Weighted average of fuzzy numbers under TW(the weakest t-norm)-based fuzzy arithmetic operations

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.

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

International Journal of Fuzzy System Applications ◽

10.4018/ijfsa.2019010103 ◽

2019 ◽

Vol 8 (1) ◽

pp. 48-64 ◽

Cited By ~ 2

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.

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

Data ◽

10.3390/data3040059 ◽

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.

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A computational method for fuzzy arithmetic operations

Daffodil International University Journal of Science and Technology ◽

10.3329/diujst.v4i1.4350 ◽

1970 ◽

Vol 4 (1) ◽

pp. 18-22 ◽

Cited By ~ 7

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

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Applying weakest t-norm based approximate intuitionistic fuzzy arithmetic operations on different types of intuitionistic fuzzy numbers to evaluate reliability of PCBA fault

Applied Soft Computing ◽

10.1016/j.asoc.2014.06.036 ◽

2014 ◽

Vol 23 ◽

pp. 387-406 ◽

Cited By ~ 25

Author(s):

Mohit Kumar

Keyword(s):

Fuzzy Numbers ◽

Fuzzy Arithmetic ◽

Arithmetic Operations ◽

Intuitionistic Fuzzy Numbers ◽

Intuitionistic Fuzzy ◽

Different Types

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Fuzzy arithmetic in economic research

SHS Web of Conferences ◽

10.1051/shsconf/202110705003 ◽

2021 ◽

Vol 107 ◽

pp. 05003

Author(s):

Kateryna Gorbatiuk ◽

Tetiana Zavhorodnia ◽

Oksana Proskurovych ◽

Olha Mantalyuk

Keyword(s):

Decision Support ◽

Numerical Methods ◽

Decision Support Systems ◽

Fuzzy Numbers ◽

Support Systems ◽

Economic Indicators ◽

Economic Research ◽

Fuzzy Arithmetic ◽

Arithmetic Operations ◽

Calculation Algorithm

Many tasks in economic research are based on arithmetic calculations of indicators that reflect the state of economic development. The general incompleteness of publicly available data, designed to solve such problems, has led to the emergence of numerous decision support systems based on fuzzy arithmetic. The article presents a study on the approach aimed at integrating fuzzy information about economic indicators into economic models. The definition of arithmetic operations on fuzzy values is given, and the methods of obtaining the resulting fuzzy indicators with the help of some software tools are considered. Analytical and numerical methods of obtaining the resulting indicators in the form of fuzzy numbers are described and analyzed. A direct calculation algorithm for all arithmetic operations is proposed, utilized, and used for the evaluation of resulting indicators. Also, analytical and numerical methods for obtaining fuzzy results are considered in the article, and some of them are proposed for utilization. On the example of economic indicators used in the labor rationing, the results of an evaluation of some indicators for a technological operation in the form of fuzzy numbers were obtained by different methods and compared. The practical recommendations, given in the article, on the use of fuzzy arithmetic in decision support systems outline the directions of further research.

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