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Rough set theory, presented by Pawlak in 1981, is one of the most well-known methods for communicating ambiguity by estimating an item based on some knowledge rather than membership. The concept of a rough function and its convexity and differentiability in regard to its boundary region are discussed in this work. The boundary notion is also used to present a new form of rough programming issue and its solutions. Finally, numerical examples are provided to demonstrate the proposed method and emphasize its advantages over other approaches.

A Novel Approach for Characterizing Solutions of Rough Optimization Problems Based on Boundary Region