scholarly journals On the Depth of Decision Trees with Hypotheses

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 116
Author(s):  
Mikhail Moshkov
Keyword(s):  
Information Systems ◽  
Decision Trees ◽  
Rough Set Theory ◽  
Test Theory ◽  
Complexity Classes ◽  
Worst Case ◽  
Exact Learning ◽  
Equivalence Queries ◽  
Problem Description ◽  
Binary Information

In this paper, based on the results of rough set theory, test theory, and exact learning, we investigate decision trees over infinite sets of binary attributes represented as infinite binary information systems. We define the notion of a problem over an information system and study three functions of the Shannon type, which characterize the dependence in the worst case of the minimum depth of a decision tree solving a problem on the number of attributes in the problem description. The considered three functions correspond to (i) decision trees using attributes, (ii) decision trees using hypotheses (an analog of equivalence queries from exact learning), and (iii) decision trees using both attributes and hypotheses. The first function has two possible types of behavior: logarithmic and linear (this result follows from more general results published by the author earlier). The second and the third functions have three possible types of behavior: constant, logarithmic, and linear (these results were published by the author earlier without proofs that are given in the present paper). Based on the obtained results, we divided the set of all infinite binary information systems into four complexity classes. In each class, the type of behavior for each of the considered three functions does not change.

scholarly journals Entropy-Based Greedy Algorithm for Decision Trees Using Hypotheses

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 808
Author(s):  
Mohammad Azad ◽  
Igor Chikalov ◽  
Shahid Hussain ◽  
Mikhail Moshkov
Keyword(s):  
Decision Trees ◽  
Greedy Algorithm ◽  
Boolean Functions ◽  
Computer Experiments ◽  
Data Sets ◽  
Exact Learning ◽  
Equivalence Queries

In this paper, we consider decision trees that use both conventional queries based on one attribute each and queries based on hypotheses of values of all attributes. Such decision trees are similar to those studied in exact learning, where membership and equivalence queries are allowed. We present greedy algorithm based on entropy for the construction of the above decision trees and discuss the results of computer experiments on various data sets and randomly generated Boolean functions.

scholarly journals Optimization of Decision Trees with Hypotheses for Knowledge Representation

Electronics ◽  
2021 ◽  
Vol 10 (13) ◽  
pp. 1580
Author(s):  
Mohammad Azad ◽  
Igor Chikalov ◽  
Shahid Hussain ◽  
Mikhail Moshkov
Keyword(s):  
Dynamic Programming ◽  
Knowledge Representation ◽  
Decision Trees ◽  
Boolean Functions ◽  
Computer Experiments ◽  
Data Sets ◽  
Exact Learning ◽  
Equivalence Queries ◽  
Programming Algorithms

In this paper, we consider decision trees that use two types of queries: queries based on one attribute each and queries based on hypotheses about values of all attributes. Such decision trees are similar to the ones studied in exact learning, where membership and equivalence queries are allowed. We present dynamic programming algorithms for minimization of the depth and number of nodes of above decision trees and discuss results of computer experiments on various data sets and randomly generated Boolean functions. Decision trees with hypotheses generally have less complexity, i.e., they are more understandable and more suitable as a means for knowledge representation.

Rough set theory for the interval-valued fuzzy information systems

2008 ◽  
Vol 178 (8) ◽  
pp. 1968-1985 ◽  
Author(s):  
Zengtai Gong ◽  
Bingzhen Sun ◽  
Degang Chen
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fuzzy Information ◽  
Interval Valued

On Quasi Discrete Topological Spaces in Information Systems

2012 ◽  
Vol 3 (2) ◽  
pp. 38-52 ◽  
Author(s):  
Tutut Herawan
Keyword(s):  
Information System ◽  
Information Systems ◽  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Topological Spaces ◽  
Discrete Topology

This paper presents an alternative way for constructing a topological space in an information system. Rough set theory for reasoning about data in information systems is used to construct the topology. Using the concept of an indiscernibility relation in rough set theory, it is shown that the topology constructed is a quasi-discrete topology. Furthermore, the dependency of attributes is applied for defining finer topology and further characterizing the roughness property of a set. Meanwhile, the notions of base and sub-base of the topology are applied to find attributes reduction and degree of rough membership, respectively.

Rough Sets for Discovering Concurrent System Models from Data Tables

2011 ◽  
pp. 239-268 ◽  
Author(s):  
Krzysztof Pancerz ◽  
Zbigniew Suraj
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Petri Net ◽  
Rough Set Theory ◽  
Research Trend ◽  
Concurrent System ◽  
System Models ◽  
Data Tables ◽  
New Research

This chapter constitutes the continuation of a new research trend binding rough set theory with concurrency theory. In general, this trend concerns the following problems: discovering concurrent system models from experimental data represented by information systems, dynamic information systems or specialized matrices, a use of rough set methods for extracting knowledge from data, a use of rules for describing system behaviors, and modeling and analyzing of concurrent systems by means of Petri nets on the basis of extracted rules. Some automatized methods of discovering concurrent system models from data tables are presented. Data tables are created on the basis of observations or specifications of process behaviors in the modeled systems. Proposed methods are based on rough set theory and colored Petri net theory.

scholarly journals Reduction of Neighborhood-Based Generalized Rough Sets

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Zhaohao Wang ◽  
Lan Shu ◽  
Xiuyong Ding
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Open Problems ◽  
The Third ◽  
Generalized Rough Sets

Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. This paper discusses five types of existing neighborhood-based generalized rough sets. The concepts of minimal neighborhood description and maximal neighborhood description of an element are defined, and by means of the two concepts, the properties and structures of the third and the fourth types of neighborhood-based rough sets are deeply explored. Furthermore, we systematically study the covering reduction of the third and the fourth types of neighborhood-based rough sets in terms of the two concepts. Finally, two open problems proposed by Yun et al. (2011) are solved.

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