Neutrosophic Bitopological Games: Strategies, Cross-Covering Properties, and Selection Principles

We introduce a framework for topological games on neutrosophic bitopological spaces. The underlying structure consists of a set equipped with two neutrosophic topologies, allowing the two players to interact with distinct notions of openness. After fixing explicit conventions for neutrosophic unions, intersections, interiors, and threshold covering, we define one-selection and finite-selection games, cross-interior covering conditions, strategies, and winning plays. We establish general implications between winning strategies and selection principles, prove a threshold monotonicity result, and investigate the behavior of the games under equality of the two topologies. Examples illustrate the difference between the two topologies and the role of the cross-interior condition. We also prove that the proposed framework reduces to the corresponding classical bitopological game in the crisp-valued case. The definitions and results are formulated so that their hypotheses and conclusions can be checked directly. The paper distinguishes the classical background of bitopological spaces and selection games from the particular neutrosophic game framework developed here.