Gavalec, Martin, Ramík, Jaroslav, Zimmermann, Karel
2015, XI, 225 p. 13 illus.
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First book combining decision analysis with max-min algebra in inexact and fuzzy environment
Investigates the well-known method of pairwise comparison and reveals surprising properties and interconnections
Uses special matrices in max-min algebra in nonstandard applications
The book is a benefit for graduate and postgraduate students in the areas of operations research, decision theory, optimization theory, linear algebra, interval analysis, and fuzzy sets. The book will also be useful for the researchers in the respective areas. The first part of the book deals with decision making problems and procedures that have been established to combine opinions about alternatives related to different points of view. Procedures based on pairwise comparisons are thoroughly investigated. In the second part we investigate optimization problems where objective functions and constraints are characterized by extremal operators such as maximum, minimum or various triangular norms (t-norms). Matrices in max-min algebra are useful in applications such as automata theory, design of switching circuits, logic of binary relations, medical diagnosis, Markov chains, social choice, models of organizations, information systems, political systems and clustering. The input data in real problems are usually not exact and can be characterized by interval values.
Special Matrices in Decision Making: Preliminaries.- Pairwise Comparison Matrices in Decision Making.- Preference Matrices with Fuzzy Elements in Decision Making.- Special Matrices in Max-Min Algebra: Optimization Problems under Max-Min Separable Constraints.