I-fp Convergence in Fuzzy Paranormed Spaces and Its Application to Robust Base-Stock Policies with Triangular Fuzzy Demand

Abstract

We introduce I-fp convergence (ideal convergence in fuzzy paranormed spaces) and develop its core theory, including stability results and an equivalence to I*-fp convergence under the AP Property. Building on this foundation, we design an adaptive base-stock policy for a single-echelon inventory system in which weekly demand is expressed as triangular fuzzy numbers while holiday or promotion weeks are treated as ideal-small anomalies. The policy is updated by a simple learning rule that can be implemented in any spreadsheet, requires no optimisation software, and remains insensitive to tuning choices. Extensive simulation confirms that the method simultaneously lowers cost, reduces average inventory and raises service level relative to a crisp benchmark, all while filtering sparse demand spikes in a principled way. These findings position I-fp convergence as a lightweight yet rigorous tool for blending linguistic uncertainty with anomaly-aware decision making in supply-chain analytics.

Keywords

• adaptive base-stock policy
• approximation property
• fuzzy paranormed space
• ideal convergence
• I-fp convergence
• inventory optimisation