Ordered Directionally Monotone Functions: Justification and Application

Bustince, Humberto; Barrenechea, Edurne; Sesma‐Sara, Mikel; Lafuente, Julio; Dimuro, Graçaliz Pereira; Mesiar, Radko; Kolesárová, Anna

doi:10.1109/tfuzz.2017.2769486

Cited by 49 publications

(32 citation statements)

References 39 publications

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“…Note that Theorem 3.1 generalizes Theorem 2.3 from [13]. Moreover, the inequality (5) has been investigated for some functions in [13]. Now, we mention two examples where the inequality (6) becomes equality.…”

Section: General Chebyshev Type Inequalitiesmentioning

confidence: 93%

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General form of Chebyshev type inequality for generalized Sugeno integral

Boczek

Hovana

Hutník

2019

International Journal of Approximate Reasoning

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We prove a general form of Chebyshev type inequality for generalized upper Sugeno integral in the form of necessary and sufficient condition. A key role in our considerations is played by the class of m-positively dependent functions which includes comonotone functions as a proper subclass. As a consequence, we state an equivalent condition for Chebyshev type inequality to be true for all comonotone functions and any monotone measure. Our results generalize many others obtained in the framework of q-integral, seminormed fuzzy integral and Sugeno integral on the real half-line. Some further consequences of these results are obtained, among others Chebyshev type inequality for any functions. We also point out some flaws in existing results and provide their improvements. * Mathematics Subject Classification (2010): Primary 28A25, 28E10, Secondary 91B06, 60E05

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Section: General Chebyshev Type Inequalitiesmentioning

confidence: 93%

“…A binary operation • : [0,ȳ] 2 → [0,ȳ] is called a fusion function. Pre-aggregation functions and aggregation functions are the most important examples of fusion functions (see [5]). We say that a function • : .…”

Section: Preliminariesmentioning

confidence: 99%

General form of Chebyshev type inequality for generalized Sugeno integral

Boczek

Hovana

Hutník

2019

International Journal of Approximate Reasoning

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“…FFT was used in this study to reduce the complexity of discrete Fourier transform computation and to rapidly transform the EEG signals into different frequency components. FFT analysis transformed the time-series EEG signals in each channel into the frequency range from 1 to 30 Hz, covering the delta (1-3 Hz), theta (4-7 Hz), alpha (8)(9)(10)(11)(12)(13), and beta (14-30 Hz) bands using a 50-point moving window segment overlapping 25 data points.…”

Section: ) Fftmentioning

confidence: 99%

“…Both make use of a fuzzy measure to consider the relevance of possible coalitions (i.e., the possible links existing between data). This feature of fuzzy integrals makes them highly appropriate for applications in which fusion of data while considering their possible interactions is a relevant step, such as in cases of image processing [11], [12]; classification [13]- [15]; or decision making [16]. Some of the most widely used averaging functions, such as weighted means or the ordered weighted averaging (OWA) operators, are specific cases of fuzzy integrals (see [8]).…”

Section: Introductionmentioning

confidence: 99%

Multimodal Fuzzy Fusion for Enhancing the Motor-Imagery-Based Brain Computer Interface

Bustince

et al. 2019

IEEE Comput. Intell. Mag.

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Brain-computer interface technologies, such as steady-state visually evoked potential, P300, and motor imagery are methods of communication between the human brain and the external devices. Motor imagery-based brain-computer interfaces are popular because they avoid unnecessary external stimulus.Although feature extraction methods have been illustrated in several machine intelligent systems in motor imagery-based brain-computer interface studies, the performance remains unsatisfactory. There is increasing interest in the use of the fuzzy integrals, the Choquet and Sugeno integrals, that are appropriate for use in applications in which fusion of data must consider possible data interactions. To enhance the classification accuracy of brain-computer interfaces, we adopted fuzzy integrals, after employing the classification method of traditional brain-computer interfaces, to consider possible links between the data. Subsequently, we proposed a novel classification framework called the multimodal fuzzy fusion-based brain-computer interface system. Ten volunteers performed a motor imagery-based brain-computer interface experiment, and we acquired electroencephalography signals simultaneously.

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“…Recently, influenced by the concept of OWA operator [20], the concept of ordered directional (OD) monotonicity has been introduced [4]. The direction of increasingness or decreasingness for ordered directionally monotone function varies depending on the point of the domain that is being considered.…”

Section: Introductionmentioning

confidence: 99%

Strengthened Ordered Directional and Other Generalizations of Monotonicity for Aggregation Functions

Sesma‐Sara

Miguel

Lafuente

et al. 2018

Communications in Computer and Information Science

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A tendency in the theory of aggregation functions is the generalization of the monotonicity condition. In this work, we examine the latest developments in terms of different generalizations. In particular, we discuss strengthened ordered directional monotonicity, its relation to other types of monotonicity, such as directional and ordered directional monotonicity and the main properties of the class of functions that are strengthened ordered directionally monotone. We also study some construction methods for such functions and provide a characterization of usual monotonicity in terms of these notions of monotonicity.

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Ordered Directionally Monotone Functions: Justification and Application

Cited by 49 publications

References 39 publications

General form of Chebyshev type inequality for generalized Sugeno integral

General form of Chebyshev type inequality for generalized Sugeno integral

Multimodal Fuzzy Fusion for Enhancing the Motor-Imagery-Based Brain Computer Interface

Strengthened Ordered Directional and Other Generalizations of Monotonicity for Aggregation Functions

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