Finding a Given Number of Solutions to a System of Fuzzy Constraints*

Abstract

A minimax modification of a fuzzy constraint satisfaction problem is considered, where constraints determine not whether a given solution is feasible but the numerical value of satisfiability. The algorithm is proposed that finds a given number of solutions with the highest value of satisfiability in polynomial time for a subclass of problems with constraints invariant to some majority operator. It is important that knowing the operator itself is not required. Moreover, it is not necessary to guarantee its existence. For any system of fuzzy constraints, the algorithm either finds a given number of best solutions or declines the problem. The latter is only possible when no such operator exists.