Fuzzy Mathematical Programming and Fuzzy Matrix Games PDF Download

Author: C. R. Bector
Publisher: Springer
ISBN: 3540323716
Category : Technology & Engineering
Languages : en
Pages : 248

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Book Description
Game theory has already proved its tremendous potential for con?ict resolution problems in the ?elds of Decision Theory and Economics. In the recent past, there have been attempts to extend the results of crisp game theory to those con?ict resolution problems which are fuzzy in nature e.g. Nishizaki and Sakawa [61] and references cited there in. These developments have lead to the emergence of a new area in the literature called fuzzy games. Another area in the fuzzy decision theory, which has been growing very fast is the area of fuzzy mathematical programming and its applications to various branches of sciences, Engineering and Management. In the crisp scenario, there exists a beautiful relationship between two person zero sum matrix game theory and duality in linear p- gramming. It is therefore natural to ask if something similar holds in the fuzzy scenario as well. This discussion essentially constitutes the core of our presentation. The objective of this book is to present a systematic and focussed study of the application of fuzzy sets to two very basic areas of decision theory, namely Mathematical Programming and Matrix Game Theory.

Author: C. R. Bector
Publisher: Springer Science & Business Media
ISBN: 3540237291
Category : Business & Economics
Languages : en
Pages : 248

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Book Description
This book presents a systematic and focused study of the application of fuzzy sets to two basic areas of decision theory, namely Mathematical Programming and Matrix Game Theory. Apart from presenting most of the basic results available in the literature on these topics, the emphasis is on understanding their natural relationship in a fuzzy environment. The study of duality theory for fuzzy mathematical programming problems plays a key role in understanding this interrelationship. For this, a theoretical framework of duality in fuzzy mathematical programming and conceptualization of the solution of a fuzzy game is created on the lines of their crisp counterparts. Most of the theoretical results and associated algorithms are illustrated through small numerical examples from actual applications.

Author: Deng-Feng Li
Publisher: Springer
ISBN: 3662484765
Category : Business & Economics
Languages : en
Pages : 176

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Book Description
This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics.

Author: Shi-Yu Huang
Publisher: Springer
ISBN: 9789401074490
Category : Business & Economics
Languages : en
Pages : 0

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Book Description
Operations Research is a field whose major contribution has been to propose a rigorous fonnulation of often ill-defmed problems pertaining to the organization or the design of large scale systems, such as resource allocation problems, scheduling and the like. While this effort did help a lot in understanding the nature of these problems, the mathematical models have proved only partially satisfactory due to the difficulty in gathering precise data, and in formulating objective functions that reflect the multi-faceted notion of optimal solution according to human experts. In this respect linear programming is a typical example of impressive achievement of Operations Research, that in its detenninistic fonn is not always adapted to real world decision-making : everything must be expressed in tenns of linear constraints ; yet the coefficients that appear in these constraints may not be so well-defined, either because their value depends upon other parameters (not accounted for in the model) or because they cannot be precisely assessed, and only qualitative estimates of these coefficients are available. Similarly the best solution to a linear programming problem may be more a matter of compromise between various criteria rather than just minimizing or maximizing a linear objective function. Lastly the constraints, expressed by equalities or inequalities between linear expressions, are often softer in reality that what their mathematical expression might let us believe, and infeasibility as detected by the linear programming techniques can often been coped with by making trade-offs with the real world.

Author: S. K. Neogy
Publisher: World Scientific
ISBN: 9812813225
Category : Mathematics
Languages : en
Pages : 498

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Book Description
This edited book presents recent developments and state-of-the-art review in various areas of mathematical programming and game theory. It is a peer-reviewed research monograph under the ISI Platinum Jubilee Series on Statistical Science and Interdisciplinary Research. This volume provides a panoramic view of theory and the applications of the methods of mathematical programming to problems in statistics, finance, games and electrical networks. It also provides an important as well as timely overview of research trends and focuses on the exciting areas like support vector machines, bilevel programming, interior point method for convex quadratic programming, cooperative games, non-cooperative games and stochastic games. Researchers, professionals and advanced graduates will find the book an essential resource for current work in mathematical programming, game theory and their applications. Sample Chapter(s). Foreword (45 KB). Chapter 1: Mathematical Programming and its Applications in Finance (177 KB). Contents: Mathematical Programming and Its Applications in Finance (L C Thomas); Anti-Stalling Pivot Rule for Linear Programs with Totally Unimodular Coefficient Matrix (S N Kabadi & A P Punnen); A New Practically Efficient Interior Point Method for Convex Quadratic Programming (K G Murty); A General Framework for the Analysis of Sets of Constraints (R Caron & T Traynor), Tolerance-Based Algorithms for the Traveling Salesman Problem (D Ghosh et al.); On the Membership Problem of the Pedigree Polytope (T S Arthanari); Exact Algorithms for a One-Defective Vertex Colouring Problem (N Achuthan et al.); Complementarity Problem Involving a Vertical Block Matrix and Its Solution Using Neural Network Model (S K Neogy et al.); Fuzzy Twin Support Vector Machines for Pattern Classification (R Khemchandani et al.); An Overview of the Minimum Sum of Absolute Errors Regression (S C Narula & J F Wellington); Hedging Against the Market with No Short Selling (S A Clark & C Srinivasan); Mathematical Programming and Electrical Network Analysis II: Computational Linear Algebra Through Network Analysis (H Narayanan); Dynamic Optimal Control Policy in Price and Quality for High Technology Product (A K Bardhan & U Chanda); Forecasting for Supply Chain and Portfolio Management (K G Murty); Variational Analysis in Bilevel Programming (S Dempe et al.); Game Engineering (R J Aumann); Games of Connectivity (P Dubey & R Garg); A Robust Feedback Nash Equilibrium in a Climate Change Policy Game (M Hennlock); De Facto Delegation and Proposer Rules (H Imai & K Yonezaki); The Bargaining Set in Effectivity Function (D Razafimahatolotra); Dynamic Oligopoly as a Mixed Large Game OCo Toy Market (A Wiszniewska-Matyszkiel); On Some Classes of Balanced Games (R B Bapat); Market Equilibrium for Combinatorial Auctions and the Matching Core of Nonnegative TU Games (S Lahiri); Continuity, Manifolds, and Arrow''s Social Choice Problem (K Saukkonen); On a Mixture Class of Stochastic Games with Ordered Field Property (S K Neogy). Readership: Researchers, professionals and advanced students in mathematical programming, game theory, management sciences and computational mathematics.

Author: Young-Jou Lai
Publisher: Springer Science & Business Media
ISBN: 364248753X
Category : Business & Economics
Languages : en
Pages : 317

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Book Description
In the last 25 years, the fuzzy set theory has been applied in many disciplines such as operations research, management science, control theory,artificial intelligence/expert system, etc. In this volume, methods and applications of fuzzy mathematical programming and possibilistic mathematical programming are first systematically and thoroughly reviewed and classified. This state-of-the-art survey provides readers with a capsule look into the existing methods, and their characteristics and applicability to analysis of fuzzy and possibilistic programming problems. To realize practical fuzzy modelling, we present solutions for real-world problems including production/manufacturing, transportation, assignment, game, environmental management, resource allocation, project investment, banking/finance, and agricultural economics. To improve flexibility and robustness of fuzzy mathematical programming techniques, we also present our expert decision-making support system IFLP which considers and solves all possibilities of a specific domain of (fuzzy) linear programming problems. Basic fuzzy set theories, membership functions, fuzzy decisions, operators and fuzzy arithmetic are introduced with simple numerical examples in aneasy-to-read and easy-to-follow manner. An updated bibliographical listing of 60 books, monographs or conference proceedings, and about 300 selected papers, reports or theses is presented in the end of this study.

Author: Young-Jou Lai
Publisher:
ISBN: 9783642487545
Category :
Languages : en
Pages : 324

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Book Description

Author: Ichiro Nishizaki
Publisher: Physica
ISBN: 3790818305
Category : Mathematics
Languages : en
Pages : 264

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Book Description
Decision makers in managerial and public organizations often encounter de cision problems under conflict or competition, because they select strategies independently or by mutual agreement and therefore their payoffs are then affected by the strategies of the other decision makers. Their interests do not always coincide and are at times even completely opposed. Competition or partial cooperation among decision makers should be considered as an essen tial part of the problem when we deal with the decision making problems in organizations which consist of decision makers with conflicting interests. Game theory has been dealing with such problems and its techniques have been used as powerful analytical tools in the resolution process of the decision problems. The publication of the great work by J. von Neumann and O. Morgen stern in 1944 attracted attention of many people and laid the foundation of game theory. We can see remarkable advances in the field of game theory for analysis of economic situations and a number of books in the field have been published in recent years. The aim of game theory is to specify the behavior of each player so as to optimize the interests of the player. It then recommends a set of solutions as strategies so that the actions chosen by each decision maker (player) lead to an outcome most profitable for himself or her self.

Author: Deng-Feng Li
Publisher: Springer
ISBN: 3642407129
Category : Technology & Engineering
Languages : en
Pages : 459

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Book Description
The focus of this book is on establishing theories and methods of both decision and game analysis in management using intuitionistic fuzzy sets. It proposes a series of innovative theories, models and methods such as the representation theorem and extension principle of intuitionistic fuzzy sets, ranking methods of intuitionistic fuzzy numbers, non-linear and linear programming methods for intuitionistic fuzzy multi-attribute decision making and (interval-valued) intuitionistic fuzzy matrix games. These theories and methods form the theory system of intuitionistic fuzzy decision making and games, which is not only remarkably different from those of the traditional, Bayes and/or fuzzy decision theory but can also provide an effective and efficient tool for solving complex management problems. Since there is a certain degree of inherent hesitancy in real-life management, which cannot always be described by the traditional mathematical methods and/or fuzzy set theory, this book offers an effective approach to using the intuitionistic fuzzy set expressed with membership and non-membership functions. This book is addressed to all those involved in theoretical research and practical applications from a variety of fields/disciplines: decision science, game theory, management science, fuzzy sets, operational research, applied mathematics, systems engineering, industrial engineering, economics, etc.

Author: Samuel Karlin
Publisher: Elsevier
ISBN: 1483222985
Category : Mathematics
Languages : en
Pages : 444

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Book Description
Matrix Games, Programming, and Mathematical Economics deals with game theory, programming theory, and techniques of mathematical economics in a single systematic theory. The principles of game theory and programming are applied to simplified problems related to economic models, business decisions, and military tactics. The book explains the theory of matrix games and some of the tools used in the analysis of matrix games. The text describes optimal strategies for matrix games which have two basic properties, as well as the construction of optimal strategies. The book investigates the structure of sets of solutions of discrete matrix games, with emphasis on the class of games whose solutions are unique. The examples show the use of dominance concepts, symmetries, and probabilistic arguments that emphasize the principles of game theory. One example involves two opposing political parties in an election campaign, particularly, how they should distribute their advertising efforts for wider exposure. The text also investigates how to determine an optimal program from several choices that results with the maximum or minimum objective. The book also explores the analogs of the duality theorem, the equivalence of game problems to linear programming problems, and also the inter-industry nonlinear activity analysis model requiring special mathematical methods. The text will prove helpful for students in advanced mathematics and calculus. It can be appreciated by mathematicians, engineers, economists, military strategists, or statisticians who formulate decisions using mathematical analysis and linear programming.