A Fuzzy Directional Distance Measure

TL;DR

This paper introduces a novel fuzzy directional distance measure that captures the uncertainty and direction of change between fuzzy sets, improving the representation of distances in fuzzy set theory.

Contribution

It develops a fuzzy distance measure that incorporates directionality and proposes a multiplicative approximation for computational feasibility.

Findings

Fuzzy directional distance measure effectively captures change direction.

A multiplicative version offers a computationally feasible approximation.

Enhances fuzzy set distance analysis with uncertainty and directionality.

Abstract

The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory, however, distance measures currently within the literature use a crisp value to represent the distance between fuzzy sets. A real valued distance measure is developed into a fuzzy distance measure which better reflects the uncertainty inherent in fuzzy sets and a fuzzy directional distance measure is presented, which accounts for the direction of change between fuzzy sets. A multiplicative version is explored as a full maximal assignment is computationally intractable so an intermediate solution is offered.