George Dantzig is widely regarded as the founder of this subject with his invention of the simplex algorithm in the 1940's. In this second volume, the theory of the items discussed in the first volume is expanded to include such additional advanced topics as variants of the simplex method; interior point methods, GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering and applied mathematics will thus find this volume of particular interest.
This book presents a novel approach to the formulation and solution of three classes of problems: the fully fuzzy transportation problem, the fully fuzzy transshipment problem, and fully fuzzy solid transportation problem. It points out some limitations of the existing formulations and approaches, indicating some possible, conceptually and algorithmically attractive solutions to alleviate them. In particular, the book describes new conceptual and algorithmic solutions for finding the fuzzy optimal solutions of the single-objective fully fuzzy transportation problems, the fully fuzzy transshipment problems and the fully fuzzy solid transportation problems. Moreover, based on the novel concepts and solutions proposed by combining the concept of a fully fuzzy solid transportation problem and a fully fuzzy transshipment problem, it describes a new class of problems, i.e. the fully fuzzy solid trans-shipment problem, together with its fuzzy linear programming formulation and some methods to find its fuzzy optimal solution. The book offers the readers a timely piece of literature in the field of fuzzy linear programming, and is expected to act as a source of inspiration for future research and applications.
In this contribution, for the first time, an effcient model of multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station is formulated.
Monte Carlo Methods in Fuzzy Optimization is a clear and didactic book about Monte Carlo methods using random fuzzy numbers to obtain approximate solutions to fuzzy optimization problems. The book includes various solved problems such as fuzzy linear programming, fuzzy regression, fuzzy inventory control, fuzzy game theory, and fuzzy queuing theory. The book will appeal to engineers, researchers, and students in Fuzziness and applied mathematics.
This book presents the necessary and essential backgrounds of fuzzy set theory and linear programming, particularly a broad range of common Fuzzy Linear Programming (FLP) models and related, convenient solution techniques. These models and methods belong to three common classes of fuzzy linear programming, namely: (i) FLP problems in which all coefficients are fuzzy numbers, (ii) FLP problems in which the right-hand-side vectors and the decision variables are fuzzy numbers, and (iii) FLP problems in which the cost coefficients, the right-hand-side vectors and the decision variables are fuzzy numbers. The book essentially generalizes the well-known solution algorithms used in linear programming to the fuzzy environment. Accordingly, it can be used not only as a textbook, teaching material or reference book for undergraduate and graduate students in courses on applied mathematics, computer science, management science, industrial engineering, artificial intelligence, fuzzy information processes, and operations research, but can also serve as a reference book for researchers in these fields, especially those engaged in optimization and soft computing. For textbook purposes, it also includes simple and illustrative examples to help readers who are new to the field.
This book presents the very concept of an index matrix and its related augmented matrix calculus in a comprehensive form. It mostly illustrates the exposition with examples related to the generalized nets and intuitionistic fuzzy sets which are examples of an extremely wide array of possible application areas. The present book contains the basic results of the author over index matrices and some of its open problems with the aim to stimulating more researchers to start working in this area.
This volume is the first of two containing selected papers from the International Conference on Advances in Mathematical Sciences, Vellore, India, December 2017 - Volume I. This meeting brought together researchers from around the world to share their work, with the aim of promoting collaboration as a means of solving various problems in modern science and engineering. The authors of each chapter present a research problem, techniques suitable for solving it, and a discussion of the results obtained. These volumes will be of interest to both theoretical- and application-oriented individuals in academia and industry. Papers in Volume I are dedicated to active and open areas of research in algebra, analysis, operations research, and statistics, and those of Volume II consider differential equations, fluid mechanics, and graph theory.
There are a myriad of mathematical problems that cannot be solved using traditional methods. The development of fuzzy expert systems has provided new opportunities for problem-solving amidst uncertainties. Fuzzy Systems: Concepts, Methodologies, Tools, and Applications is a comprehensive reference source on the latest scholarly research and developments in fuzzy rule-based methods and examines both theoretical foundations and real-world utilization of these logic sets. Featuring a range of extensive coverage across innovative topics, such as fuzzy logic, rule-based systems, and fuzzy analysis, this is an essential publication for scientists, doctors, engineers, physicians, and researchers interested in emerging perspectives and uses of fuzzy systems in various sectors.
This book constitutes the refereed proceedings of the International Conference on Logic, Information, Control and Computation, ICLICC 2011, held in Gandhigram, India, in February 2011. The 52 revised full papers presented were carefully reviewed and selected from 278 submissions. The papers are organized in topical sections on control theory and its real time applications, computational mathematics and its application to various fields, and information sciences focusing on image processing and neural networks.
