Fuzzy Decision Procedures with Binary Relations

Fuzzy Decision Procedures with Binary Relations

In decision theory there are basically two appr~hes to the modeling of individual choice: one is based on an absolute representation of preferences leading to a ntDnerical expression of preference intensity. This is utility theory.

Author: Leonid Kitainik

Publisher: Springer Science & Business Media

ISBN: 9789401119603

Category: Mathematics

Page: 255

View: 969

In decision theory there are basically two appr~hes to the modeling of individual choice: one is based on an absolute representation of preferences leading to a ntDnerical expression of preference intensity. This is utility theory. Another approach is based on binary relations that encode pairwise preference. While the former has mainly blossomed in the Anglo-Saxon academic world, the latter is mostly advocated in continental Europe, including Russia. The advantage of the utility theory approach is that it integrates uncertainty about the state of nature, that may affect the consequences of decision. Then, the problems of choice and ranking from the knowledge of preferences become trivial once the utility function is known. In the case of the relational approach, the model does not explicitly accounts for uncertainty, hence it looks less sophisticated. On the other hand it is more descriptive than normative in the first stand because it takes the pairwise preference pattern expressed by the decision-maker as it is and tries to make the best out of it. Especially the preference relation is not supposed to have any property. The main problem with the utility theory approach is the gap between what decision-makers are and can express, and what the theory would like them to be and to be capable of expressing. With the relational approach this gap does not exist, but the main difficulty is now to build up convincing choice rules and ranking rules that may help the decision process.
Categories: Mathematics

Fuzzy Sets in Decision Analysis Operations Research and Statistics

Fuzzy Sets in Decision Analysis  Operations Research and Statistics

Kitainik L (1993) Fuzzy Decision Procedures with Binary Relations. Towards a Unified Theory, Kluwer Academic Publishers, Dordrecht.

Author: Roman Slowiński

Publisher: Springer Science & Business Media

ISBN: 9781461556459

Category: Mathematics

Page: 453

View: 586

Fuzzy Sets in Decision Analysis, Operations Research and Statistics includes chapters on fuzzy preference modeling, multiple criteria analysis, ranking and sorting methods, group decision-making and fuzzy game theory. It also presents optimization techniques such as fuzzy linear and non-linear programming, applications to graph problems and fuzzy combinatorial methods such as fuzzy dynamic programming. In addition, the book also accounts for advances in fuzzy data analysis, fuzzy statistics, and applications to reliability analysis. These topics are covered within four parts: Decision Making, Mathematical Programming, Statistics and Data Analysis, and Reliability, Maintenance and Replacement. The scope and content of the book has resulted from multiple interactions between the editor of the volume, the series editors, the series advisory board, and experts in each chapter area. Each chapter was written by a well-known researcher on the topic and reviewed by other experts in the area. These expert reviewers sometimes became co-authors because of the extent of their contribution to the chapter. As a result, twenty-five authors from twelve countries and four continents were involved in the creation of the 13 chapters, which enhances the international character of the project and gives an idea of how carefully the Handbook has been developed.
Categories: Mathematics

Cost Benefit Analysis and the Theory of Fuzzy Decisions

Cost Benefit Analysis and the Theory of Fuzzy Decisions

[ 737 ] Kitainik , L. , Fuzzy Decision Procedures with Binary Relations : Toward a Unified Theory , Boston , Mass . Kluwer , 1993 .

Author: Kofi Kissi Dompere

Publisher: Springer Science & Business Media

ISBN: 3540221611

Category: Mathematics

Page: 346

View: 828

Criticism is the habitus of the contemplative intellect, whereby we try to recognize with probability the genuine quality of a l- erary work by using appropriate aids and rules. In so doing, c- tain general and particular points must be considered. The art of interpretation or hermeneutics is the habitus of the contemplative intellect of probing into the sense of somewhat special text by using logical rules and suitable means. Note : Hermeneutics differs from criticism as the part does from the whole. Antonius Gvilielmus Amo Afer (1727) There is no such thing as absolute truth. At best it is a subj- tive criterion, but one based upon valuation. Unfortunately, too many people place their fate in the hands of subjective without properly evaluating it. Arnold A. Kaufmann and Madan M. Gupta The development of cost benefit analysis and the theory of fuzzy decision was divided into two inter-dependent structures of identification and measurement theory on one hand and fuzzy value theory one the other. Each of them has sub-theories that constitute a complete logical system.
Categories: Mathematics

Cost Benefit Analysis and the Theory of Fuzzy Decisions

Cost Benefit Analysis and the Theory of Fuzzy Decisions

[ 737 ] Kitainik , L. , Fuzzy Decision Procedures with Binary Relations : Toward a Unified Theory , Boston , Mass . Kluwer , 1993 .

Author: K. K. Dompere

Publisher: Springer Science & Business Media

ISBN: 3540221549

Category: Business & Economics

Page: 399

View: 663

This monograph is devoted to the identification and measurement theory of costs and benefits in a fuzzy information environment. The process of cost-benefit analysis is presented, requiring the development of real cost-benefit databases and the construction of cost-benefit criterion. These steps are accomplished with various theoretical constructs that provide sets of self-contained algorithms for application. This book integrates cost-benefit analysis, theory of fuzzy decisions and social decisions into unified decision algorithms accessible to practitioners, researchers, and graduate students. It features the essentials of fuzzy mathematics and algorithms in a comprehensive way, exposing a multi-disciplinary approach for the development of cost-benefit decision making in the framework of fuzziness and soft computing.
Categories: Business & Economics

Handbook of Fuzzy Computation

Handbook of Fuzzy Computation

Kitainik L 1993 Fuzzy Decision Procedures with Binary Relations . Toward a Unified Theory ( Dordrecht : Kluwer ) Kitainik L , Orlovski S and Roubens M 1993 ...

Author: E Ruspini

Publisher: CRC Press

ISBN: 9781420050394

Category: Computers

Page: 1500

View: 837

Initially conceived as a methodology for the representation and manipulation of imprecise and vague information, fuzzy computation has found wide use in problems that fall well beyond its originally intended scope of application. Many scientists and engineers now use the paradigms of fuzzy computation to tackle problems that are either intractable
Categories: Computers

Optimization Models Using Fuzzy Sets and Possibility Theory

Optimization Models Using Fuzzy Sets and Possibility Theory

FUZZY INCLUSIONS AND FUZZY DICHOTOMOUS DECISION PROCEDURES L. M. Kitainik MLTI, ... to decision making with an arbitrary antireflexive fuzzy binary relation ...

Author: J. Kacprzyk

Publisher: Springer Science & Business Media

ISBN: 9789400938694

Category: Mathematics

Page: 462

View: 586

Optimization is of central concern to a number of discip lines. Operations Research and Decision Theory are often consi dered to be identical with optimizationo But also in other areas such as engineering design, regional policy, logistics and many others, the search for optimal solutions is one of the prime goals. The methods and models which have been used over the last decades in these areas have primarily been "hard" or "crisp", i. e. the solutions were considered to be either fea sible or unfeasible, either above a certain aspiration level or below. This dichotomous structure of methods very often forced the modeller to approximate real problem situations of the more-or-less type by yes-or-no-type models, the solutions of which might turn out not to be the solutions to the real prob lems. This is particularly true if the problem under considera tion includes vaguely defined relationships, human evaluations, uncertainty due to inconsistent or incomplete evidence, if na tural language has to be modelled or if state variables can only be described approximately. Until recently, everything which was not known with cer tainty, i. e. which was not known to be either true or false or which was not known to either happen with certainty or to be impossible to occur, was modelled by means of probabilitieso This holds in particular for uncertainties concerning the oc currence of events.
Categories: Mathematics

Fuzzy Rationality

Fuzzy Rationality

[R5.72] Kacprzyk, J.: Multistage Decision-Making Under Fuzziness. ... L.: Fuzzy Decision Procedures with Binary Relations: Toward a Unified Theory.

Author: Kofi Kissi Dompere

Publisher: Springer Science & Business Media

ISBN: 9783540880820

Category: Mathematics

Page: 283

View: 849

Philosophy involves a criticism of scientific knowledge, not from a point of view ultimately different from that of science, but from a point of view less concerned with details and more concerned with the h- mony of the body of special sciences. Here as elsewhere, while the older logic shut out possibilities and imprisoned imagination within the walls of the familiar, the newer logic shows rather what may happen, and refuses to decide as to what must happen. Bertrand Russell At any particular stage in the development of humanity knowledge comes up against limits set by the necessarily limited character of the experience available and the existing means of obtaining knowledge. But humanity advances by overcoming such limits. New experience throws down the limits of old experience; new techniques, new means of obtaining knowledge throw down the limits of old techniques and old means of obtaining knowledge. New limits then once again appear. But there is no more reason to suppose these new limits absolute and final than there was to suppose the old ones absolute and final.
Categories: Mathematics

Fuzzy Preference Modelling and Multicriteria Decision Support

Fuzzy Preference Modelling and Multicriteria Decision Support

This book provides in-depth coverage of the most important results about fuzzy logic including negations, conjunctions, disjunctions, implications and gives the interrelations between those different connectives.

Author: J.C. Fodor

Publisher: Springer Science & Business Media

ISBN: 9789401716482

Category: Business & Economics

Page: 256

View: 878

This book provides in-depth coverage of the most important results about fuzzy logic including negations, conjunctions, disjunctions, implications and gives the interrelations between those different connectives. The work brings together multiple results about valued binary relations satisfying diverse transitivity-type conditions. The authors propose the first sound introduction to valued preference modelling through the systematic use of fuzzy set theory and functional equations and derive the possible foundations for multicriteria decision aid using aggregation, ranking and choice procedures on the basis of axiomatic results. The text presents a unified view of various multicriteria decision making tools that have been independently derived in the past, dealing with pairwise comparisons. The monograph is mathematically oriented but the results will be of the greatest interest for engineers and economists who design and implement decision support systems in practice. It is also supplied with a sufficient number of examples to make it attractive to nonspecialists.
Categories: Business & Economics

Preferences and Decisions under Incomplete Knowledge

Preferences and Decisions under Incomplete Knowledge

Fuzzy Decision Procedures with Binary Relations. Kluwer Academic Pub., Boston, 1993. J. Montero and J. Tejada, A necessary and sufficient condition for the ...

Author: Janos Fodor

Publisher: Physica

ISBN: 9783790818482

Category: Business & Economics

Page: 208

View: 181

Nowadays, decision problems are pervaded with incomplete knowledge, i.e., imprecision and/or uncertain information, both in the problem description and in the preferential information. In this volume leading scientists in the field address various theoretical and practical aspects related to the handling of this incompleteness. The problems discussed are taken from multi-objective linear programming, rationality considerations in preference modelling, non-probabilistic utility theory, data fusion, group decision making and multicriteria decision aid. The book is oriented towards researchers, graduate and postgraduate students in decision analysis, fuzzy sets and fuzzy logic, and operations research/management science.
Categories: Business & Economics

Fuzzy Applications in Industrial Engineering

Fuzzy Applications in Industrial Engineering

(1988) Non-conventional Preference Relations in Decision Making, ... Fuzzy Decision Procedures with Binary Relations: Towards a Unified Theory.

Author: Cengiz Kahraman

Publisher: Springer

ISBN: 9783540335177

Category: Mathematics

Page: 598

View: 301

After an introductory chapter explaining recent applications of fuzzy sets in IE, this book explores the seven major areas of IE to which fuzzy set theory can contribute: Control and Reliability, Engineering Economics and Investment Analysis, Group and Multi-criteria Decision-making, Human Factors Engineering and Ergonomics, Manufacturing Systems and Technology Management, Optimization Techniques, and Statistical Decision-making. Under these major areas, every chapter includes didactic numerical applications.
Categories: Mathematics

Fuzziness and Approximate Reasoning

Fuzziness and Approximate Reasoning

[R5.72] Kacprzyk, J.: Multistage Decision-Making Under Fuzziness. ... L.: Fuzzy Decision Procedures with Binary Relations: Toward a Unified Theory.

Author: Kofi Kissi Dompere

Publisher: Springer Science & Business Media

ISBN: 9783540880868

Category: Computers

Page: 289

View: 565

This monograph is special in its orientation and contribution to current state of our understanding of decision-choice process and knowledge production. Its special orientation is to bring to the scientific community the discussions on the epistemic structure of the relationships among uncertainty, expectations, risk, possibility, probability and how the rules of fuzzy paradigm and the methods of fuzzy rationality bring new and different understanding to the relationships. At the level of theory of knowledge, it presents the structure and epistemic analysis of uncertainty, expectations and risk in decision-choice actions through the characteristics of substitution-transformation and input-output processes in categorial dynamics of actual-potential duality. The interactive effects of rationality and expectation are examined around belief, prospect, time and conditions of belief justification where the relationship between possibility and probability as a sequential link between potential and actual is analyzed to provide some understanding of the role of relative costs and benefits in defining risk in both nature and society. The concepts of possibilistic and probabilistic beliefs are explicated in relation to rationality and the decision-choice process where the analytical relationship between uncertainty and expectation formation is presented leading to the introduction of two types of uncertainty composed of fuzzy uncertainty and stochastic uncertainty.
Categories: Computers

Recent Developments in the Ordered Weighted Averaging Operators Theory and Practice

Recent Developments in the Ordered Weighted Averaging Operators  Theory and Practice

Fuzzy Sets and Systems 10, 37–43 (1983) Kitainik, L.: Fuzzy Decision Procedures with Binary Relations: Towards a Unified Theory. Kluwer Academic Publishers ...

Author: Ronald R. Yager

Publisher: Springer

ISBN: 9783642179105

Category: Mathematics

Page: 298

View: 274

This volume presents the state of the art of new developments, and some interesting and relevant applications of the OWA (ordered weighted averaging) operators. The OWA operators were introduced in the early 1980s by Ronald R. Yager as a conceptually and numerically simple, easily implementable, yet extremely powerful general aggregation operator. That simplicity, generality and implementability of the OWA operators, combined with their intuitive appeal, have triggered much research both in the foundations and extensions of the OWA operators, and in their applications to a wide variety of problems in various fields of science and technology. Part I: Methods includes papers on theoretical foundations of OWA operators and their extensions. The papers in Part II: Applications show some more relevant applications of the OWA operators, mostly means, as powerful yet general aggregation operators. The application areas are exemplified by environmental modeling, social networks, image analysis, financial decision making and water resource management.
Categories: Mathematics

Fundamentals of Fuzzy Sets

Fundamentals of Fuzzy Sets

Fuzzy Decision Procedures with Binary Relations. Kluwer Academic Publishers, Dordrecht. Klawonn, F. and Kruse, R. (1993). Equality relations as a basis for ...

Author: Didier Dubois

Publisher: Springer Science & Business Media

ISBN: 9781461544296

Category: Mathematics

Page: 647

View: 358

Fundamentals of Fuzzy Sets covers the basic elements of fuzzy set theory. Its four-part organization provides easy referencing of recent as well as older results in the field. The first part discusses the historical emergence of fuzzy sets, and delves into fuzzy set connectives, and the representation and measurement of membership functions. The second part covers fuzzy relations, including orderings, similarity, and relational equations. The third part, devoted to uncertainty modelling, introduces possibility theory, contrasting and relating it with probabilities, and reviews information measures of specificity and fuzziness. The last part concerns fuzzy sets on the real line - computation with fuzzy intervals, metric topology of fuzzy numbers, and the calculus of fuzzy-valued functions. Each chapter is written by one or more recognized specialists and offers a tutorial introduction to the topics, together with an extensive bibliography.
Categories: Mathematics

Aggregation and Fusion of Imperfect Information

Aggregation and Fusion of Imperfect Information

Fuzzy Decision Procedures with Binary Relations. Kluwer Academic Pub., Boston, 1993. 12. J. Montero. Arrow's theorem under fuzzy rationality.

Author: Bernadette Bouchon-Meunier

Publisher: Physica

ISBN: 9783790818895

Category: Computers

Page: 278

View: 149

This book presents the main tools for aggregation of information given by several members of a group or expressed in multiple criteria, and for fusion of data provided by several sources. It focuses on the case where the availability knowledge is imperfect, which means that uncertainty and/or imprecision must be taken into account. The book contains both theoretical and applied studies of aggregation and fusion methods in the main frameworks: probability theory, evidence theory, fuzzy set and possibility theory. The latter is more developed because it allows to manage both imprecise and uncertain knowledge. Applications to decision-making, image processing, control and classification are described.
Categories: Computers

Applied Decision Support with Soft Computing

Applied Decision Support with Soft Computing

[ 8 ] Kitainik L. , " Fuzzy Decision Procedures with Binary Relations : Towards a Unified Theory " , Kluwer Academic Publishers , Boston / Dordrecht ...

Author: Xinghuo Yu

Publisher: Springer Science & Business Media

ISBN: 3540024913

Category: Business & Economics

Page: 418

View: 334

Soft computing has provided sophisticated methodologies for the development of intelligent decision support systems. Fast advances in soft computing technologies, such as fuzzy logic and systems, artificial neural networks and evolutionary computation, have made available powerful problem representation and modelling paradigms, and learning and optimisation mechanisms for addressing modern decision making issues. This book provides a comprehensive coverage of up-to-date conceptual frameworks in broadly perceived decision support systems and successful applications. Different from other existing books, this volume predominately focuses on applied decision support with soft computing. Areas covered include planning, management finance and administration in both the private and public sectors.
Categories: Business & Economics

Multiple Criteria Decision Analysis

Multiple Criteria Decision Analysis

Fuzzy Sets in Decision Analysis, Operations Research and Statistics, pp. ... 195–220 (2001) Kitainik, L.: Fuzzy Decision Procedures With Binary Relations.

Author: Salvatore Greco

Publisher: Springer

ISBN: 9781493930944

Category: Business & Economics

Page: 1347

View: 266

In two volumes, this new edition presents the state of the art in Multiple Criteria Decision Analysis (MCDA). Reflecting the explosive growth in the field seen during the last several years, the editors not only present surveys of the foundations of MCDA, but look as well at many new areas and new applications. Individual chapter authors are among the most prestigious names in MCDA research, and combined their chapters bring the field completely up to date. Part I of the book considers the history and current state of MCDA, with surveys that cover the early history of MCDA and an overview that discusses the “pre-theoretical” assumptions of MCDA. Part II then presents the foundations of MCDA, with individual chapters that provide a very exhaustive review of preference modeling, along with a chapter devoted to the axiomatic basis of the different models that multiple criteria preferences. Part III looks at outranking methods, with three chapters that consider the ELECTRE methods, PROMETHEE methods, and a look at the rich literature of other outranking methods. Part IV, on Multiattribute Utility and Value Theories (MAUT), presents chapters on the fundamentals of this approach, the very well known UTA methods, the Analytic Hierarchy Process (AHP) and its more recent extension, the Analytic Network Process (ANP), as well as a chapter on MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). Part V looks at Non-Classical MCDA Approaches, with chapters on risk and uncertainty in MCDA, the decision rule approach to MCDA, the fuzzy integral approach, the verbal decision methods, and a tentative assessment of the role of fuzzy sets in decision analysis. Part VI, on Multiobjective Optimization, contains chapters on recent developments of vector and set optimization, the state of the art in continuous multiobjective programming, multiobjective combinatorial optimization, fuzzy multicriteria optimization, a review of the field of goal programming, interactive methods for solving multiobjective optimization problems, and relationships between MCDA and evolutionary multiobjective optimization (EMO). Part VII, on Applications, selects some of the most significant areas, including contributions of MCDA in finance, energy planning problems, telecommunication network planning and design, sustainable development, and portfolio analysis. Finally, Part VIII, on MCDM software, presents well known MCDA software packages.
Categories: Business & Economics

Fuzzy Logic and its Applications to Engineering Information Sciences and Intelligent Systems

Fuzzy Logic and its Applications to Engineering  Information Sciences  and Intelligent Systems

Fuzzy Relation Equations and Their Applications to Knowledge Engineering. ... 0-7923-2324-6 L. Kitainik: Fuzzy Decision Procedures with Binary Relations.

Author: Zeungnam Bien

Publisher: Springer Science & Business Media

ISBN: 9789400901254

Category: Mathematics

Page: 483

View: 624

Fuzzy technology has emerged as one of the most exciting new concepts available. Fuzzy Logic and its Applications... covers a wide range of the theory and applications of fuzzy logic and related systems, including industrial applications of fuzzy technology, implementing human intelligence in machines and systems. There are four main themes: intelligent systems, engineering, mathematical foundations, and information sciences. Both academics and the technical community will learn how and why fuzzy logic is appreciated in the conceptual, design and manufacturing stages of intelligent systems, gaining an improved understanding of the basic science and the foundations of human reasoning.
Categories: Mathematics

Computation Cryptography and Network Security

Computation  Cryptography  and Network Security

in our formula and we would like to further examine this process and its results. ... Kitainik, L.: Fuzzy Decision Procedures with Binary Relations.

Author: Nicholas J. Daras

Publisher: Springer

ISBN: 9783319182759

Category: Mathematics

Page: 756

View: 984

Analysis, assessment, and data management are core competencies for operation research analysts. This volume addresses a number of issues and developed methods for improving those skills. It is an outgrowth of a conference held in April 2013 at the Hellenic Military Academy, and brings together a broad variety of mathematical methods and theories with several applications. It discusses directions and pursuits of scientists that pertain to engineering sciences. It is also presents the theoretical background required for algorithms and techniques applied to a large variety of concrete problems. A number of open questions as well as new future areas are also highlighted. This book will appeal to operations research analysts, engineers, community decision makers, academics, the military community, practitioners sharing the current “state-of-the-art,” and analysts from coalition partners. Topics covered include Operations Research, Games and Control Theory, Computational Number Theory and Information Security, Scientific Computing and Applications, Statistical Modeling and Applications, Systems of Monitoring and Spatial Analysis.
Categories: Mathematics

Fuzzy Logic and Mathematics

Fuzzy Logic and Mathematics

Fuzzy Decision Procedures with Binary Relations: Towards a Unified Theory. Dordrecht: Kluwer. Klaua, D. 1965. Úber einen Ansatz zur mehrwertigen Mengenlehre ...

Author: Radim Belohlávek

Publisher: Oxford University Press

ISBN: 9780190200015

Category: Mathematics

Page: 544

View: 905

The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of truth. This opens a new way of thinking---thinking in terms of degrees rather than absolutes. For example, it leads to the definition of a new kind of sets, referred to as fuzzy sets, in which membership is a matter of degree. The book examines the genesis and development of fuzzy logic. It surveys the prehistory of fuzzy logic and inspects circumstances that eventually lead to the emergence of fuzzy logic. The book explores in detail the development of propositional, predicate, and other calculi that admit degrees of truth, which are known as fuzzy logic in the narrow sense. Fuzzy logic in the broad sense, whose primary aim is to utilize degrees of truth for emulating common-sense human reasoning in natural language, is scrutinized as well. The book also examines principles for developing mathematics based on fuzzy logic and provides overviews of areas in which this has been done most effectively. It also presents a detailed survey of established and prospective applications of fuzzy logic in various areas of human affairs, and provides an assessment of the significance of fuzzy logic as a new paradigm.
Categories: Mathematics

Decision Making Process

Decision Making Process

Fuzzy Decision Procedures with Binary Relations. Kluwer Academic, Dordrecht, 1993. [KOL 33] AN. Kolmogorov. Grundbegriffe der Warscheinlichkeitsrechnung.

Author: Denis Bouyssou

Publisher: John Wiley & Sons

ISBN: 9781118619520

Category: Business & Economics

Page: 928

View: 517

This book provides an overview of the main methods and results in the formal study of the human decision-making process, as defined in a relatively wide sense. A key aim of the approach contained here is to try to break down barriers between various disciplines encompassed by this field, including psychology, economics and computer science. All these approaches have contributed to progress in this very important and much-studied topic in the past, but none have proved sufficient so far to define a complete understanding of the highly complex processes and outcomes. This book provides the reader with state-of-the-art coverage of the field, essentially forming a roadmap to the field of decision analysis. The first part of the book is devoted to basic concepts and techniques for representing and solving decision problems, ranging from operational research to artificial intelligence. Later chapters provide an extensive overview of the decision-making process under conditions of risk and uncertainty. Finally, there are chapters covering various approaches to multi-criteria decision-making. Each chapter is written by experts in the topic concerned, and contains an extensive bibliography for further reading and reference.
Categories: Business & Economics