scholarly journals Real-Time Fuzzy Data Processing Based on a Computational Library of Analytic Models

Data ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 59
Author(s):  
Yuriy Kondratenko ◽  
Nina Kondratenko
Keyword(s):  
Data Processing ◽  
Fuzzy Sets ◽  
Real Time ◽  
Fuzzy Numbers ◽  
Fuzzy Arithmetic ◽  
Fuzzy Data ◽  
Triangular Fuzzy Numbers ◽  
Arithmetic Operations ◽  
Automatic Mode ◽  
Analytic Models

This work focuses on fuzzy data processing in control and decision-making systems based on the transformation of real-timeseries and high-frequency data to fuzzy sets with further implementation of diverse fuzzy arithmetic operations. Special attention was paid to the synthesis of the computational library of horizontal and vertical analytic models for fuzzy sets as the results of fuzzy arithmetic operations. The usage of the developed computational library allows increasing the operating speed and accuracy of fuzzy data processing in real time. A computational library was formed for computing of such fuzzy arithmetic operations as fuzzy-maximum. Fuzzy sets as components of fuzzy data processing were chosen as triangular fuzzy numbers. The analytic models were developed based on the analysis of the intersection points between left and right branches of considered triangular fuzzy numbers with different relations between their parameters. Our study introduces the mask for the evaluation of the relations between corresponding parameters of fuzzy numbers that allows to determine the appropriate model from the computational library in automatic mode. The simulation results confirm the efficiency of the proposed computational library for different applications.

scholarly journals A study on multiplication operation on triangular fuzzy numbers

2021 ◽  
Vol 5 (2) ◽  
pp. 55-62
Author(s):  
Mohamed Ali A ◽  
Maanvizhi P
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Fuzzy Arithmetic ◽  
Triangular Fuzzy Numbers ◽  
Arithmetic Operations ◽  
Multiplication Operation ◽  
Cut Method ◽  
Standard Approximation ◽  
Basic Content

The arithmetic operations on fuzzy number are basic content in fuzzy mathematics. But still the operations of fuzzy arithmetic operations are not established. There are some arithmetic operations for computing fuzzy number. Certain are analytical methods and further are approximation methods. In this paper we, compare the multiplication operation on triangular fuzzy number between α-cut method and standard approximation method and give some examples.

scholarly journals Genetic Algorithm for Fuzzy Neural Networks using Locally Crossover

2011 ◽  
Vol 6 (1) ◽  
pp. 8 ◽  
Author(s):  
Dragos Arotaritei
Keyword(s):  
Neural Networks ◽  
Fuzzy Numbers ◽  
Signal Propagation ◽  
Fuzzy Neural Networks ◽  
Fuzzy Arithmetic ◽  
Recurrent Networks ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Neural ◽  
Sinusoidal Oscillations ◽  
Real World Problems

Fuzzy feed-forward (FFNR) and fuzzy recurrent networks (FRNN) proved to be solutions for "real world problems". In the most cases, the learning algorithms are based on gradient techniques adapted for fuzzy logic with heuristic rules in the case of fuzzy numbers. In this paper we propose a learning mechanism based on genetic algorithms (GA) with locally crossover that can be applied to various topologies of fuzzy neural networks with fuzzy numbers. The mechanism is applied to FFNR and FRNN with L-R fuzzy numbers as inputs, outputs and weights and fuzzy arithmetic as forward signal propagation. The α-cuts and fuzzy biases are also taken into account. The effectiveness of the proposed method is proven in two applications: the mapping a vector of triangular fuzzy numbers into another vector of triangular fuzzy numbers for FFNR and the dynamic capture of fuzzy sinusoidal oscillations for FRNN.

scholarly journals Convexity Invariance of Fuzzy Sets under the Extension Principles

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Dong Qiu ◽  
Weiquan Zhang
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Arithmetic Operations ◽  
Extension Principles ◽  
Necessary And Sufficient

We discuss the convexity invariance of fuzzy sets under the extension principles. Particularly, we give a necessary and sufficient condition for a mapping to be an inverse *-convex transformation, and also obtain some sufficient conditions for a mapping to be an *-convex transformation. Two applications are given to illustrate the obtained results. Finally, we give some applications of the main results to the hyperstructure convexity invariance of type 2 fuzzy sets under hyperalgebra operations, and to the convexity invariance of fuzzy numbers under basic arithmetic operations.

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