A Fuzzy Directional Distance Measure
Josie C. McCullochy, Chris J. Hinde, Christian Wagner, Uwe Aickelin

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.
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Taxonomy
TopicsMulti-Criteria Decision Making · Fuzzy Systems and Optimization · Fuzzy and Soft Set Theory
