'fuzzily-produced' is a modern English compound formed from the adverb 'fuzzily' (from 'fuzzy') and the past participle 'produced' (from 'produce').

'produced' comes from Latin 'producere' via Old French 'produire' and Middle English 'producen' to modern English 'produce'; 'fuzzy' developed in English from the noun 'fuzz' (late 18th–19th century) meaning 'a mass of loose fibers,' later extended metaphorically to mean 'indistinct' or 'blurred', and then adverbialized to 'fuzzily'. These elements combined in modern English to form the descriptive compound 'fuzzily-produced'.

The components originally referred to physical 'fuzz' and the act 'to lead forth/bring forth'; over time 'fuzzy' took on the figurative sense of 'indistinct', and the compound came to mean 'made in an indistinct or imprecise way'.