ISSN 2071-8594

Editor-in-Chief

## A.V. Radaev, A.V. Korobov, B.I. Yatsalo F-Calc: Computer System for Calculating Functions of Fuzzy Arguments

### Abstract.

Calculating functions of fuzzy arguments plays an important role in a large number of applications of fuzzy sets theory. Within Fuzzy Multi-criteria Decision Analysis (Fuzzy MCDA), the problem of calculating functions of fuzzy numbers is a key one. The Zadeh’s extension principle can be used for assessing functions of fuzzy arguments, however, it is ineffective even in case of the simplest arithmetic operations. In most applications, instead of direct use of the extension principle, approaches for approximate assessing functions with triangular or trapezoid fuzzy numbers are implemented. This paper presents the F-Calc (Fuzzy Calculator) system, which allows calculating functions of fuzzy arguments with the use of several methods. It can implement approximate calculations (for example, the result of the product of two fuzzy triangular numbers is a triangular fuzzy number), calculations based on standard fuzzy arithmetic with a specified number of alpha-cuts, as well as calculations with the use of Reduced and General Transformation Methods. The input values can be crisp, triangular, trapezoidal, and piecewise linear fuzzy numbers with any degree of complexity, as well as fuzzy numbers with upper semi-continuous membership functions. An overview of existing systems, which implement computing functions of fuzzy numbers, is given. The structure of the F-Calc system, input and output forms are presented. Examples of computing functions of fuzzy numbers with the use of different implemented methods are given. These examples stress the features of the computational methods under consideration as well as the possibilities of F-Calc system as a whole.

### Keywords:

fuzzy set, fuzzy number, standard fuzzy arithmetic, reduced transformation method, general transformation method, fuzzy system.

PP. 78-90.

DOI 10.14357/20718594190409

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