Fuzzy dual numbers. Theory and applications
This book concentrates on a special class of fuzzy numbers, fuzzy dual numbers which are at the crossroad between classical fuzzy numbers and dual numbers in an attempt to take benefits from the properties of both of them. Besides offering a guide to their properties, operations, and applications, it discusses some of their advantages concerning classical fuzzy numbers and describes the most important operations together with a set of interesting applications in e.g. optimization, decision-making, and system design. The book provides the necessary theoretical background to apply this particular subset of fuzzy numbers to decision-making problems involving uncertainty. Thus, fuzzy dual calculus has been developed in such a way that the interpretation of their dual part as an uncertainty level remains valid through the basic operations with these numbers. Further, it shows how to solve selected engineering and management problems and includes detailed numerical examples. May be deemed that the approach developed in this book provides a way to tackle a large class of analysis and optimization problems under uncertainty with possible respect between the accuracy of the representation of uncertainty and the resulting computer load.
scientific article; zbMATH DE number 6833068