Generalized Fuzzy Matrices And Relations

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(Generalized) Fuzzy Matrices And Relations

The book provides an overview of the main concepts and results related to fuzzy matrices and fuzzy relations, using 'fuzzy' in a general sense to mean many-valued. This overview, along with numerous references to original contributions dispersed across various journals, serves as a comprehensive guide for further exploration.This volume can be viewed in two ways: (i) as a companion to the author's previous work, 'Relations: Concrete, Abstract, and Applied' (published by WSPC, 2020), but with a distinct emphasis on many-valued concepts; or (ii) as a standalone volume that can be read independently, which necessarily includes some repetition of material from the earlier book as preliminary or reference content.Similar to the previous book, this one does not present new findings but offers a self-contained compilation of known results selected from the extensive research conducted over the past five decades, arranged in a systematic manner.The topics covered in this text have been the subject of intensive research over the last two decades, yet there has been no book publication on this subject for over 15 years. This book aims to bridge that gap.
(generalized) Fuzzy Matrices Relationshb

Author: Herbert Toth
language: en
Publisher: World Scientific Publishing Company
Release Date: 2025
"The book provides an overview on the main concepts and results around fuzzy matrices and fuzzy relations ('fuzzy' taken in a general sense, meaning many-valued). This overview, together with a lot of links to original contributions scattered over many journals, should provide a sufficient guide for where to proceed. There are two ways how this volume can be regarded: (i) as a companion to my Relations: Concrete, Abstract, and Applied (also published by WSPC, 2020), but this time with a clear emphasis on the many-valued concepts, or (ii) as a stand-alone volume that can be read independently, hence necessarily including some repetitions from the former one as preliminary or reference material. As my former book, also this one does not really present new, but tries to give a rather self-contained compilation of known results selected from the huge amount attained over the last five decades and structured in a hopefully somewhat systematic arrangement. The topics dealt with in the current text have seen intensive research activities during the last two decades, but there has been no book publication for more than 15 years. So I have taken the opportunity to reduce the resulting gap"--
Fuzzy Matrix

This book aims to introduce fuzzy matrix theory as a basic framework for characterizing the full scope of the fuzzy sets concept and its relationship with the increasingly important concept of information and complexity in various sciences and professions. The book provides a wide coverage on the theoretical developments of fuzzy matrices and fuzzy vector spaces, on the theory of generalized inverses for fuzzy matrices, on fuzzy relations and on partial orderings on fuzzy matrices. The book also discusses the role of fuzzy matrices in the spectral theory of linear transformations on finite dimensional vector spaces. The concept of fuzzy matrix and its applications in document retrieval system, medical diagnosis, database management system, decision making theory and dynamical systems are developediteratively and illustrated with suitable examples wherever necessary. Each chapter has brief notes and exercises for the benefit of students.