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Pawlak (1982) introduced an approach for uncertain administration called, RST. This method presented a great sign in the areas of image processing, machine learning, data mining, artificial intelligence, medical applications and multiple other fields (Nasiri, 2009; Rizk-Allah, 2018; Hassanien, 2018; Pramanik, 2015).
Youness (2006) introduced a Non-Linear Problems (NLPs)with rough constraints. Even though, presented new concepts like a convex rough set, local and global rough optimal solution, and roughness measure of optimality with NLPs. Osman et al. (2011) presented a new form of Rough Programming Problems (RPPs). Even though defined a rough feasibility, optimality, optimal set, and value.
Hamazehee et al. (2014) presented an approach for solving Linear Programming Problems (LPPs) with rough intervals (RIs) parameters and explained that each one of them can be decomposed into four LPPs with interval parameters. Even though defined a surely, possibly optimal range and completely and rather satisfactory solutions.
Ammar and Khalifa (2014) introduced a new approach for solving Rough Interval Multi-Objective Transportation (RIMOT) called, separation method. In this method, transportation cost, demand, and supply are in the form of RIs. Even though, presented the separation method as an essential methodology for the DMs when discussing different types of logistic transportation problems having coefficients in the form of RIs.
Osman et al. (2016) introduced an approach for solving RIMOTP problems. The solution methodology is based on conventional interval programming and fuzzy programming. Pandian et al. (2016) formulated Rough Integer Interval Transportation Problem (RIITP). Even though, an approach named a slice-sum is presented to find the solution for RIITP. In this form, transportation cost, demand, and supply are in the form of rough integer intervals.
Emam et al. (2016) introduced a new solution methodology for fully rough three level large-scale integer linear programming problem with RIs decision parameters and variables in the objective functions and constraints. The solution approach is depended on the interval method and slice-sum method in an interactive environment to reach a compromised solution for fully rough three level large-scale integer linear programming problem (Lai, 1995).