The results presented here (including the assessment of a new tool – inhibitory trees) offer valuable tools for researchers in the areas of data mining, knowledge discovery, and machine learning, especially those whose work involves decision tables with many-valued decisions. The authors consider various examples of problems and corresponding decision tables with many-valued decisions, discuss the difference between decision and inhibitory trees and rules, and develop tools for their analysis and design. Applications include the study of totally optimal (optimal in relation to a number of criteria simultaneously) decision and inhibitory trees and rules; the comparison of greedy heuristics for tree and rule construction as single-criterion and bi-criteria optimization algorithms; and the development of a restricted multi-pruning approach used in classification and knowledge representation.

This book constitutes the refereed post-conference proceedings of the 4th International Conference on Intelligence Science, ICIS 2020, held in Durgapur, India, in February 2021 (originally November 2020). The 23 full papers and 4 short papers presented were carefully reviewed and selected from 42 submissions. One extended abstract is also included. They deal with key issues in brain cognition; uncertain theory; machine learning; data intelligence; language cognition; vision cognition; perceptual intelligence; intelligent robot; and medical artificial intelligence.

The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery, and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence. Volume XXII in the series is a continuation of a number of research streams that have grown out of the seminal work of Zdzislaw Pawlak during the first decade of the 21st century.

This book compares four parameters of problems in arbitrary information systems: complexity of problem representation and complexity of deterministic, nondeterministic, and strongly nondeterministic decision trees for problem solving. Deterministic decision trees are widely used as classifiers, as a means of knowledge representation, and as algorithms. Nondeterministic (strongly nondeterministic) decision trees can be interpreted as systems of true decision rules that cover all objects (objects from one decision class). This book develops tools for the study of decision trees, including bounds on complexity and algorithms for construction of decision trees for decision tables with many-valued decisions. It considers two approaches to the investigation of decision trees for problems in information systems: local, when decision trees can use only attributes from the problem representation; and global, when decision trees can use arbitrary attributes from the information system. For both approaches, it describes all possible types of relationships among the four parameters considered and discusses the algorithmic problems related to decision tree optimization. The results presented are useful for researchers who apply decision trees and rules to algorithm design and to data analysis, especially those working in rough set theory, test theory and logical analysis of data. This book can also be used as the basis for graduate courses.

Dynamic programming is an efficient technique for solving optimization problems. It is based on breaking the initial problem down into simpler ones and solving these sub-problems, beginning with the simplest ones. A conventional dynamic programming algorithm returns an optimal object from a given set of objects. This book develops extensions of dynamic programming, enabling us to (i) describe the set of objects under consideration; (ii) perform a multi-stage optimization of objects relative to different criteria; (iii) count the number of optimal objects; (iv) find the set of Pareto optimal points for bi-criteria optimization problems; and (v) to study relationships between two criteria. It considers various applications, including optimization of decision trees and decision rule systems as algorithms for problem solving, as ways for knowledge representation, and as classifiers; optimization of element partition trees for rectangular meshes, which are used in finite element methods for solving PDEs; and multi-stage optimization for such classic combinatorial optimization problems as matrix chain multiplication, binary search trees, global sequence alignment, and shortest paths. The results presented are useful for researchers in combinatorial optimization, data mining, knowledge discovery, machine learning, and finite element methods, especially those working in rough set theory, test theory, logical analysis of data, and PDE solvers. This book can be used as the basis for graduate courses.

Discusses all the major tools and techniques for Decision Support System supported by examples Techniques are explained considering their deterministic and stochastic aspects Covers network tools including GERT and Q-GERT Explains application of both probability and fuzzy orientation in the pertinent techniques Includes a number of relevant case studies along with a dedicated chapter on software

This book constitutes the refereed proceedings of the International Joint Conference on Rough Sets, IJCRS 2023, held in Krakow, Poland, during October 5–8, 2023. The 43 full papers included in this book were carefully reviewed and selected from 83 submissions. They were organized in topical sections as follows: Rough Set Models, Foundations, Three-way Decisions, Granular Models, Distances and Similarities, Hybrid Approaches, Applications, Cybersecurity and IoT.

In this book, the concept of a hypothesis about the values of all attributes is added to the standard decision tree model, considered, in particular, in test theory and rough set theory. This extension allows us to use the analog of equivalence queries from exact learning and explore decision trees that are based on various combinations of attributes, hypotheses, and proper hypotheses (analog of proper equivalence queries). The two main goals of this book are (i) to provide tools for the experimental and theoretical study of decision trees with hypotheses and (ii) to compare these decision trees with conventional decision trees that use only queries, each based on a single attribute. Both experimental and theoretical results show that decision trees with hypotheses can have less complexity than conventional decision trees. These results open up some prospects for using decision trees with hypotheses as a means of knowledge representation and algorithms for computing Boolean functions. The obtained theoretical results and tools for studying decision trees with hypotheses are useful for researchers using decision trees and rules in data analysis. This book can also be used as the basis for graduate courses.