Decision Making and Optimization

This book offers insights into decision-making and optimization techniques for students and researchers, focusing on practical applications and theoretical foundations.

The book Decision Making and Optimization serves as a valuable resource for graduate and postgraduate students across various fields, including operations research, decision theory, optimization theory, linear algebra, interval analysis, and fuzzy sets. It also provides significant insights for researchers engaged in these areas. By addressing both theoretical and practical aspects, this book aims to enhance the understanding of complex decision-making processes and optimization techniques.

In the initial section of Decision Making and Optimization, the focus is on decision-making problems and the methodologies developed for integrating diverse opinions regarding alternatives. The text delves deeply into procedures based on pairwise comparisons, offering a comprehensive examination of their applications and effectiveness in various scenarios. This foundational knowledge sets the stage for the subsequent exploration of optimization challenges.

The latter part of the book shifts attention to optimization problems characterized by objective functions and constraints defined through extremal operators, such as maximum, minimum, or triangular norms (t-norms). The discussion of matrices in max-min algebra reveals their practical applications in fields such as automata theory, circuit design, medical diagnosis, and social choice. The book also emphasizes the importance of handling input data that may not be precise, often represented by interval values, reflecting the complexities encountered in real-world problems.