Is there any way of formulating linear/non-linear programming problems in terms of YES, NO, and MAYBE instead of just $0-1$ programming?
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A google search for "fuzzy linear programming" yields this, and for "fuzzy nonlinear programming" yields this (I recall I've seen such programming mentioned in fuzzy logic books before also... I think Klir and Yuan's "Fuzzy Sets and Fuzzy Logic: Theory and Applications" has a very,very short section on this). So, unless I've misinterpreted something here, the answer is "yes".