially non-stationary. To accommodate dynamic change, GT2FC relies on a new semi-supervised online learning algorithm called 2G2M (Growing Gaussian Mixture Model). In particular, 2G2M is used to generate the type-2 fuzzy membership functions to build the type-2 fuzzy rules. GT2FC is designed to accommodate data online and to reconcile labeled and unlabeled data using selflearning. Moreover. GT2FC maintains low complexity of the rule base using online optimization and feature selection mechanisms.GT2FC is tested on data obtained from an ambient intelligence (AmI) application where the goal is to exploit sensed data to monitor the living space on behalf of the inhabitants. Because sensors are prone to faults and noise, type-2 fuzzy modeling is very suitable for dealing with such an application. Thus, GT2FC offers the advantage of dealing with uncertainty in addition to self-adaptation in an online manner. For illustration purposes, GT2FC is also validated on synthetic and classic UCI data sets. The detailed empirical study shows that GT2FC performs very well under various experimental settings.

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Section: B Rule Base Optimizationmentioning

confidence: 99%

GT2FC: An Online Growing Interval Type-2 Self-Learning Fuzzy Classifier

Bouchachia

Vanaret

2014

IEEE Trans. Fuzzy Syst.

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“…In general, granulation is hierarchical in nature.". The notions of similarity, equivalence, and indistinguishability relations have been well investigated with set-based approaches (Bittner & Stell, 2003;Chen & Yao, 2006;Hata & Mukaidono, 1999;Keet, 2007a;Mencar et al, 2007;Peters et al, 2002;Skowron & Peters, 2003;Yao, 2004). However, this set-based approach has issues that can be better addressed with mereology proper (Abelló et al, 2006;Bittner & Smith, 2003;Keet, 2008a).…”

Section: Related Workmentioning

confidence: 99%

A Top-Level Categorization of Types of Granularity

Keet

2010

Novel Developments in Granular Computing

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Abstract. Multiple different understandings and uses exist of what granularity is and how to implement it, where the former influences success of the latter with regards to storing granular data and using granularity for automated reasoning over the data or information, such as granular querying for information retrieval. We propose a taxonomy of types of granularity and discuss for each leaf type how the entities or instances relate within its granular level and between levels. Such distinctions give guidelines to a modeler to better distinguish between the types of granularity in the design phase and the software developer to improve on implementations of granularity. Moreover, these foundational semantics of granularity provide a basis from which to develop a comprehensive theory of granularity.

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“…One concerns the value or value range for each granule within a granulation hierarchy, such as km 2 and m 2 , and the other the precision of each specific level, or the refinement of measurements for the granule, such as "km 2 ± 1 m 2 " or "km 2 ± 1 cm 2 ", where the choice for m 2 or cm 2 is provided by the approximation space that covers both intended and enforced indistinguishability 2 . Examples of degrees of membership are properties such as colour shades, but this is rarely used as a criterion for granulation of universals (although it can be used as an indirect means [19], [20]).…”

Section: A Indiscernibilitymentioning

confidence: 99%

Granulation with Indistinguishability, Equivalence, or Similarity

Keet

2007

2007 IEEE International Conference on Granular Computing (GRC 2007)

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Abstract-One of the relations used with granularity is indistinguishability, where distinguishable entities in a finer-grained granule are indistinguishable in a coarser-grained granule. This relation is a subtype of equivalence relation, which is used in the other direction to create finer-grained granules. Together with the notion of similarity, we formally prove some intuitive properties of the indistinguishability relation for both qualitative and quantitative granularity, that with a given granulation there must be at least two granules (levels of granularity) for it to be granular, and derive a strict order between finer and coarser granules. Based on these results, granulation hierarchy is defined as extra assisting structure to augment implementations.

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Distinguishability quantification of fuzzy sets

Cited by 45 publications

References 20 publications

GT2FC: An Online Growing Interval Type-2 Self-Learning Fuzzy Classifier

GT2FC: An Online Growing Interval Type-2 Self-Learning Fuzzy Classifier

A Top-Level Categorization of Types of Granularity

Granulation with Indistinguishability, Equivalence, or Similarity

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