A Fuzzy Relational Framework for Modeling Uncertain Dependence in Financial Markets

Abstract

Financial markets are characterized by complex and evolving dependence structures among assets, institutions, and market sectors. In practice, these relationships are often influenced by ambiguity, incomplete information, and qualitative judgment, making precise probabilistic modeling difficult. Traditional correlation-based approaches may therefore fail to capture the full structure of market interdependence. This paper proposes a fuzzy relational framework for modeling uncertain dependence in financial markets. Financial assets are represented as elements of a fuzzy set, while their interdependencies are described using fuzzy relations with membership values in the unit interval. Fundamental structural properties of fuzzy relationsreflexivity, symmetry, and transitivityare examined under max–min and min–max composition operators. Using matrix representations, we analyze how dependence propagates through indirect asset interactions and identify conditions under which market dependence structures remain stable or become distorted.

Keywords

References