Fuzzy CSP

In a fuzzy constraint satisfaction problem each constraint $LaTeX: C$ and instantiation $LaTeX: I$ is assigned a degree of satisfaction $LaTeX: sat(C,I)$, which is a value in the [0,1] real interval indicating the degree that $LaTeX: C$ is satisfied by $LaTeX: I$. If this value is 1, $LaTeX: C$ is satisfied and if this value is 0, $LaTeX: C$ is violated. In the most common interpretation of fuzzy CSPs, the task is to find an instantiation $LaTeX: I$ for which the minimum of $LaTeX: sat(C,I)$ with $LaTeX: C$ ranging over all the constraints (i.e. the smallest degree of satisfaction for the instantition $LaTeX: I$) is maximal.