A Fuzzy Directional Distance Measure
This addresses a fundamental limitation in fuzzy set theory for researchers and practitioners, though it appears incremental as it builds on existing real-valued distance measures.
The paper tackles the problem that existing distance measures between fuzzy sets use crisp values, which doesn't reflect their inherent uncertainty, by developing a fuzzy distance measure and a fuzzy directional distance measure that accounts for direction of change, with a multiplicative version offered as a computationally tractable intermediate solution.
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.