Arithmetic of fuzzy numbers and intervals -- a new perspective with examples

TL;DR

This paper introduces a novel approach to arithmetic with fuzzy intervals using generalized inversion formulas, offering a practical and accessible method for handling complex fuzzy data.

Contribution

It presents a new method based on generalized inversion formulas for arithmetic on fuzzy intervals, applicable to discontinuous and non-monotonic functions, with illustrative examples.

Findings

New inversion-based arithmetic technique for fuzzy intervals

Applicable to discontinuous and piecewise constant functions

Accessible, textbook-style presentation with examples

Abstract

This article is meant to give a lucid and widely accessible, self-contained account of a novel way of performing arithmetic operations on fuzzy intervals. Based on two formulae of generalized inversion (the first in close analogy to the inversion of cumulative distribution functions in probability and statistics, and subsequent re-inversion which in this form seems to be new in the literature) the technique could prove to be of some importance for the practical handling of fuzzy intervals whose characterizing functions are discontinuous and/or not strictly monotonic, e.g. piecewise constant. Notwithstanding its innovative nature, the article is written in the style of an introductory textbook featuring a multitude of illustrated examples.