The increase in the volumes and complexity of processed information makes the use of artificial intelligence systems more and more actual. In such systems, one of the most widespread knowledge representation models is the production model, and search algorithms are based on the inference engine. In practice, the values measurement of the features of the classified objects from some data domain is a time-consuming operation for many problems. These tasks appear, for example, when the robot explores the surface of another planet. If the goal of the robot is to get to some rock, but the future route is observed only partially, then the robot should try to make the best decision on how to achieve the goal, taking into account limitation of the resources available to additional exploration of terrain. Another example, in which the cost of obtaining new information may be high, is the commercial medicine. To minimize costs, it is necessary to find the acceptable treatment method using the minimum number of analyses performed in minimal time. The delay in providing treatment, caused by the additional analyses, leads to increased costs. Moreover, the condition of a patient who was not provided timely assistance, can significantly deteriorate. Also, the cost of additional research is essential in the field of mineral exploration. It can turn out that a more cost-effective solution is to begin drilling, if confidence of the success is 95 %, than to spend the considerable resources to achieve the 98 % confidence. The complexity of the operations of data acquisition necessary for decision-making, leads to the problem of minimizing the number of requests for information about values of the features of the classified object during inference. This problem is NP-hard. To achieve global minimization there is the general method of LP-inference with exponential computational complexity relative to the number of atomic facts in the knowledge base. However, some of its heuristic modifications have polynomial complexity. The goal of the provided research is development of the approximating method to better minimize the number of feature values requests performed in the inference. Earlier, the questions of implementation of computing approximate estimates of the number of layers without cycles in the fuzzy LP-inference task were considered. This paper presents the mathematical statement of the fuzzy LP-inference task, researches the monotonicity properties of the function evaluating the number of layers without cycles, and presents the clustering algorithm of the set of layers — singleton samples from equivalence classes of the quotient set, that obtained by partitioning of the binary relation by the unique right parts of pairs. This algorithm is designed for the iterative analysis of such subsets of productions, which most significantly influence to the relevancy. The presented approach can be used to accelerate the reverse inference in production type systems of artificial intelligence.