In chemical systems, molecular properties such as electronegativity are often subject to uncertainty due to environmental fluctuations, measurement errors, or intrinsic variability. Fuzzy set theory provides a framework to model such uncertainties, allowing chemical descriptors to be expressed as degrees of membership rather than fixed values. This paper develops a rigorous order-theoretic framework for studying fuzzy structures arising from property-induced partially ordered sets (posets) in molecular systems. By extending classical poset theory through fuzzy relations, we formalize graded comparability and inclusion principles that naturally occur in chemical and molecular structures. The proposed approach preserves essential order-theoretic properties while allowing flexible representation of uncertainty.

We further establish a connection between fuzzy molecular relations and abstract algebra by mapping these relations onto Baer \( * \)-semigroups, algebraic structures with zero elements and idempotent-generated annihilators. We present a structure theorem for finite Baer \( * \)-semigroups, develop an \( O(n^3) \) recognition algorithm, and prove categorical completeness and cocompleteness. Applications to functional group classification, reaction mechanism modeling, stereochemistry, pharmacophore analysis, and QSAR enhancement demonstrate the practical utility of the framework. Illustrative examples show that the fuzzy poset approach captures resonance effects and stereochemical hierarchies, providing a unified mathematical tool for chemical informatics that bridges computational chemistry and abstract algebra.