Definition of general aggregation operators through similarity relations

Beliakov, Gleb

doi:10.1016/s0165-0114(98)00194-8

Cited by 24 publications

(7 citation statements)

References 40 publications

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“…Returning to aggregation operators, it would be interesting to consider ideal samples that characterize the classes, and then adopt a metric that can be learnt with the help of particular aggregation operators [33].…”

Section: Discussionmentioning

confidence: 99%

A Relevance-Based Learning Model of Fuzzy Similarity Measures

Capitaine

2012

IEEE Trans. Fuzzy Syst.

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Matching pairs of objects is a fundamental operation in data analysis. However, it requires to define a similarity measure between objects to be matched. The similarity measure may not be adapted to the various properties of each object. Consequently, designing a method to learn a measure of similarity between pairs of objects is an important generic problem in machine learning. In this paper, a general framework of fuzzy logical-based similarity measures based on T-equalities derived from residual implication functions is proposed. Then a model allowing to learn the parametric similarity measures is introduced. This is achieved by an online learning algorithm with an efficient implication-based loss function. Experiments on real datasets show that the learned measures are efficient at a wide range of scales, and achieve better results than existing fuzzy similarity measures. Moreover, the learning algorithm is fast, so that it can be used in real world applications, where computation times are a key-feature when one chooses an inference system.

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Section: Discussionmentioning

confidence: 99%

A Relevance-Based Learning Model of Fuzzy Similarity Measures

Capitaine

2012

IEEE Trans. Fuzzy Syst.

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“…As indicated earlier, the associations between fuzzy relations and similarity/distance metrics have been widely studied. According to [26], aggregating operations can also be interpreted in terms of distance measurements. In particular, when appropriate weights are selected, an OWA operator can act as a distance metric, being a positive mapping which satisfies identity, symmetry, and triangle inequality [9,27].…”

Section: Novel Owa Of Fuzzy Relationsmentioning

confidence: 99%

Ordered weighted aggregation of fuzzy similarity relations and its application to detecting water treatment plant malfunction

Shen

Chen

et al. 2017

Engineering Applications of Artificial Intelligence

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Ordered weighted aggregation procedures have been introduced in many applications with promising results. In this paper, an innovative approach for ordered weighted aggregation of fuzzy relations is proposed. It allows the integration of component relations generated from different perspectives of a certain observation to form an overall fuzzy relation, deriving a useful similarity measure for observed data points. Two types of aggregation are investigated: a) min/max operators are employed for the aggregation of component re- lations dened by the minimum T-norm; and b) sum/product operators are employed for the aggregation of component relations dened by the Lukasiewicz T-norm. The resultant ordered weighted aggregations prove to preserve the desirable reexivity and symmetry properties, with T-transitivity also conditionally preserved if appropriate weighting vectors are adopted. The conditions upon which the proposed aggregated relations preserve T-transitivity are studied. The characteristics of applying an aggregated relation in combination with clustering procedures is also experimentally examined, where fuzzy similarity relations regarding individual features are aggregated to support hierarchical clustering. An application to the detection of water treatment plant malfunction demonstrates that better results can be obtained with the transitive fuzzy relations acting as the required similarity measures, as compared to the use of non-transitive ones. By introducing transitivity to the aggregation the interpretability of the detection system is also enriched.Peer reviewe

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“…Classification, modifications, properties and application domains of fuzzy aggregation operators are given in the literature, e.g. [1,3,9,19,23]. In Let us try to determine only one fuzzy set out of this interval, which takes proper account of the values of all the other members of the given finite collection of fuzzy sets.…”

Section: Proofmentioning

confidence: 99%

A method for fuzzy aggregation based on group expert evaluations

Tsabadze

2006

Fuzzy Sets and Systems

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Definition of general aggregation operators through similarity relations

Cited by 24 publications

References 40 publications

A Relevance-Based Learning Model of Fuzzy Similarity Measures

A Relevance-Based Learning Model of Fuzzy Similarity Measures

Ordered weighted aggregation of fuzzy similarity relations and its application to detecting water treatment plant malfunction

A method for fuzzy aggregation based on group expert evaluations

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