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Assessment measures of an ensemble classifier based on the distributivity equation to predict the presence of severe coronary artery disease

Rak Ewa, Szczur Adam, Bazan Jan G., Bazan-Socha Stanisława

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 3

361--377

EN

The aim of this study is to apply and evaluate the usefulness of the hybrid classifier to predict the presence of serious coronary artery disease based on clinical data and 24-hour Holter ECG monitoring. Our approach relies on an ensemble classifier applying the distributivity equation aggregating base classifiers accordingly. Such a method may be helpful for physicians in the management of patients with coronary artery disease, in particular in the face of limited access to invasive diagnostic tests, i.e., coronary angiography, or in the case of contraindications to its performance. The paper includes results of experiments performed on medical data obtained from the Department of Internal Medicine, Jagiellonian University Medical College, Kraków, Poland. The data set contains clinical data, data from Holter ECG (24-hour ECG monitoring), and coronary angiography. A leave-one-out cross-validation technique is used for the performance evaluation of the classifiers on a data set using the WEKA (Waikato Environment for Knowledge Analysis) tool. We present the results of comparing our hybrid algorithm created from aggregation with the distributive equation of selected classification algorithms (multilayer perceptron network, support vector machine, k-nearest neighbors, naïve Bayes, and random forests) with themselves on raw data.

2

Application of uninorms to aggregate uncertainty from many classifiers

Drygaś Paweł, Bazan Jan G., Pusz Piotr, Knap Maksymilian

Journal of Automation Mobile Robotics and Intelligent Systems

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2019

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Vol. 13, No. 4

85--90

EN

In this contribution we want to present the concept of uncertainty area of classifiers and an algorithm that uses uninorms to minimize the area of uncertainty in the pre‐ diction of new objects by complex classifiers.

3

A three-level aggregation model for evaluating software usability by fuzzy logic

Rakovská Eva, Hudec Miroslav

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 3

489--501

EN

Rapid deployment of IT brings about new issues with software usability measurement. Usability is based on users’ experience and is strongly subjective, having a qualitative character. The users’ comfort is usually collected by surveys in their daily work. The present article stems from an experimental study related to the evaluation of the usability of tools by a rule-based system. The work suggests a robust computational model that will be able to avoid the main problems arising from the experimental study (a large and less-legible rule base) and to deal with the vagueness of IT user experience, different levels of skills and various numbers of filled questionnaires in different departments. The computational model is based on three hierarchical levels of aggregation supported by fuzzy logic. Choices for the most suitable aggregation functions in each level are advocated and illustrated with examples. The number of questions and granularity of answers in this approach can be adjusted to each user group, which could reduce the response burden and errors. Finally, the paper briefly describes further possibilities of the suggested approach.

4

Aggregation and related functions in fuzzy set theory: dualities and monotonicity-based generalizations

Mesiar R., Kolesarova A.

Journal of Automation Mobile Robotics and Intelligent Systems

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2017

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Vol. 11, No. 3

58--61

EN

We discuss several extensions of binary Boolean functions acting on the domain [0, 1]. Formally, there are 16 disjoint classes of such functions, covering a majority of binary functions considered in fuzzy set theory. We introduce and discuss dualities in this framework, stressing the links between different subclasses of considered functions, e.g., the link between conjunctive and implication functions. Special classes of considered functions are characterized, among others, by particular kinds of monotonicity. Relaxing these constraints by considering monotonicity in one direction only, we generalize standard classes of aggregation functions, implications, semicopulas, etc., into larger classes called pre-aggregations, pre-implications, pre-semicopulas, etc. Note that the dualities discussed for the standard classes also relate the new extended classes of pre-functions.

5

Determining models of influence

Grabisch M., Rusinowska A.

Operations Research and Decisions

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2016

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Vol. 26, No. 2

69--85

EN

We consider a model of opinion formation based on aggregation functions. Each player modifies his opinion by arbitrarily aggregating the current opinion of all players. A player is influential on another player if the opinion of the first one matters to the latter. Generalization of an influential player to a coalition whose opinion matters to a player is called an influential coalition. Influential players (coalitions) can be graphically represented by the graph (hypergraph) of influence, and convergence analysis is based on properties of the hypergraphs of influence. In the paper, we focus on the practical issues of applicability of the model w.r.t. a standard framework for opinion formation driven by Markov chain theory. For a qualitative analysis of convergence, knowing the aggregation functions of the players is not required, one only needs to know the set of influential coalitions for each player. We propose simple algorithms that permit us to fully determine the influential coalitions. We distinguish three cases: a symmetric decomposable model, an anonymous model, and a general model.

6

Group Decision Making Problem by General Convexity or Concavity and Aggregation Process

Pękala B.

Journal of Automation Mobile Robotics and Intelligent Systems

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2016

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Vol. 10, No. 4

62--69

EN

The averaging aggregation operators are defined and some interesting properties are derived. Moreover, we have extended concave and convex property. The main results concerning aggregation of generalized quasiconcave and quasiconvex functions are presented and some their properties are derived and discussed. The class of concavity and convexity of two variable aggregation operators that preserve these properties are studied.

7

Comparison of Algorithms for Decision Making Problems and Preservation of α-properties of Fuzzy Relations in Aggregation Process

Bentkowska U., Balicki K.

Journal of Automation Mobile Robotics and Intelligent Systems

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2016

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Vol. 10, No. 2

25--39

EN

In the paper the problem of preservation of properties of fuzzy relations during aggregation process is considered. It means that properties of fuzzy relations R1, … , R2 on a set X are compared with properties of the aggregated fuzzy relation RF = F(R1, … , R2), where R is a function of the type F ∶ [0, 1]n → [0, 1]. There are discussed α-properties (which may be called graded properties - to some grade R) as reflexivity, irreflexivity, symmetry, asymmetry, antisymmetry, connectedness and transitivity, where α ∈ [0, 1]. Fuzzy relations with a given graded property are analyzed (there may be diverse grades of the same property) and the obtained grade of the aggregated fuzzy relation is provided. There is also discussed the „converse” problem. Namely, relation RF = F(R1, … , Rn) is assumed to have a graded property and the properties of relations R1, … , Rn are examined (possibly with some assumptions on F). Presented here considerations have possible applications in decision making algorithms. This is why interpretation of the considered graded properties and possible potential in decision making is presented.

8

Evaluating Answer Set Programming with Non-Convex Recursive Aggregates

Alviano M.

Fundamenta Informaticae

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2016

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Vol. 149, nr 1/2

1--34

EN

Aggregation functions are widely used in answer set programming (ASP) for representing and reasoning on knowledge involving sets of objects collectively. These sets may also depend recursively on the results of the aggregation functions, even if so far the support for such recursive aggregations was quite limited in ASP systems. In fact, recursion over aggregates was restricted to convex aggregates, i.e., aggregates that may have only one transition from false to true, and one from true to false, in this specific order. Recently, such a restriction has been overcome, so that the user can finally use non-convex recursive aggregates in ASP programs. An evaluation of ASP programs with non-convex recursive aggregates is reported in this paper, also testing a recently proposed extension of the concept of the positive extension graph to the case of programs with aggregates. Moreover, as an additional contribution, new rewritings for EVEN and ODD are presented: EVEN maps to true aggregation sets containing an even number of true literals, and ODD maps to true aggregation sets containing an odd number of true literals. Both aggregates are non-convex, and previously replaced by a conjunction of non-convex sums, whose size is quadratic with respect to the number of literals in the aggregation set. A different rewriting is presented in this paper, whose size is linear with respect to the number of literals in the aggregation set.

9

Development of the mean concept

Dudziak U.

Journal of Mathematics and Applications

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2006

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Vol. 28

25-39

EN

This paper deals with the concept of mean. We make an overview of axioms used for the description of families of means and their consequences. We give examples of means fulfilling the respective sets of axioms, and moreover, some applications are indicated.