Fuzzy Automata Theory offers the first in-depth treatment of the theory and mathematics of fuzzy automata and fuzzy languages. It effectively compares and contrasts the different approaches used in fuzzy mathematics and automata and includes complete proofs of the theoretical results presented. More than 60 figures and 125 examples illustrate the results, and exercises in each chapter serve not only to test understanding, but also to present material not covered in detail within the text. Although the book is theoretical in nature, the authors also discuss applications in a variety of fields, including databases, medicine, learning systems, and pattern recognition.

This book consists of selected papers written by the founder of fuzzy set theory, Lotfi A Zadeh. Since Zadeh is not only the founder of this field, but has also been the principal contributor to its development over the last 30 years, the papers contain virtually all the major ideas in fuzzy set theory, fuzzy logic, and fuzzy systems in their historical context. Many of the ideas presented in the papers are still open to further development. The book is thus an important resource for anyone interested in the areas of fuzzy set theory, fuzzy logic, and fuzzy systems, as well as their applications. Moreover, the book is also intended to play a useful role in higher education, as a rich source of supplementary reading in relevant courses and seminars.The book contains a bibliography of all papers published by Zadeh in the period 1949-1995. It also contains an introduction that traces the development of Zadeh's ideas pertaining to fuzzy sets, fuzzy logic, and fuzzy systems via his papers. The ideas range from his 1965 seminal idea of the concept of a fuzzy set to ideas reflecting his current interest in computing with words — a computing in which linguistic expressions are used in place of numbers.Places in the papers, where each idea is presented can easily be found by the reader via the Subject Index.

Ten years ago, Zadeh has brought into vogue the use of a name. Scientists no is an increasing less than poets strike off words that fit a situation. Today there recognition that for understanding vagueness, a fuzzy approach is required. We are just going through ~ transient period. From discussions of general philosophy to practical methods for system analysis. Unfortunately, much of the existing research is scattered. The practitioner interested in these methods face the challenge of sorting through a vast amount of literature to find a core on which to build. One of the objects of this book was to facilitate communication by bringing toge ther different viewpoints and coloring them from a common viewpoint. Since the romanian version appeared, at the very beginning of 1974, there has been a rapid growth in the literature of fuzzy modelling. A minor revision would have left the book quite out-of-date. The opportunity has been taken to correct, clarify, and update. Inexactness is implicit in human behaviour and erare humanum est. It is a pleasure to acknowledge the help we have received in preparing this version. The opportunity to see an english edition was a powerful stimulus, and we are grateful to Salomon Klaczko for making this possible. Another debt is to all fuzzy authors we have quoted. Their fascinating papers kindled our interest in the subject.

Lotfi Zadeh introduced the notion of a fuzzy subset of a set in 1965. Ris seminal paper has opened up new insights and applications in a wide range of scientific fields. Azriel Rosenfeld used the notion of a fuzzy subset to put forth cornerstone papers in several areas of mathematics, among other discplines. Rosenfeld is the father of fuzzy abstract algebra. Kuroki is re sponsible for much of fuzzy ideal theory of semigroups. Others who worked on fuzzy semigroup theory, such as Xie, are mentioned in the bibliogra phy. The purpose of this book is to present an up to date account of fuzzy subsemigroups and fuzzy ideals of a semigroup. We concentrate mainly on theoretical aspects, but we do include applications. The applications are in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. An extensive account of fuzzy automata and fuzzy languages is given in [100]. Consequently, we only consider results in these areas that have not appeared in [100] and that pertain to semigroups. In Chapter 1, we review some basic results on fuzzy subsets, semigroups, codes, finite state machines, and languages. The purpose of this chapter is to present basic results that are needed in the remainder of the book. In Chapter 2, we introduce certain fuzzy ideals of a semigroup, namely, fuzzy two-sided ideals, fuzzy bi-ideals, fuzzy interior ideals, fuzzy quasi ideals, and fuzzy generalized bi-ideals.

The purpose of this book is to present an up to date account of fuzzy ideals of a semiring. The book concentrates on theoretical aspects and consists of eleven chapters including three invited chapters. Among the invited chapters, two are devoted to applications of Semirings to automata theory, and one deals with some generalizations of Semirings. This volume may serve as a useful hand book for graduate students and researchers in the areas of Mathematics and Theoretical Computer Science.

A step-by-step development of the theory of automata, languages and computation. Intended for use as the basis of an introductory course at both junior and senior levels, the text is organized so as to allow the design of various courses based on selected material. It features basic models of computation, formal languages and their properties; computability, decidability and complexity; a discussion of modern trends in the theory of automata and formal languages; design of programming languages, including the development of a new programming language; and compiler design, including the construction of a complete compiler. Alexander Meduna uses clear definitions, easy-to-follow proofs and helpful examples to make formerly obscure concepts easy to understand. He also includes challenging exercises and programming projects to enhance the reader's comprehension, and many 'real world' illustrations and applications in practical computer science.