Measures of Linear and Nonlinear Interval-Valued Hexagonal Fuzzy Number

2020 ◽  
Vol 9 (4) ◽  
pp. 21-60
Author(s):  
Najeeb Alam Khan ◽  
Oyoon Abdul Razzaq ◽  
Avishek Chakraborty ◽  
Sankar Parsad Mondal ◽  
Shariful Alam
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Simulated Annealing ◽  
Level Sets ◽  
Fuzzy Numbers ◽  
Membership Functions ◽  
Ecological Functions ◽  
Linear And Nonlinear ◽  
Growth Problem ◽  
Interval Valued

In the view of significant exposure of multifarious interval-valued fuzzy numbers in neoteric studies, different measures of interval-valued generalized hexagonal fuzzy numbers (IVGHFN) associated with assorted membership functions (MF) are explored in this article. Considering the symmetricity and asymmetricity of the hexagonal fuzzy structures, the idea of MF is generalized a bit more, to nonlinear membership functions. The construction of level sets, accordingly for each case of linear and nonlinear MF are also carried out. In addition, the concepts of generalized Hukuhara (gH) differentiability for the interval-valued generalized hexagonal fuzzy functions (IVGHFF) are also the main features of this framework. Illustratively, the developed intellects are implemented on a logistic population growth problem, by taking ecological functions as IVGHFFs. For the further numerical demonstrations of the model, artificial neural network with simulated annealing (ANNSA) algorithm is utilized.

scholarly journals The Pentagonal Fuzzy Number:Its Different Representations, Properties, Ranking, Defuzzification and Application in Game Problems

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 248 ◽  
Author(s):  
Avishek Chakraborty ◽  
Sankar Prasad Mondal ◽  
Shariful Alam ◽  
Ali Ahmadian ◽  
Norazak Senu ◽  
...  
Keyword(s):  
Real World ◽  
Level Sets ◽  
Fuzzy Numbers ◽  
Evaluation Process ◽  
Game Problem ◽  
Ranking Method ◽  
Membership Functions ◽  
Linear And Nonlinear ◽  
Interval Valued ◽  
Real World Problems

In this paper, different measures of interval-valued pentagonal fuzzy numbers (IVPFN) associated with assorted membership functions (MF) were explored, considering significant exposure of multifarious interval-valued fuzzy numbers in neoteric studies.Also, the idea of MF is generalized somewhat to nonlinear membership functions for viewing the symmetries and asymmetries of the pentagonal fuzzy structures. Accordingly,the construction of level sets, for each case of linear and nonlinear MF was also carried out. Besides, defuzzification was undertaken using three methods and a ranking method, which were also the main features of this framework.The developed intellects were implemented in a game problem by taking the parameters as PFNs, ultimately resulting in a new direction for modeling real world problems and to comprehend the uncertainty of the parameters more precisely in the evaluation process.

scholarly journals A Convex Combination Approach for Artificial Neural Network of Interval Data

2021 ◽  
Vol 11 (9) ◽  
pp. 3997
Author(s):  
Woraphon Yamaka ◽  
Rungrapee Phadkantha ◽  
Paravee Maneejuk
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Convex Combination ◽  
Reference Points ◽  
Combination Method ◽  
Suitable Alternative ◽  
Input And Output ◽  
Artificial Neural ◽  
Conventional Models ◽  
Interval Valued

As the conventional models for time series forecasting often use single-valued data (e.g., closing daily price data or the end of the day data), a large amount of information during the day is neglected. Traditionally, the fixed reference points from intervals, such as midpoints, ranges, and lower and upper bounds, are generally considered to build the models. However, as different datasets provide different information in intervals and may exhibit nonlinear behavior, conventional models cannot be effectively implemented and may not be guaranteed to provide accurate results. To address these problems, we propose the artificial neural network with convex combination (ANN-CC) model for interval-valued data. The convex combination method provides a flexible way to explore the best reference points from both input and output variables. These reference points were then used to build the nonlinear ANN model. Both simulation and real application studies are conducted to evaluate the accuracy of the proposed forecasting ANN-CC model. Our model was also compared with traditional linear regression forecasting (information-theoretic method, parametrized approach center and range) and conventional ANN models for interval-valued data prediction (regularized ANN-LU and ANN-Center). The simulation results show that the proposed ANN-CC model is a suitable alternative to interval-valued data forecasting because it provides the lowest forecasting error in both linear and nonlinear relationships between the input and output data. Furthermore, empirical results on two datasets also confirmed that the proposed ANN-CC model outperformed the conventional models.

scholarly journals Interval-valued data prediction via regularized artificial neural network

2019 ◽  
Vol 331 ◽  
pp. 336-345 ◽  
Author(s):  
Zebin Yang ◽  
Dennis K.J. Lin ◽  
Aijun Zhang
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Data Prediction ◽  
Artificial Neural ◽  
Interval Valued

scholarly journals Modeling Nonlinear Transfer Functions from Speech Envelopes to Encephalography with Neural Networks

2019 ◽  
Vol 11 (4) ◽  
pp. 1 ◽  
Author(s):  
Tobias de Taillez ◽  
Florian Denk ◽  
Bojana Mirkovic ◽  
Birger Kollmeier ◽  
Bernd T. Meyer
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Artificial Neural Network ◽  
Linear Models ◽  
Transfer Functions ◽  
Event Related Potentials ◽  
Stimulus Presentation ◽  
Related Potentials ◽  
Linear And Nonlinear ◽  
Artificial Neural

Diferent linear models have been proposed to establish a link between an auditory stimulus and the neurophysiological response obtained through electroencephalography (EEG). We investigate if non-linear mappings can be modeled with deep neural networks trained on continuous speech envelopes and EEG data obtained in an auditory attention two-speaker scenario. An artificial neural network was trained to predict the EEG response related to the attended and unattended speech envelopes. After training, the properties of the DNN-based model are analyzed by measuring the transfer function between input envelopes and predicted EEG signals by using click-like stimuli and frequency sweeps as input patterns. Using sweep responses allows to separate the linear and nonlinear response components also with respect to attention. The responses from the model trained on normal speech resemble event-related potentials despite the fact that the DNN was not trained to reproduce such patterns. These responses are modulated by attention, since we obtain significantly lower amplitudes at latencies of 110 ms, 170 ms and 300 ms after stimulus presentation for unattended processing in contrast to the attended. The comparison of linear and nonlinear components indicates that the largest contribution arises from linear processing (75%), while the remaining 25% are attributed to nonlinear processes in the model. Further, a spectral analysis showed a stronger 5 Hz component in modeled EEG for attended in contrast to unattended predictions. The results indicate that the artificial neural network produces responses consistent with recent findings and presents a new approach for quantifying the model properties.

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