Essays on TOPSIS for sorting with applications in finance

Abstract

TOPSIS consists of a popular method with a wide range of applications in ranking problems. Here, we propose novel methods based on TOPSIS that sort alternatives into pre- defined and ordered classes, using boundary or characteristic profiles. Initially, the methods TOPSIS-Sort-B (boundary profiles) and TOPSIS-Sort-C (characteristic profiles) are proposed for problems that deal with crisp information. Next, adaptations of the methods are proposed for a fuzzy environment, based on the vertex distance used in the traditional Fuzzy-TOPSIS. The proposed methods that deal with fuzzy information are called FTOPSIS-Sort-B and FTOPSIS-Sort-C. In addition, the use of preference disaggregation models to infer the parameters for the sorting procedure of TOPSIS-Sort-C is discussed. Therefore, the method PDTOPSIS-Sort-C is proposed, where characteristic profiles and weights are inferred from decision examples, which represent an easier way to consider the DM’s preferences into the multicriteria model. This method joins the recently proposed PDTOPSIS-Sort, which infers boundary profiles for the TOPSIS-Sort-B. The multicriteria problems discussed in this thesis include the assessment of the economic freedom of 180 countries, which are sorted into five ordered classes; a real estate investment funds evaluation with verbal information that is dealt with fuzzy sets; and a financial performance assessment of companies that performed IPOs in the Brazilian stock market in the last decade. Among the main results, TOPSIS-Sort-B and TOPSIS-Sort-C assigned respectively 89.44% and 90% of the countries to the same classes of economic freedom that the Heritage Foundation had originally allocated. Changes occurred only between consecutive categories, and they were expected due to the difference between the methodologies. Consistent results were also found with the preference disaggregation variants of the methods. A simulation demonstrated that small sizes of reference sets achieved average similarities higher than 70%. In the case of the real estate investment funds, the FTOPSIS-Sort-B and FTOPSIS-Sort-C methods were demonstrated. A set of 16 funds was allocated into three ordered classes, according to their evaluation regarding five criteria. Additional experiments showed how the assignments change when one varies the linguistic assignment of the weights, and the results showed robustness.