Abstract
Usually, the statistical estimators (or mathematical functions) are the base of scientific decision making. In applied situations, at least one of the parameters or variables of the decision function may be fuzzy valued, instead of real valued. In such vague situations, one way to perform the calculations is using extension principle approach which has a complex form. Recently, two software packages have been freely available to perform some facilities in calculation and computation based on fuzzy numbers. In other words, these two software packages have the role of the first calculator on fuzzy numbers. This paper discussed and compared two software packages “FuzzyNumbers” and “Calculator.LR.FNs” which were recently published on CRAN by Gagolewski and Parchami, respectively. These packages have the ability of installation on R software, and in fact they propose some useful instruments and functions to the users for drawing and easily using arithmetic operators on the set of fuzzy numbers. For the convenience of the readers, the proposed methods and functions have been presented with several numerical examples to help in better understanding.
Highlights
R is an open source programming language and software environment for statistical computing and graphics that is supported by the R foundation for statistical computing
A core set of packages is included with the installation of R, with more than 10,162 additional packages available at the Comprehensive R Archive Network (CRAN)
The “Task Views” page on the CRAN website lists a wide range of tasks to which R has been applied and for which packages are available [18]
Summary
Classical arithmetic operations can be extended by the extension principle approach, the complexity of this principle causes some computational challenges/difficulties. It must be mentioned that this is one of the simplest versions of the problem to show the computational challenges, since here it is assumed that: (1) the shape functions of all L R fuzzy numbers are the same, (2) the triangular fuzzy data is considered, and (3) the sample size is small. As a matter of fact, the shape functions of these squares are not same and their summation is not computable To avoid this difficulty, we discuss three possible approaches/strategies ass follows: 1. This numerical example can be developed for computing the membership function of fuzzy standard deviation, and computing the membership function of fuzzy covariance between two vectors of fuzzy numbers. Some basic functions of package “FuzzyNumbers” has been presented and reviewed from [9] with several numerical examples
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