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

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 A Method to Find the Membership Functions of Maximum and Minimum of Fuzzy Numbers

1970 ◽  
Vol 30 ◽  
pp. 89-99
Author(s):  
Shapla Shirin
Keyword(s):  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Membership Functions ◽  
New Approach ◽  
The Core ◽  
Decreasing Functions

In this paper, a new approach for computation of membership functions of the maximum and minimum of more than two upper semi-continuous fuzzy numbers has been introduced. This method is also applicable for piece-wise continuous fuzzy numbers or the fuzzy numbers which are only continuous from right or only continuous from left. The core of fuzzy numbers should have a singleton set. Keywords: Continuous fuzzy number; piece-wise continuous fuzzy number; Maximum (MAX) and Minimum (MIN) of fuzzy number; core; α-cut; bounded increasing and bounded decreasing functions; membership function. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 89-99  DOI: http://dx.doi.org/10.3329/ganit.v30i0.8506

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.

Intuitionistic Fuzzy Measures of Correlation Coefficient of Intuitionistic Fuzzy Numbers Under Weakest Triangular Norm

2019 ◽  
Vol 8 (1) ◽  
pp. 48-64 ◽  
Author(s):  
Mohit Kumar
Keyword(s):  
Correlation Coefficient ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Fuzzy Arithmetic ◽  
Triangular Norm ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Technology Level

The correlation coefficient of variables has wide applications in statistics and is often calculated in crisp or fuzzy environment. This article extends the application of correlation coefficient to intuitionistic fuzzy environment. In this article, a new method is proposed to measure the correlation coefficient of intuitionistic fuzzy numbers using weakest triangular norm based intuitionistic fuzzy arithmetic operations. Different from previous studies, the correlation coefficient computed in this article is an intuitionistic fuzzy number rather than a crisp or fuzzy number. It is well known that the weakest t-norm arithmetic operations effectively reduce fuzzy spreads (fuzzy intervals) and provide more exact results. Therefore, a simplified, effective and exact method based on weakest t-norm arithmetic operations is presented to compute the correlation coefficient of intuitionistic fuzzy numbers. To illustrate the proposed method, the correlation coefficient between the technology level and management achievement from a sample of 15 machinery firms in Taiwan is calculated using proposed approach.

A METHOD FOR FINDING CRITICAL PATH WITH SYMMETRIC OCTAGONAL INTUITIONISTIC FUZZY NUMBERS

2020 ◽  
Vol 9 (11) ◽  
pp. 9273-9286
Author(s):  
N. Rameshan ◽  
D.S. Dinagar
Keyword(s):  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Membership Functions ◽  
Intuitionistic Fuzzy Number ◽  
Lower And Upper Bounds ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Membership Function

The concept of this paper represents finding fuzzy critical path using octagonal fuzzy number. In project scheduling, a new method has been approached to identify the critical path by using Symmetric Octagonal Intuitionistic Fuzzy Number (SYMOCINTFN). For getting a better solution, we use the fuzzy octagonal number rather than other fuzzy numbers. The membership functions of the earliest and latest times of events are by calculating lower and upper bounds of the earliest and latest times considering octagonal fuzzy duration. The resulting conditions omit the negative and infeasible solution. The membership function takes up an essential role in finding a new solution. Based on membership function, fuzzy number can be identified in different categories such as Triangular, Trapezoidal, pentagonal, hexagonal, octagonal, decagonal, hexa decagonal fuzzy numbers etc.

Methods for evaluating the computer network security with fuzzy number intuitionistic fuzzy dual Hamy mean operators

2020 ◽  
Vol 39 (3) ◽  
pp. 4427-4441
Author(s):  
Bin Xu
Keyword(s):  
Network Security ◽  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Computer Network ◽  
Information Aggregation ◽  
Security Evaluation ◽  
Uncertain Information ◽  
Intuitionistic Fuzzy ◽  
Computer Network Security

The concept of fuzzy number intuitionistic fuzzy sets (FNIFSs) is designed to effectively depict uncertain information in decision making problems which fundamental characteristic of the FNIFS is that the values of its membership function and non-membership function are depicted with triangular fuzzy numbers (TFNs). The dual Hamy mean (DHM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this paper, we used the dual Hamy mean (DHM) operator and dual weighted Hamy mean (WDHM) operator with fuzzy number intuitionistic fuzzy numbers (FNIFNs) to propose the fuzzy number intuitionistic fuzzy dual Hamy mean (FNIFDHM) operator and fuzzy number intuitionistic fuzzy weighted dual Hamy mean (FNIFWDHM) operator. Then the MADM methods are proposed along with these operators. In the end, we utilize an applicable example for computer network security evaluation to prove the proposed methods.

scholarly journals Evaluating the Efficiency of School Preceptors by Fuzzy Risk Analysis

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Rasoul Saneifard ◽  
Rahim Saneifard
Keyword(s):  
Risk Analysis ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
New Method ◽  
Arithmetic Operations ◽  
Fuzzy Risk Analysis ◽  
Fuzzy Weights

This paper presents a new method for evaluating the efficiency of school preceptors based on fuzzy number arithmetic operations. It uses fuzzy numbers to represent fuzzy grades. The fuzzy weights of criteria are automatically generated from the opinions of evaluators. The simplified fuzzy number arithmetic operations are used for calculating the average of fuzzy numbers. It can evaluate the efficiency of school preceptors in a more flexible and more intelligent manner.

scholarly journals The differences between the horizontal membership function used in multidimensional fuzzy arithmetic and the inverse membership function used in gradual arithmetic

2021 ◽  
Author(s):  
Andrzej Piegat ◽  
Marcin Pluciński
Keyword(s):  
Differential Equations ◽  
Membership Function ◽  
Interval Arithmetic ◽  
Fuzzy Arithmetic ◽  
Scientific Journals ◽  
Scientific Papers ◽  
Fuzzy Equations

AbstractIn the last few years, the number of applications of the multidimensional fuzzy arithmetic (MFA) and the multidimensional interval arithmetic is expanding. Authors of new papers about applications of MFA are often faced with comments from other researchers, especially the gradual arithmetic (GA) proponents, that the horizontal membership function (HMF) used in MFA is the same as the inverse membership function (InvMF) used in GA, and that MFA itself adds nothing new to the fuzzy arithmetic. This view leads to unfair evaluations of scientific papers about MFA applications submitted to scientific journals and to unnecessary disagreements between MFA and GA proponents. The purpose of this paper is to carefully analyze the two types of functions (HMF and InvMF) and to demonstrate their important differences. The basic and decisive difference is the dimensionality of both functions, which is illustrated by examples. It should also be added that HMF has proven its usefulness in solving difficult problems such as: systems of fuzzy equations or fuzzy differential equations, which is confirmed by numerous publications. The paper enable the reader to have a deeper understanding of the multidimensional fuzzy arithmetic.

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