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2018 | Buch

Edgeworth-Pareto Principle Kapitel lesen Erstes Kapitel lesen

Reduction of the Pareto Set

An Axiomatic Approach

verfasst von: Prof. Dr. Vladimir D. Noghin

Verlag: Springer International Publishing

Buchreihe : Studies in Systems, Decision and Control

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book focuses on the issues of decision-making with several numerical criteria. It introduces an original general approach to solving multicriteria problems given quantitative information about the preference relation of a decision-maker. It considers the problems with crisp as well as fuzzy preference relations, accepting the four axioms of “reasonable choice”. Further, it defines the notion of an information quantum about the preference relation of a decision-maker and studies the reduction of the Pareto set using a finite collection of information quanta, demonstrating that the original approach yields a good approximation for the set of nondominated alternatives in a multicriteria problem. Lastly, it analyzes a possible combination of the axiomatic approach with other well-known methods. Intended for a wide range of professionals involved in solving multicriteria problems, including researchers, design engineers, product engineers, developers and analysts, the book is also a valuable resource for undergraduate and postgraduate students of mathematics, economics, and engineering.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Edgeworth-Pareto Principle
Abstract
This chapter introduces and discusses the basic notions of decision-making in a multicriteria environment, namely, the set of feasible alternatives, the vector criterion and the preference relation of a decision-maker. Here we formulate the multicriteria choice problem. In addition, Chap. 1 defines a pair of fundamentally important notions, the set of nondominated alternatives and the Pareto set, which are vital for the statement and rigorous substantiation of the Edgeworth-Pareto principle.
Vladimir D. Noghin
Chapter 2. Pareto Set Reduction Based on Elementary Information Quantum
Abstract
The current chapter lays the foundation for the original axiomatic approach. First, we introduce the last (fourth) axiom on the invariance of preference relation.
Vladimir D. Noghin
Chapter 3. Pareto Set Reduction Based on General Information Quantum
Abstract
The notion of an elementary information quantum for two criteria (see Chap. 2) is extended to the general case of two groups of criteria. We study the properties of a general information quantum, demonstrating how it should be used for Pareto set reduction.
Vladimir D. Noghin
Chapter 4. Pareto Set Reduction Using Elementary Collections of Information Quanta
Abstract
This chapter focuses on the application of some “simple” collections of information quanta. We establish that some collections can be inconsistent.
Vladimir D. Noghin
Chapter 5. Pareto Set Reduction Based on Collections of Information Quanta
Abstract
Here we further develop the results of the previous chapter on Pareto set reduction using given finite collections of mutually dependent information quanta about the DM’s preference relation.
Vladimir D. Noghin
Chapter 6. Completeness Property of Information Quanta
Abstract
In this chapter, we justify theoretically the original axiomatic approach to Pareto set reduction based on a finite collection of information quanta. Here the exposition seems most difficult in mathematical terms, but the readers with an insufficient background may skip it without losing the comprehension of further material. The whole essence of the results derived below can be expressed as follows. Information in the form of quanta is complete: for any multicriteria choice problem from a definite (rather wide) class, it is possible to find the unknown set of nondominated vectors (nondominated alternatives) with an arbitrary accuracy only based on such information. Moreover, if the number of feasible vectors is finite, then the set of nondominated vectors can be constructed precisely.
Vladimir D. Noghin
Chapter 7. Pareto Set Reduction Using Fuzzy Information
Abstract
In a series of applications-relevant multicriteria choice problems, the available information about the DM’s preference relation can be fuzzy in the sense that it is impossible to define explicitly the preference for one alternative rather than another, since there exist the pros and cons of it.
Vladimir D. Noghin
Chapter 8. Decision-Making Based on Information Quanta: Methodology and Practice
Abstract
This chapter considers in brief the aspects of decision-making by humans and then presents the axiomatic approach to Pareto set (domain of compromise) reduction based on information quanta about the DM’s preference relation. The corresponding theoretical background can be found in the previous chapters, and here we describe the axiomatic approach without mathematical details, as well as give some recommendations on usage. In addition, possible ways to combine this approach with some multicriteria scalarization methods and some potential extensions are discussed.
Vladimir D. Noghin
Backmatter
Metadaten
Titel
Reduction of the Pareto Set
verfasst von
Prof. Dr. Vladimir D. Noghin
Copyright-Jahr
2018
Electronic ISBN
978-3-319-67873-3
Print ISBN
978-3-319-67872-6
DOI
https://doi.org/10.1007/978-3-319-67873-3

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