Joseph Gogodze

This study proposes and analyzes a new method for the post-Pareto analysis of multicriteria decision-making (MCDM) problems: the revealed comparative advantage (RCA) assessment method. An interesting feature of the suggested method is that it uses the solution to a special eigenvalue problem and can be considered an analog/modification in the MCDM context of well-known ranking methods including the authority-hub method, PageRank method, and so on, which have been successfully applied to such fields as economics, bibliometrics, web search design, and so on. For illustrative purposes, this study discusses a particular MCDM problem to demonstrate the practicality of the method. The theoretical considerations and conducted calculations reveal that the RCA assessment method is self-consistent and easily implementable. Moreover, comparisons with well-known tools of an MCDM analysis shows that the results obtained using this method are appropriate and competitive. An important particularity of the RCA assessment method is that it can be useful for decision-makers in the case in which no decision-making authority is available or when the relative importance of various criteria has not been preliminarily evaluated.

In this note, we propose a game-theoretic approach for benchmarking computational problems and their solvers. The approach takes an assessment matrix as a payoff matrix for some zero-sum matrix game in which the first player chooses a problem and the second player chooses a solver. The solution in mixed strategies of this game is used to construct a notionally objective ranking of the problems and solvers under consideration. The proposed approach is illustrated in terms of an example to demonstrate its viability and its suitability for applications.

The Pareto optimality is a widely used concept for the multicriteria decision-making problems. However, this concept has a significant drawback-the set of Pareto optimal alternatives usually is large. Correspondingly, the problem of choosing a specific Pareto optimal alternative for the decision implementation is arising. This study proposes a new approach to select an "appropriate" alternative from the set of Pareto optimal alternatives. The proposed approach is based on ranking-theory methods used for ranking participants in sports tournaments. In the framework of the proposed approach, we build a special score matrix for a given multicriteria problem, which allows the use of the mentioned ranking methods and to choose the corresponding best-ranked alternative from the Pareto set as a solution of the problem. The proposed approach is particularly useful when no decision-making authority is available, or when the relative importance of various criteria has not been evaluated previously. The proposed approach is tested on an example of a materials-selection problem for a sailboat mast.

Assessing/ranking the innovative advantages of countries is a problem of current interest. However, the set of tools used for this purpose are very narrow and often prone to criticism. The aim of this study is to somewhat extend the arsenal of methods used to this end. For this purpose, based on a data set from the Global Innovation Index, this study develops a special multi-objective decision-making problem, the aim of which is to identify the "best countries" in the sense of their innovative advantage. Moreover, applying ranking methods (in our case the Markov-chain method and analytic hierarchy process) to this multi-objective decision-making problem, we obtain new alternative ratings/rankings of the innovative advantages of countries.