Measuring the Directional Distance Between Fuzzy Sets

TL;DR

This paper introduces a novel distance measure for fuzzy sets that incorporates the direction of change, enhancing applications like Computing With Words by providing more informative comparisons.

Contribution

It proposes a new directional distance measure for fuzzy sets, applicable to various types, and demonstrates its usefulness with real-world data.

Findings

The new measure captures the direction of change between fuzzy sets.

Application to MovieLens data shows improved interpretability.

The measure is versatile for different fuzzy set types.

Abstract

The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory. However, current distance measures within the literature do not account for the direction of change between fuzzy sets; a useful concept in a variety of applications, such as Computing With Words. In this paper, we highlight this utility and introduce a distance measure which takes the direction between sets into account. We provide details of its application for normal and non-normal, as well as convex and non-convex fuzzy sets. We demonstrate the new distance measure using real data from the MovieLens dataset and establish the benefits of measuring the direction between fuzzy sets.