Year: 2026
Type: article
Abstract: Sequential decision-making problems are frequently formulated under the assumption that feasible decision sets are precisely specified.In many practical settings, however, such sets may be incompletely characterized or subject to boundary ambiguity, making conventional dynamic programming (DP) formulations difficult to apply directly.In this paper, a rough dynamic programming (RDP) framework is developed for multi-stage optimization problems in which feasible decision sets are represented by their lower and upper approximations.Within this framework, the lower approximation is used to represent decisions that can be regarded as certainly feasible, whereas the upper approximation encompasses decisions that may be feasible under the available information.An RDP algorithm is formulated by embedding these rough-set representations within the recursive structure of DP, thereby allowing a deterministic objective function to be optimized while the imprecision of the feasible region is explicitly retained.The sequential dependence of decisions across stages is preserved through stage-wise state transitions and recursive valuefunction evaluation.Three representative rough dynamic programming problems (RDPPs) are formulated and solved to demonstrate the implementation of our proposed framework and to examine its behavior under different forms of imprecise feasibility.The resulting solutions illustrate how lower and upper feasible approximations can be incorporated into multi-stage optimization without requiring the uncertain feasible region to be reduced to a single precisely defined set.This framework provides a systematic basis for extending DP to sequential optimization problems in which feasibility information is incomplete, imprecise or boundary-ambiguous.Furthermore, it establishes a foundation for further investigation of solution properties, computational efficiency, and decision robustness in rough optimization.
DOI: 10.18280/isi.310701
Institutions: Cairo University, Higher Technological Institute, Tanta University
Language: English
Topic: Rough Sets and Fuzzy Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7204492602