Fuzzy Satissability
نویسنده
چکیده
This paper deenes a problem that we called \fuzzy satissability" or \-satissability." It describes in mathematical terms the semantics of satisfying clauses and formulas using fuzzy logic, by converting a boolean formula into an arithmetic expression via t-norm and t-conorm operators. It is shown that for any (t-norm, t-conorm) pair, the corresponding-satissability problem is NP-hard when the values of the variables are restricted to f0; 1g. More interesting , even when the values of the variables are in the closed interval 0; 1], a large class of t-conorms exists for which the-satissability problem remains NP-hard. A simple suucient condition is provided for t-conorms to be in this class. It is shown that the optimization versions of the problems discussed here can be formulated as special cases of nonlinear programming .
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