Properties of f correlated fuzzy numbers

TL;DR

This paper introduces the concept of f-correlated fuzzy numbers within interactive fuzzy number theory, demonstrating that f-correlation preserves the shape of LR-type fuzzy numbers and exploring operations relevant to applications like biomathematics.

Contribution

It defines f-correlated fuzzy numbers, shows shape preservation under f-correlation for LR-type fuzzy numbers, and discusses new operations with potential applications.

Findings

f-correlation preserves the shape of LR-type fuzzy numbers

Operations with f-correlated fuzzy numbers are suitable for biomathematics

Main result extends the theory of interactive fuzzy numbers

Abstract

This paper presents some concepts of the theory of interactive fuzzy numbers, and mainly, a class of interactive fuzzy numbers, called $f$-correlated fuzzy numbers. We start from the foundations of general fuzzy mathematics and go through operations and the notion of interactivity for fuzzy numbers. The main result is that $f$-correlation preserve the shape of certains fuzzy numbers. More specificaly, if two fuzzy numbers are $f$ correlated, and one is a LR-type fuzzy number, the other is also a LR-type fuzzy number. This paper also presents some operations with the $f$-correlated fuzzy numbers wich are interesting to applications like biomathematics.