Many-valued Decisions Research Articles

Comparative Analysis of Deterministic and Nondeterministic Decision Trees for Decision Tables from Closed Classes.

In this paper, we consider classes of decision tables with many-valued decisions closed under operations of the removal of columns, the changing of decisions, the permutation of columns, and the duplication of columns. We study relationships among three parameters of these tables: the complexity of a decision table (if we consider the depth of the decision trees, then the complexity of a decision table is the number of columns in it), the minimum complexity of a deterministic decision tree, and the minimum complexity of a nondeterministic decision tree. We consider the rough classification of functions characterizing relationships and enumerate all possible seven types of relationships.

Bi-criteria optimization problems for decision rules

We consider bi-criteria optimization problems for decision rules and rule systems relative to length and coverage. We study decision tables with many-valued decisions in which each row is associated with a set of decisions as well as single-valued decisions where each row has a single decision. Short rules are more understandable; rules covering more rows are more general. Both of these problems—minimization of length and maximization of coverage of rules are NP-hard. We create dynamic programming algorithms which can find the minimum length and the maximum coverage of rules, and can construct the set of Pareto optimal points for the corresponding bi-criteria optimization problem. This approach is applicable for medium-sized decision tables. However, the considered approach allows us to evaluate the quality of various heuristics for decision rule construction which are applicable for relatively big datasets. We can evaluate these heuristics from the point of view of (i) single-criterion—we can compare the length or coverage of rules constructed by heuristics; and (ii) bi-criteria—we can measure the distance of a point (length, coverage) corresponding to a heuristic from the set of Pareto optimal points. The presented results show that the best heuristics from the point of view of bi-criteria optimization are not always the best ones from the point of view of single-criterion optimization.

Multi-stage optimization of decision and inhibitory trees for decision tables with many-valued decisions

We study problems of optimization of decision and inhibitory trees for decision tables with many-valued decisions. As cost functions, we consider depth, average depth, number of nodes, and number of terminal/nonterminal nodes in trees. Decision tables with many-valued decisions (multi-label decision tables) are often more accurate models for real-life data sets than usual decision tables with single-valued decisions. Inhibitory trees can sometimes capture more information from decision tables than decision trees. In this paper, we create dynamic programming algorithms for multi-stage optimization of trees relative to a sequence of cost functions. We apply these algorithms to prove the existence of totally optimal (simultaneously optimal relative to a number of cost functions) decision and inhibitory trees for some modified decision tables from the UCI Machine Learning Repository.

Concept Compression in Formal Concept Analysis Using Entropy-Based Attribute Priority

ABSTRACTDiscovering important concepts in formal concept analysis (FCA) is an important issue due to huge number of concepts arising out of complicated contexts. To address this issue, this paper proposes a method for concept compression in FCA, involving many-valued decision context, based on information entropy. The precedence order of attributes is obtained by using entropy theory developed by Shannon. The set of concepts is compressed using the precedence order thus determined. An algorithm namely Entropy based concept compression (ECC) is developed for this purpose. Further, similarity measures between the actual and compressed concepts are examined using the deviance analysis and percentage error calculation on the deviance of input weights of concepts. From the experiments, it is found that the compressed concepts inherit association rules to the maximum extent.

Minimization of Decision Tree Average Depth for Decision Tables with Many-valued Decisions

The paper is devoted to the analysis of greedy algorithms for the minimization of average depth of decision trees for decision tables such that each row is labeled with a set of decisions. The goal is to find one decision from the set of decisions. When we compare with the optimal result obtained from dynamic programming algorithm, we found some greedy algorithms produces results which are close to the optimal result for the minimization of average depth of decision trees.

A Greedy Algorithm for Construction of Decision Trees for Tables with Many-Valued Decisions --A Comparative Study

In the paper, we study a greedy algorithm for construction of decision trees. This algorithm is applicable to decision tables with many-valued decisions where each row is labeled with a set of deci...

A Greedy Algorithm for Construction of Decision Trees for Tables with Many-Valued Decisions – A Comparative Study

In the paper, we study a greedy algorithm for construction of decision trees. This algorithm is applicable to decision tables with many-valued decisions where each row is labeled with a set of decisions. For a given row, we should find a decision from the set attached to this row. Experimental results for data sets from UCI Machine Learning Repository and randomly generated tables are presented. We make a comparative study of the depth and average depth of the constructed decision trees for proposed approach and approach based on generalized decision. The obtained results show that the proposed approach can be useful from the point of view of knowledge representation and algorithm construction.

Decision Rules, Trees and Tests for Tables with Many-valued Decisions–comparative Study

In this paper, we present three approaches for construction of decision rules for decision tables with many-valued decisions. We construct decision rules directly for rows of decision table, based on paths in decision tree, and based on attributes contained in a test (super-reduct). Experimental results for the data sets taken from UCI Machine Learning Repository, contain comparison of the maximum and the average length of rules for the mentioned approaches.

Greedy Algorithms for Construction of Approximate Tests for Decision Tables with Many-Valued Decisions

The paper is devoted to the study of a greedy algorithm for construction of approximate tests super-reducts. This algorithm is applicable to decision tables with many-valued decisions where each row is labeled with a set of decisions. For a given row, we should find a decision from the set attached to this row. We consider bounds on the precision of this algorithm relative to the cardinality of tests.