Vol.:(0123456789) SN Computer Science (2020) 1:68 https://doi.org/10.1007/s42979-020-0072-2 SN Computer Science ORIGINAL RESEARCH Superposition of Choice Functions and Its Application to Tornado Prediction and Search Problems Fuad Aleskerov 1,2  · Sergey Demin 1,2  · Sergey Shvydun 1,2 Received: 29 January 2020 / Accepted: 31 January 2020 © Springer Nature Singapore Pte Ltd 2020 Abstract The paper examines the choice problem when the total number of observations and criteria is too large. There are many diferent procedures, which are used for decision-making process under multiple criteria; however, most of them cannot be applied to large datasets due to their computational complexity while others provide sufcient accuracy. To solve the prob- lem, we consider the idea of superposition, which consists in the sequential application of choice functions where the result of the previous function is the input for the next function. Among the main benefts of the superposition are its manageable computational complexity and high performance. We analyze normative properties of the superposition that characterize how stable and sensible the fnal choice is. We also consider the application of superposition to tornado prediction and search problems. As a result, we show that superposition of choice functions provides higher efciency values compared to traditional solutions. Keywords Composition · Superposition · Normative properties · Tornado prediction · Search problem Introduction The choice of the best alternatives among a set of all possi- ble alternatives has attracted a lot of attention because it has many applications in various felds of applied mathematics and computer science. However, the exponential growth of information, source digitalization and ever-widening access to all kinds of data make the problem both important and complicated. Let us defne the choice problem more formally. Con- sider a fnite set A of alternatives ( A > 2) where any subset X ∈ 2 A may be presented for choice. We denote by C(⋅) a choice function that performs the mapping 2 A → 2 A with the restriction C(X) ⊆ X for any X ∈ 2 A . A choice consists in the selection according to some rule from some set X of the non-empty subset of alternatives Y ⊆ X. When there is only one criterion, the choice of alterna- tives is accomplished on a given optimality criterion with the use of some extremization procedure. However, most real-life choice problems usually deal with multiple cri- teria. Currently, there are many methods of transforming multi-criteria optimization problem into a single criterion optimization problem. For instance, there are diferent multi- criteria rules that assign scores to alternatives or perform their pairwise comparison. Unfortunately, these rules cannot always be applied to solve the choice problem. First, most of them have a high computational complexity. Even the quadratic complexity may be inadmissible when we deal with large datasets. For instance, choice procedures based on the majority relation require pairwise comparisons of all alternatives and, con- sequently, if the number of alternatives is more than 10 5 , more than 10 10 comparisons should be performed which is not always possible to do in a sufcient time. Second, one can observe that after applying some choice procedures the obtained set of alternatives remains too large. It means that other choice procedures should be applied in order to nar- row the initial set of alternatives. Finally, some criteria may confict with others, and in that case, the choice problem lies * Sergey Demin sdemin@hse.ru Fuad Aleskerov alesk@hse.ru Sergey Shvydun shvydun@hse.ru 1 National Research University Higher School of Economics, Moscow, Russia 2 V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia