Decision Making and Optimization

1. Front Matter

   Pages i-xi

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2. Special Matrices in Decision Making

   1. Front Matter

      Pages 1-1

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   2. Preliminaries

      • Martin Gavalec, Jaroslav Ramík, Karel Zimmermann

      Pages 3-28

   3. Pairwise Comparison Matrices in Decision Making

      • Martin Gavalec, Jaroslav Ramík, Karel Zimmermann

      Pages 29-90

   4. Preference Matrices with Fuzzy Elements in Decision Making

      • Martin Gavalec, Jaroslav Ramík, Karel Zimmermann

      Pages 91-115

3. Special Matrices in Max-Min Algebra

   1. Front Matter

      Pages 117-117

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   2. Optimization Problems Under Max-Min Separable Equation and Inequality Constraints

      • Martin Gavalec, Jaroslav Ramík, Karel Zimmermann

      Pages 119-161

   3. Interval Eigenproblem in Max-Min Algebra

      • Martin Gavalec, Jaroslav Ramík, Karel Zimmermann

      Pages 163-181

   4. Eigenproblem in Max-Drast and Max-Łukasiewicz Algebra

      • Martin Gavalec, Jaroslav Ramík, Karel Zimmermann

      Pages 183-221

4. Back Matter

   Pages 223-225

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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.

• Decision analysis
• Matrix analysis
• Max-min algebra
• Pairwise comparison
• t-norms
• Engineering Economics

“The main purpose of this monograph is to report on recent developments in the field of decision making and optimization, with a strong emphasis on useful techniques and ingenious ideas from matrix analysis and fuzzy set theory. … a wide variety of examples and counterexamples are included in order to help the interested reader to clarify difficult parts of the book. The book can be read by researchers and at some points by advanced graduates or undergraduates.” (Vasilios N. Katsikis, Mathematical Reviews, June, 2015)

“The authors present some special cases of matrices and discuss their various properties and applications. … In each chapter some theory is presented and followed by description of solving methods and examples. The book is a valuable contribution, useful for both graduate students and researchers.” (Marcin Anholcer, zbMATH 1317.90004, 2015)

• University of Hradec Kralove, Hradec Kralove, Czech Republic

  Martin Gavalec

• Silesian University in Opava, Karvina, Czech Republic

  Jaroslav Ramík

• Charles University in Prague, Prague, Czech Republic

  Karel Zimmermann

Prof. Martin Gavalec, Ph.D. is a professor of Applied Mathematics at the University of Hradec Kralove, Faculty of Informatics and Management, Czech Republic. His professional interests include non-standard optimization methods based on the maximum operation, in combination with further ones, such as the minimum or the fuzzy triangular norm operations. He is an author and co-author of 3 books in English and more than 45 papers listed in WoS.

Prof. Jaroslav Ramik, Ph.D. is a professor of Mathematics, Statistics and Operations Research at the Silesian University Opava, School of Business Karvina, Czech Republic. He is a head of Department of Mathematical methods in Economics. His professional interests include optimization methods in economics and decision making. He is an author of 6 books in English and more than 50 papers listed in WoS. He is active in the Czech Society for Operations Research where he served as a former president of the Society in two time periods.

Prof. Karel Zimmermann, D.Sc. is a professor of mathematics and operations research at the Faculty of mathematics and physics, Charles University in Prague, Czech Republic. His professional interests include optimization methods in economics. He is an author of 5 books in English and more than 40 papers listed in WoS.

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