Reduction of the Pareto Set

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.

Edgeworth-Pareto Principle.- Pareto set reduction based on elementary information quantum.- Pareto set reduction based on general information quantum.- Pareto set reduction using elementary collections of information quanta.- Pareto set reduction based on collections of information quanta.- Completeness property of information quanta.- Pareto set reduction using fuzzy information.- Decision-making based on information quanta: Methodology and Practice.