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The article considers one of the possible generalizations of constraintsatisfaction problems where relations are replaced by multivalued membershipfunctions. In this case operations of disjunction and conjunction are replacedby maximum and minimum, and consistency of a solution becomes multivaluedrather than binary. The article studies the problem of finding d mostadmissible solutions for a given d. A tractable subclass of these problems isdefined by the concepts of invariants and polymorphisms similar to the classicconstraint satisfaction approach. These concepts are adapted in two ways.Firstly, the correspondence of "invariant-polymorphism" is generalized to(min,max) semirings. Secondly, we consider non-uniform polymorphisms, whereeach variable has its own operator, in contrast to the case of one operatorcommon for all variables. The article describes an algorithm that finds $d$most admissible solutions in polynomial time, provided that the problem isinvariant with respect to some non-uniform majority operator. It is essentialthat this operator needs not to be known for the algorithm to work. Moreover,even a guarantee for the existence of such an operator is not necessary. Thealgorithm either finds the solution or discards the problem. The latter ispossible only if the problem has no majority polymorphism.

M-best solutions for a class of fuzzy constraint satisfaction problems