The notions of fuzzy upward β-covering, the fuzzy upward β-neighborhood, upward β-neighborhood and fuzzy complement β-neighborhood are introduced and several related properties are studied. Furthermore, multigranulation optimistic/pessimistic fuzzy rough sets based on fuzzy upward β-covering are initiated and their fundamental properties are investigated. We also find the upward β-neighborhood in the fuzzy upward covering approximation space and present the optimistic/pessimistic multigranulation rough sets to further enrich the presented notions. The medicine selection via fuzzy upward β-covering rough sets in medical diagnosis is another main contribution of the present work. It is also explored that which medicine can be prescribed for which particular symtom(s) and which disease.
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