This paper introduces and studies the notion of spherical fuzzy lattice-ordered subsemigroup and their corresponding spherical fuzzy lattice-ordered ideal within the framework of lattice-ordered semigroup. By extending classical lattice-ordered subsemigroup and ideal to the spherical fuzzy environment — where uncertainty is modeled by a triplet Formula: see text satisfying the spherical constraint Formula: see text — a coherent algebraic framework capable of handling bounded indeterminacy is developed. Rigorous definitions of spherical fuzzy lattice-ordered subsemigroup and ideal are formulated, and several fundamental properties are investigated. In particular, closure properties under intersection, behavior under homomorphic images, and structural relationships between spherical fuzzy lattice-ordered subsemigroup and ideal are examined. The results enrich the theory of spherical fuzzy algebraic structures and provide a solid mathematical foundation for applications in uncertainty-aware algebraic modeling, soft computing, and logic-based information systems.
Nasreen et al. (Wed,) studied this question.