19 research outputs found
Generation of Exhaustive Set of Rules within Dominance-based Rough Set Approach
AbstractThe rough sets theory has proved to be a useful mathematical tool for the analysis of a vague description of objects. One of extensions of the classic theory is the Dominance-based Set Approach (DRSA) that allows analysing preference-ordered data. The analysis ends with a set of decision rules induced from rough approximations of decision classes. The role of the decision rules is to explain the analysed phenomena, but they may also be applied in classifying new, unseen objects. There are several strategies of decision rule induction. One of them consists in generating the exhaustive set of minimal rules. In this paper we present an algorithm based on Boolean reasoning techniques that follows this strategy with in DRSA
Towards Explainable TOPSIS: Visual Insights into the Effects of Weights and Aggregations on Rankings
Multi-Criteria Decision Analysis (MCDA) is extensively used across diverse
industries to assess and rank alternatives. Among numerous MCDA methods
developed to solve real-world ranking problems, TOPSIS remains one of the most
popular choices in many application areas. TOPSIS calculates distances between
the considered alternatives and two predefined ones, namely the ideal and the
anti-ideal, and creates a ranking of the alternatives according to a chosen
aggregation of these distances. However, the interpretation of the inner
workings of TOPSIS is difficult, especially when the number of criteria is
large. To this end, recent research has shown that TOPSIS aggregations can be
expressed using the means (M) and standard deviations (SD) of alternatives,
creating MSD-space, a tool for visualizing and explaining aggregations. Even
though MSD-space is highly useful, it assumes equally important criteria,
making it less applicable to real-world ranking problems. In this paper, we
generalize the concept of MSD-space to weighted criteria by introducing the
concept of WMSD-space defined by what is referred to as weight-scaled means and
standard deviations. We demonstrate that TOPSIS and similar distance-based
aggregation methods can be successfully illustrated in a plane and interpreted
even when the criteria are weighted, regardless of their number. The proposed
WMSD-space offers a practical method for explaining TOPSIS rankings in
real-world decision problems
Can Confirmation Measures Reflect Statistically Sound Dependencies in Data? The Concordance-based Assessment
The paper considers particular interestingness measures, called confirmation measures (also known as Bayesian confirmation measures), used for the evaluation of “if evidence, then hypothesis” rules. The agreement of such measures with a statistically sound (significant) dependency between the evidence and the hypothesis in data is thoroughly investigated. The popular confirmation measures were not defined to possess such form of agreement. However, in error-prone environments, potential lack of agreement may lead to undesired effects, e.g. when a measure indicates either strong confirmation or strong disconfirmation, while in fact there is only weak dependency between the evidence and the hypothesis. In order to detect and prevent such situations, the paper employs a coefficient allowing to assess the level of dependency between the evidence and the hypothesis in data, and introduces a method of quantifying the level of agreement (referred to as a concordance) between this coefficient and the measure being analysed. The concordance is characterized and visualised using specialized histograms, scatter-plots, etc. Moreover, risk-related interpretations of the concordance are introduced. Using a set of 12 confirmation measures, the paper presents experiments designed to establish the actual concordance as well as other useful characteristics of the measures
Can interestingness measures be usefully visualized?
The paper presents visualization techniques for interestingness measures. The process of measure visualization provides useful insights into different domain areas of the visualized measures and thus effectively assists their comprehension and selection for different knowledge discovery tasks. Assuming a common domain form of the visualized measures, a set of contingency tables, which consists of all possible tables having the same total number of observations, is constructed. These originally four-dimensional data may be effectively represented in three dimensions using a tetrahedron-based barycentric coordinate system. At the same time, an additional, scalar function of the data (referred to as the operational function, e.g., any interestingness measure) may be rendered using colour. Throughout the paper a particular group of interestingness measures, known as confirmation measures, is used to demonstrate the capabilities of the visualization techniques. They cover a wide spectrum of possibilities, ranging from the determination of specific values (extremes, zeros, etc.) of a single measure, to the localization of pre-defined regions of interest, e.g., such domain areas for which two or more measures do not differ at all or differ the most
Identifying Regularities in Stock Portfolio Tilting
The paper deals with the issues associated with identification of stocks generating abnormal returns. Following the findings of a finance theory regarding portfolio tilting, a set of price-related stocks' attributes was analyzed. The analysis was conducted with the help of rough sets methodology which allows to distinguish "important" attributes for problem description, and to generate decision rules which can be later used to predict stocks' performance. Validity of the approach was tested on the Toronto Stock Exchange data. Keywords: rough sets, decision rules, reducts, portfolio tilting, anomalies theory About the Authors Roman Slowinski is Professor of Decision and Computer Sciences and Head of the Laboratory of Intelligent Decision Support Systems, Institute of Computer Science, Poznan University of Technology, Poznan, Poland. Robert Susmaga is on the research and teaching staff of the Institute of Computer Science at Poznan University of Technology, Poznan, Poland. Wojtek Mic..