Rafik A Aliev

The Arithmetic of Z-Numbers: Theory and Applications

Real-world information is imperfect and is usually described in natural language (NL). Moreover, this information is often partially reliable and a degree of reliability is also expressed in NL. In view of this, the concept of a Z-number is a more adequate concept for the description of real-world information. The main critical problem that naturally arises in processing Z-numbers-based information is the computation with Z-numbers. Nowadays, there is no arithmetic of Z-numbers suggested in existing literature. This book is the first to present a comprehensive and self-contained theory of Z-arithmetic and its applications. Many of the concepts and techniques described in the book, with carefully worked-out examples, are original and appear in the literature for the first time.The book will be helpful for professionals, academics, managers and graduate students in fuzzy logic, decision sciences, artificial intelligence, mathematical economics, and computational economics. Readership: Researchers, academics, professionals and graduate students in fuzzy logic, decision sciences and artificial intelligence.

Decision Theory with Imperfect Information

Every day decision making in complex human-centric systems are characterized by imperfect decision-relevant information. The principal problems with the existing decision theories are that they do not have capability to deal with situations in which probabilities and events are imprecise. In this book, we describe a new theory of decision making with imperfect information. The aim is to shift the foundation of decision analysis and economic behavior from the realm bivalent logic to the realm fuzzy logic and Z-restriction, from external modeling of behavioral decisions to the framework of combined states. This book will be helpful for professionals, academics, managers and graduate students in fuzzy logic, decision sciences, artificial intelligence, mathematical economics, and computational economics. Readership: Professionals, academics, managers and graduate students in fuzzy logic, decision sciences, artificial intelligence, mathematical economics, and computational economics.

BEHAVIORAL DECISION MAKING WITH COMBINED STATES UNDER IMPERFECT INFORMATION

Behavioral decision making is an area of multidisciplinary research attracting growing interest of scientists and practitioners, economists, and business people. A wide spectrum of successful theories is present now, including Prospect theory, multiple priors models, studies on altruism, trust and fairness. However, these theories are developed for precise and complete information, whereas real information concerning a decision makers (DM) behavior and environment is imperfect, qualitative, and, as a result, often described in natural language (NL). We suggest an approach based on modeling a DMs behavior by a set of states. Each state represents a certain principal behavior. In our approach, states of nature and DMs states constitute a single space of combined states. For formalizing relevant information described in NL, we use fuzzy set theory. The utility model is based on Choquet-like integration over combined states. The investigations show that Expected Utility, Choquet Expected Utility and Cumulative Prospect Theory are special cases of the suggested approach. We apply the suggested approach to solving a benchmark and a real-life decision problem. The obtained results show validity of the suggested approach.