Final answer:
Inflammatory breast cancer is known to have the worst prognosis among the listed types due to its aggressive nature and propensity to metastasize quickly.
Step-by-step explanation:
Among the types of breast cancer listed, Inflammatory breast cancer has the worst prognosis. Ductal carcinoma in situ (DCIS) is non-invasive and can often be cured with surgery alone. Triple-negative breast cancer, a more aggressive form, lacks the receptors that often make hormone or targeted therapy effective and thus has a poorer prognosis than hormone receptor-positive cancers. Lobular carcinoma, another subtype, tends to be slower growing but can be more difficult to detect. Inflammatory breast cancer, however, is a rare and very aggressive disease in which cancer cells block lymph vessels in the skin of the breast. This type is particularly fast-growing and has a higher chance of metastasis, making its prognosis less favorable compared to the other types listed.