Qualitative integrals on Dragonfly algebras

TL;DR

This paper introduces qualitative integrals on Dragonfly algebras, which are designed for data analysis with missing or unknown data, and explores their properties and potential applications.

Contribution

It defines and analyzes qualitative integrals on Dragonfly algebras, a novel algebraic structure for handling incomplete data in fuzzy data analysis.

Findings

Qualitative integrals on Dragonfly algebras are monotonic.

Characterization of when integrals return known or unknown values.

Illustrative example demonstrating the concepts.

Abstract

In this paper, we investigate qualitative integrals (generalizations of Sugeno integral) acting on recently introduced Dragonfly algebras. These algebras are designed for applications in data analysis (based on fuzzy relational compositions) when some data are unknown (e.g., missing). Unknown data are represented by the additional dummy value. Definitions of operations on Dragonfly algebras follow lower estimation strategy, i.e., results of operations can be interpreted as lower estimations of results obtained when unknown values are replaced by known ones. We define qualitative integrals on Dragonfly algebras and show their monotonicity. We also prove results characterizing when these integrals return known (or unknown) values. We also present an illustrative example and hint directions of further research.