Purpose - the purpose of the article is to develop mathematical methods for processing "big data". This is based on the system analysis of properties for their structural organization. These methods allow us to optimize the basic characteristics of "big data". This includes increasing the search speed to process large volumes of fast incoming data while preserving their relevance. We suggested mathematical methods to work with a data structure "m-tuples based on ordered sets of arbitrary cardinality (OSAC)". We determined pairwise combinations of Boolean elements as operands of the operations investigated. The foregoing is based on the analysis of the data structure properties. We also calculated the dynamics of changes in the constituent pairwise combinations of the Boolean elements depending on the basis set cardinality for different groups of the given data structure. We estimated the time needed to execute methods of working with the OSAC data structure as functional dependencies of the amount of data O( f (n)). We also determined the component of combinations for Boolean elements. For these elements, the execution of algorithms that implement the operation investigated is not required as the desired result is defined in the data structure property. We further developed a mathematical method which allows us to forecast the result of performing certain operations on elements of ordered data structure. This takes into account the position of the elements in the structure without using the computational algorithm. For the first time, we obtained an analytical dependency to determine the component number for Boolean elements of length m2. This includes an element represented by a tuple of smaller length m1 in relation to the total number of Boolean elements of length m2. For the first time we also obtained an analytical dependency to determine the minimum maxima of the functional dependency described above. The results obtained in this paper can be used to minimize the time and computational resources needed to process "big data" represented by m-tuples based on OSAC.

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