Kernel functions in Takagi-Sugeno-Kang fuzzy system with nonsingleton fuzzy input

Guevara, Javier; Hirata, Roberto; Canu, Stéphane

doi:10.1109/fuzz-ieee.2013.6622409

Cited by 13 publications

(22 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…• We show that the kernel presented in [19] satisfy our definition of kernel on fuzzy sets and we proof that such kernel is a fuzzy equivalence relation and is a fuzzy logic formula for fuzzy rules.…”

Section: B Contributionsmentioning

confidence: 99%

“…But, all the positive definite kernels on those works are functions defined only on R D × R D . To the best of our knowledge, the first attempt to fill this gap, is the work [19] giving a formulation to construct positive definite kernels on fuzzy sets and experimenting with those kernels using fuzzy and interval datasets.…”

Section: A Previous Work Using Positive Definite Kernels and Fuzzy Setsmentioning

confidence: 99%

“…. , A 5 are fuzzy sets [19] In this paper, we give the theoretical basis to construct positive definite kernel on fuzzy sets, that is, we are going to consider the set E as the set of all the fuzzy sets. This will allow us to use all the stuff of kernel methods in datasets whose observations are given by fuzzy sets.…”

mentioning

confidence: 99%

“…This will allow us to use all the stuff of kernel methods in datasets whose observations are given by fuzzy sets. As an example, Figure 1 shows a nonlinear classifier obtained from a support vector machine using a dataset whose observations are fuzzy sets, using a positive definite kernel on fuzzy sets [19].…”

mentioning

confidence: 99%

See 3 more Smart Citations

Positive definite kernel functions on fuzzy sets

Guevara

Hirata

Canu

2014

2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

Self Cite

View full text Add to dashboard Cite

Abstract-Embedding non-vectorial data into a normed vectorial space is very common in machine learning, aiming to perform tasks such classification, regression, clustering and so on. Fuzzy datasets or datasets whose observations are fuzzy sets, are an example of non-vectorial data and, many of fuzzy pattern recognition algorithms analyze them in the space formed by the set of fuzzy sets. However, the analysis of fuzzy data in such space has the limitation of not being a vectorial space. To overcome such limitation, in this work, we propose the embedding of fuzzy data into a proper Hilbert space of functions called the Reproducing Kernel Hilbert Space or RKHS. This embedding is possible using a positive definite kernel function defined on fuzzy sets. As a result, we present a formulation of a real-valued kernels on fuzzy sets, particularly, we define the intersection kernel and the cross product kernel on fuzzy sets giving some examples of them using T-norm operators. Also, we analyze the nonsingleton TSK fuzzy kernel and, finally, we gave several examples of kernels on fuzzy sets, that can be easily constructed from the previous ones.

show abstract

Section: B Contributionsmentioning

confidence: 99%

Section: A Previous Work Using Positive Definite Kernels and Fuzzy Setsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Positive definite kernel functions on fuzzy sets

Guevara

Hirata

Canu

2014

2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Untuk mendefinisikan hubungan atau korelasi antar himpunan, berbeda dengan fuzzy mamdani, metode fuzzy sugeno memiliki definisi output (konsekuen) berupa konstanta (orde nol) atau persamaan linier (orde satu) sedangkan output dalam metode Mamdani berbentuk langsung himpunan fuzzy [11]. Berikut adalah bentuk persamaan metode fuzzy sugeno [12,13] …”

Section: Sistem Inferensi Fuzzy Metode Sugenounclassified

Aplikasi Sistem Peringatan Tabrakan Pada Kapal Berbasis Data GPS Menggunakan Logika Fuzzy

Sarena¹,

Adhitya²,

Handoko³

et al. 2016

Media Komunikasi Teknologi

View full text Add to dashboard Cite

Automatic Identification System (AIS) is an important equipment in ship for Keywords: GPS, Zero-Order Sugeno Fuzzy Logic, Ship Collision ABSTRAKAutomatic Identification System (AIS) pada kapal, memberikan informasi mengenai identitas dan beberapa kondisi suatu kapal kepada kapal lain maupun kepada pihak otoritas darat. Namun didalam AIS tidak tersedia suatu rekomendasi terhadap pengaturan arah dan kecepatan kapal secara otomatis. Pada penelitian ini dibuat sebuah aplikasi sistem peringatan dini otomatis untuk menghindari tabrakan berdasarkan data AIS yang disimulasikan menggunakan GPS receiver. Metode yang digunakan adalah logika fuzzy sugeno orde nol yang berfungsi untuk mengolah data posisi dan kecepatan kapal. Obyek dalam penelitian ini adalah prototype kapal dengan perangkat GPS. Respon yang dihasilkan oleh sistem peringatan ini adalah informasi berupa kecepatan dan arah haluan yang harus ditempuh agar tidak terjadi tabrakan sesuai dengan aturan yang telah ditentukan IMO (International Maritime Organization PENDAHULUANKondisi pelabuhan internasional di Indonesia yang memiliki alur pelayaran sempit dan dan lalu lintas padat seperti contohnya pelabuhan Tanjung Perak, dapat menyebabkan terjadinya tabrakan antar kapal. Rekap data Komite Nasional Keselamatan Transportasi (KNKT) pada tahun 2011-2014 [1] menyebutkan bahwa selama kurun waktu tersebut di Indonesia telah terjadi total 21 kecelakaan laut dimana 33% di antaranya adalah tubrukan antar kapal. Kecelakaan laut akibat tubrukan antar kapal ini selalu terjadi setiap tahun dengan persentase antara 25%-50% dari total kecelakaan laut per tahunnya. Salah satunya bahkan tubrukan yang terjadi antara tiga kapal sekaligus pada tahun 2014 di alur pelayaran Tanjung Perak, Surabaya [2].Allianz Safety and Shipping Review 2015 mencatat perairan Indonesia sebagai salah satu "top loss hotspots", yaitu perairan dengan tingkat kecelakaan di laut yang tinggi [3]. Salah satu upaya peningkatan keselamatan maritim melalui penggunaan teknologi navigasi dilakukan dengan diberlakukannya pemasangan AIS (Automatic Identification System) untuk beberapa tipe dan

show abstract

Fuzzy neural network with support vector-based learning for classification and regression

Khodabandelou¹,

Ebadzadeh²

2019

Soft Comput

View full text Add to dashboard Cite

Fuzzy Neural Network (FNN) and Support Vector Machine (SVM) are two prominent and powerful learning models broadly used for classification and regression. FNN has a significant local representation and human reasoning advantage. However, the drawback of such a network is that the focal point of the learning algorithms (e.g., backpropagation) is minimizing empirical risk. In contrary to FNN, SVM emphasizes simultaneously on minimizing empirical and expected risks, which theoretically leads to an excellent generalization performance power. Nevertheless, this depends on determining an adequate kernel function which is consistent with the data properties. Some approaches have been proposed to take advantage of one to deal with disadvantage of the other by combining SVM kernel and FFN. In this paper, we show that a Takagi-Sugeno-Kang (TSK)-type-based fuzzy neural network is, in fact, equivalent to an SVM with an adaptive kernel based on fuzzy rules generated in this FNN. Consequently, it is possible to learn the last layer of the FNN using the concepts of SVM and thus taking the advantage of SVM in generalization. In fact, on the one side, the proposed method is an SVM with an adaptive kernel based on fuzzy rules and on the other side, it is a TSK-FNN with SVM-based learning. Therefore, the FNN with SVM-based learning has the benefit of SVM which is minimizing both learning and testing errors. Besides, such FNN does not have the disadvantages of the SVM which is finding an appropriate kernel and training the kernel parameters. As a matter of fact, the defined kernel in FNN is an adaptive kernel based on data characteristics, which is derived from the fuzzy rules generated by the FNN itself. As a result, it is expected that the results of the proposed method for classification and regression outperform the results of SVM with the conventional kernels and fuzzy neural network trained in the conventional way. This claim is confirmed with the results obtained in this paper.

show abstract

Kernel functions in Takagi-Sugeno-Kang fuzzy system with nonsingleton fuzzy input

Cited by 13 publications

References 38 publications

Positive definite kernel functions on fuzzy sets

Positive definite kernel functions on fuzzy sets

Aplikasi Sistem Peringatan Tabrakan Pada Kapal Berbasis Data GPS Menggunakan Logika Fuzzy

Fuzzy neural network with support vector-based learning for classification and regression

Contact Info

Product

Resources

About