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It can be read on Wikipedia that MIS is NP-hard. However, is it also NP-complete?

This article says:

"Thus, the Maximum Clique Problem(MCP) and the Maximum Independent Set(MIS) Problem are equivalent. In addition, both problems are NP—complete".

However, a professor told me that MIS cannot be NP-complete because only decision problems can be NP-complete. According to him, MIS is an optimization problem, and therefore it is not in NP.

Ruan
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    There are many relevant questions already answered on this site, for example https://cs.stackexchange.com/questions/939/optimization-version-of-decision-problems, https://cs.stackexchange.com/questions/79707/does-every-computational-problem-have-a-decision-version, https://cs.stackexchange.com/questions/56518/can-the-decision-version-of-an-optimization-problem-in-np-be-in-p. – Yuval Filmus Dec 09 '20 at 15:35
  • and also https://cs.stackexchange.com/q/982/755 – D.W. Dec 09 '20 at 17:22

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