In contrast with conventional dynamic programming algorithms that return one solution, extensions of dynamic programming allows us to work with the whole set of solutions or its essential part, to perform multi-stage optimization relative to different criteria, to count the number of solutions, and to find the set of Pareto optimal points for bi-criteria optimization problems. The presentation is based on the results considered in three books published or accepted by Springer.

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The aim of this series is to publish a Reference Library, including novel advances and developments in all aspects of Intelligent Systems in an easily accessible and well structured form. The series includes reference works, handbooks, compendia, textbooks, well-structured monographs, dictionaries, and encyclopedias. It contains well integrated knowledge and current information in the field of Intelligent Systems. The series covers the theory, applications, and design methods of Intelligent Systems. Virtually all disciplines such as engineering, computer science, avionics, business, e-commerce, environment, healthcare, physics and life science are included. The list of topics spans all the areas of modern intelligent systems such as:

Multi-stage optimization of decision and inhibitory trees for decision tables with many-valued decisions Item Type Article Authors Azad, Mohammad; Moshkov, Mikhail Citation Azad M, Moshkov M (2017) Multi-stage optimization of decision and inhibitory trees for decision tables with many-valued decisions. European Journal of Operational Research.

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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.