Series:

Studies in Fuzziness and Soft Computing

10 primary works

Book 20

Cover of Fuzzy Mathematics
This text deals with fuzzy graph theory, fuzzy topology, fuzzy geometry, and fuzzy abstract algebra. The purpose of the book is to present the concepts of fuzzy mathematics which have applications to engineering, computer science, and mathematics. Some specific applications areas are cluster analysis, digital image processing, fractal compression, chaotic fuzzy mappings, coding theory, automata theory, and nonlinear systems of fuzzy equations. The book is written with engineers and computer scientists in mind. Some mathematical sophistication is required of the reader. However the style is geared to a general audience. Most theorems are stated without proof and many examples are presented. Results of mathematics are reviewed as needed.

Book 46

Cover of Fuzzy Graphs and Fuzzy Hypergraphs
In the course of fuzzy technological development, fuzzy graph theory was identified quite early on for its importance in making things work. Two very important and useful concepts are those of granularity and of nonlinear ap proximations. The concept of granularity has evolved as a cornerstone of Lotfi A.Zadeh's theory of perception, while the concept of nonlinear approx imation is the driving force behind the success of the consumer electronics products manufacturing. It is fair to say fuzzy graph theory paved the way for engineers to build many rule-based expert systems. In the open literature, there are many papers written on the subject of fuzzy graph theory. However, there are relatively books available on the very same topic. Professors' Mordeson and Nair have made a real contribution in putting together a very com prehensive book on fuzzy graphs and fuzzy hypergraphs. In particular, the discussion on hypergraphs certainly is an innovative idea. For an experienced engineer who has spent a great deal of time in the lab oratory, it is usually a good idea to revisit the theory. Professors Mordeson and Nair have created such a volume which enables engineers and design ers to benefit from referencing in one place. In addition, this volume is a testament to the numerous contributions Professor John N. Mordeson and his associates have made to the mathematical studies in so many different topics of fuzzy mathematics.

Book 58

Cover of Fuzzy Discrete Structures
This ambitious exposition by Malik and Mordeson on the fuzzification of discrete structures not only supplies a solid basic text on this key topic, but also serves as a viable tool for learning basic fuzzy set concepts "from the ground up" due to its unusual lucidity of exposition. While the entire presentation of this book is in a completely traditional setting, with all propositions and theorems provided totally rigorous proofs, the readability of the presentation is not compromised in any way; in fact, the many ex­ cellently chosen examples illustrate the often tricky concepts the authors address. The book's specific topics - including fuzzy versions of decision trees, networks, graphs, automata, etc. - are so well presented, that it is clear that even those researchers not primarily interested in these topics will, after a cursory reading, choose to return to a more in-depth viewing of its pages. Naturally, when I come across such a well-written book, I not only think of how much better I could have written my co-authored monographs, but naturally, how this work, as distant as it seems to be from my own area of interest, could nevertheless connect with such. Before presenting the briefest of some ideas in this direction, let me state that my interest in fuzzy set theory (FST) has been, since about 1975, in connecting aspects of FST directly with corresponding probability concepts. One chief vehicle in carrying this out involves the concept of random sets.

Book 130

Cover of Uncertainty in Multi-Source Databases

Database and database systems have become an essential part of everyday life, such as in banking activities, online shopping, or reservations of airline tickets and hotels. These trends place more demands on the capabilities of future database systems, which need to evolve into decision making systems based on data from multiple sources with varying reliability. In this book a model for the next generation of database systems is presented. It is demonstrated how to quantize favorable and unfavorable qualitative facts so that they can be stored and processed efficiently, as well as how to use the reliability of the contributing sources in our decision makings. The concept of a confidence index set (ciset), is introduced in order to mathematically model the above issues. A simple introduction to relational database systems is given allowing anyone with no background in database theory to appreciate the further contents of this work, especially the extended relational operations and semantics of the ciset relational database model.

Book 131

Cover of Fuzzy Semigroups
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.

Book 182

Cover of Fuzzy Group Theory

This book presents an up-to-date account of research in important topics of fuzzy group theory. It concentrates on the theoretical aspects of fuzzy subgroups of a group. It includes applications to abstract recognition problems and to coding theory. The book begins with basic properties of fuzzy subgroups. Fuzzy subgroups of Hamiltonian, solvable, P-Hall, and nilpotent groups are discussed. Construction of free fuzzy subgroups is determined. Numerical invariants of fuzzy subgroups of Abelian groups are developed. The problem in group theory of obtaining conditions under which a group can be expressed as a direct product of its normal subgroups is considered. Methods for deriving fuzzy theorems from crisp ones are presented and the embedding of lattices of fuzzy subgroups into lattices of crisp groups is discussed as well as deriving membership functions from similarity relations. The material presented makes this book a good reference for graduate students and researchers working in fuzzy group theory.

Book 225

Cover of Applying Fuzzy Mathematics to Formal Models in Comparative Politics

This book explores the intersection of fuzzy mathematics and the spatial modeling of preferences in political science. Beginning with a critique of conventional modeling approaches predicated on Cantor set theoretical assumptions, the authors outline the potential benefits of a fuzzy approach to the study of ambiguous or uncertain preference profiles. This is a good text for a graduate seminar in formal modeling. It is also suitable as an introductory text in fuzzy mathematics.

Book 278

Cover of Fuzzy Semirings with Applications to Automata Theory

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.

Book 363

Cover of Fuzzy Graph Theory

This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. It introduces readers to fundamental theories, such as Craine's work on fuzzy interval graphs, fuzzy analogs of Marczewski's theorem, and the Gilmore and Hoffman characterization. It also introduces them to the Fulkerson and Gross characterization and Menger's theorem, the applications of which will be discussed in a forthcoming book by the same authors. This book also discusses in detail important concepts such as connectivity, distance and saturation in fuzzy graphs.

Thanks to the good balance between the basics of fuzzy graph theory and new findings obtained by the authors, the book offers an excellent reference guide for advanced undergraduate and graduate students in mathematics, engineering and computer science, and an inspiring read for all researchers interested in new developments in fuzzy logic and applied mathematics.

Book 375

Cover of Advanced Topics in Fuzzy Graph Theory

This book builds on two recently published books by the same authors on fuzzy graph theory. Continuing in their tradition, it provides readers with an extensive set of tools for applying fuzzy mathematics and graph theory to social problems such as human trafficking and illegal immigration. Further, it especially focuses on advanced concepts such as connectivity and Wiener indices in fuzzy graphs, distance, operations on fuzzy graphs involving t-norms, and the application of dialectic synthesis in fuzzy graph theory. Each chapter also discusses a number of key, representative applications. Given its approach, the book provides readers with an authoritative, self-contained guide to – and at the same time an inspiring read on – the theory and modern applications of fuzzy graphs. For newcomers, the book also includes a brief introduction to fuzzy sets, fuzzy relations and fuzzy graphs.