Computational method for fuzzy arithmetic operations on triangular fuzzy numbers by extension principle

2019 ◽  
Vol 106 ◽  
pp. 172-193 ◽  
Author(s):  
Nima Gerami Seresht ◽  
Aminah Robinson Fayek
Keyword(s):  
Fuzzy Numbers ◽  
Computational Method ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
Triangular Fuzzy Numbers ◽  
Arithmetic Operations

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 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 computational method for fuzzy arithmetic operations

1970 ◽  
Vol 4 (1) ◽  
pp. 18-22 ◽  
Author(s):  
Thowhida Akther ◽  
Sanwar Uddin Ahmad
Keyword(s):  
Membership Function ◽  
Interval Arithmetic ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Computational Method ◽  
Fuzzy Arithmetic ◽  
Membership Functions ◽  
Computer Implementation ◽  
Arithmetic Operations ◽  
International University

In this paper, a computer implementation to evaluate the arithmetic operations on two fuzzy numbers with linear membership functions has been developed. The fuzzy arithmetic approached by the interval arithmetic is used here. The algorithm of the developed method with a numerical example is also provided. Using this method four basic arithmetic operations between any two TFNs can be evaluated without complexity. Keywords: Fuzzy arithmetic, Fuzzy number, Membership Function, Interval arithmetic, α - cut. DOI: 10.3329/diujst.v4i1.4350 Daffodil International University Journal of Science and Technology Vol.4(1) 2009 pp.18-22

Fuzzy Reliability of an Imprecise Failure to Start of an Automobile Using Pseudo-Parabolic Fuzzy Numbers

2018 ◽  
Vol 14 (03) ◽  
pp. 323-341 ◽  
Author(s):  
F. Abbasi
Keyword(s):  
Fuzzy Systems ◽  
Fuzzy Numbers ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
Fuzzy Reliability ◽  
Fuzzy Environment ◽  
Distributed Components ◽  
Proposed Model ◽  
New Type ◽  
The Membership Function

In this paper, we propose the notion of pseudo-parabolic fuzzy numbers and the component failure probabilities are considered as a new type of fuzzy number as pseudo-parabolic to incorporate the uncertainties in the parameter, due to a more realistic estimate of them. Then, we analyze the reliability of fuzzy system (particularly, series and parallel system) with independent and non-identically distributed components, and using the new operations of TA [F. Abbasi et al., Journal of Intelligent and Fuzzy Systems 29 (2015) 851–861], due to the smaller results support, easier calculations and special properties than fuzzy arithmetic operations based on the extension principle (in the domain of the membership function) and the interval arithmetic (in the domain of the [Formula: see text]-cuts). We provide a more realistic fuzzy reliability analysis. Finally, an imprecise failure to start of an automobile is considered in fuzzy environment. The reliability of components of the proposed model is considered as pseudo-parabolic fuzzy numbers.

scholarly journals Fuzzy Number Addition with the Application of Horizontal Membership Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Andrzej Piegat ◽  
Marcin Pluciński
Keyword(s):  
Interval Arithmetic ◽  
Fuzzy Numbers ◽  
Order Relation ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
Multidimensional Approach ◽  
Membership Functions ◽  
Multidimensional Information ◽  
Rdm Arithmetic ◽  
Horizontal Membership Functions

The paper presents addition of fuzzy numbers realised with the application of the multidimensional RDM arithmetic and horizontal membership functions (MFs). Fuzzy arithmetic (FA) is a very difficult task because operations should be performed here on multidimensional information granules. Instead, a lot of FA methods useα-cuts in connection with 1-dimensional classical interval arithmetic that operates not on multidimensional granules but on 1-dimensional intervals. Such approach causes difficulties in calculations and is a reason for arithmetical paradoxes. The multidimensional approach allows for removing drawbacks and weaknesses of FA. It is possible thanks to the application of horizontal membership functions which considerably facilitate calculations because now uncertain values can be inserted directly into equations without using the extension principle. The paper shows how the addition operation can be realised on independent fuzzy numbers and on partly or fully dependent fuzzy numbers with taking into account the order relation and how to solve equations, which can be a difficult task for 1-dimensional FAs.

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.

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