Rafik A Aliev

Oleg H Huseynov

Rashad R Aliyev

Akif A Alizadeh

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. Contents:The General Concept of a Restriction and Z-numbersDefinitions and Main Properties of Z-NumbersOperations on Continuous Z-NumbersOperations on Discrete Z-NumbersAlgebraic System of Z-NumbersZ-Number Based Operation Research ProblemsApplication of Z-Numbers Readership: Researchers, academics, professionals and graduate students in fuzzy logic, decision sciences and artificial intelligence. Keywords:Z-Number;Fuzzy Number;Interval Number;Random Number;Z-Information;Uncertain Numbers;Z-Arithmetic;Z-Regression;Z-Linear Programming;T-Norm

Theory and Applications

The Arithmetic of Z-Numbers

Lotfi A Zadeh

Nowadays, voluminous textbooks and monographs in fuzzy logic are devoted only to separate or some combination of separate facets of fuzzy logic. There is a lack of a single book that presents a comprehensive and self-contained theory of fuzzy logic and its applications. Written by world renowned authors, Lofti Zadeh, also known as the Father of Fuzzy Logic, and Rafik Aliev, who are pioneers in fuzzy logic and fuzzy sets, this unique compendium includes all the principal facets of fuzzy logic such as logical, fuzzy-set-theoretic, epistemic and relational. Theoretical problems are prominently illustrated and illuminated by numerous carefully worked-out and thought-through examples. This invaluable volume will be a useful reference guide for academics, practitioners, graduates and undergraduates in fuzzy logic and its applications.

Rafik A Aliev

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