We give a survey of approaches for analyzing the sensitivity of non-dominated alternatives to changes in the parameters of partial quasi-orderings that define preferences. Such parameters can include values of importance coefficients for different criteria or boundaries of interval estimates of the degrees of superiority in the importance of some criteria over others, boundaries of intervals of criteria value tradeoffs uncertainty, and others.
The problem of developing a chain of charging stations for electric vehicles along a highway crossing a geographic region is considered. A tool for determining an optimal structure of this chain is proposed. The use of the tool, particularly, allows one to estimate the cost of (and thus the needed volume of investment for) developing the chain proceeding from a) the demand for electricity in the chain, b) the existing technological and legal requirements to the structure of such a chain, c) the expected production capacities of all the types of renewable sources of energy, which can effectively be deployed at each charging station from the chain, and d) the cost of the equipment to be acquired and installed at each charging station to provide the chain customers with electricity to be received by each charging station in the chain from both electrical grids and renewable sources of energy, the cost of maintaining this equipment, and the cost of operating it. The problem under consideration is formulated as a nonlinear mixed programming one of maximizing the minimum function of a sum of several linear and two bilinear functions of vector arguments. It is proven that under certain natural and verifiable assumptions, finding solutions to this problem turns out to be reducible to solving either a mixed programming problem with linear constraints or a linear programming problem and an integer programming one. For a set of model data, an illustrative example of formulating and solving the problem under consideration is provided, and the way to use the tool in negotiations with potential investors in the project is discussed.
We define and find a most specific generalization of a fuzzy set of topics assigned to leaves of the rooted tree of a taxonomy. This generalization lifts the set to a “head subject” in the higher ranks of the taxonomy, that is supposed to “tightly” cover the query set, possibly bringing in some errors, both “gaps” and “offshoots”. The method globally minimizes a penalty combining head subjects and gaps and offshoots. We apply this to extract research tendencies from a collection of about 18000 research papers published in Springer journals on data science. We consider a taxonomy of Data Science based on the Association for Computing Machinery Classification of Computing System 2012 (ACM-CCS). We find fuzzy clusters of leaf topics over the text collection and use thematic clusters’ head subjects to make some comments on the tendencies of research.