A comparison of arithmetical operations with $f$ correlated fuzzy numbers

TL;DR

This paper introduces $f$-correlated fuzzy numbers, providing formulas for their arithmetic operations and analyzing their properties, which simplifies calculations involving dependent fuzzy quantities.

Contribution

It defines $f$-correlated fuzzy numbers and derives direct calculation formulas for their sums and products, advancing fuzzy arithmetic methods.

Findings

Correlated and standard sums of $f$-correlated fuzzy numbers coincide.

The correlated product is contained within the standard product.

Formulas use only basic real operations and the defining function.

Abstract

We present a brief introduction to a class of interactive fuzzy numbers, called $f$-correlated fuzzy numbers, which consist of pairs of fuzzy numbers where one is dependent on the other by a continuous monotone injective function. We have deduced some equations that can directly calculate the results of the sums and products of $f$-correlated fuzzy numbers, using only basic operations with real numbers, intervals on the real line and the function that relates the fuzzy numbers being considered. We proved that their correlated and standard sum coincide, and that in a certain sense, the correlated product is contained in the standard product.