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.