This book starts with the basic concepts of Fuzzy Logic: the membership function, the intersection and the union of fuzzy sets, fuzzy numbers, and the extension principle underlying the algorithmic operations.
This book starts with the basic concepts of Fuzzy Logic: the membership function, the intersection and the union of fuzzy sets, fuzzy numbers, and the extension principle underlying the algorithmic operations. Several chapters are devoted to applications of Fuzzy Logic in Operations Research: PERT planning with uncertain activity durations, Multi-Criteria Decision Analysis (MCDA) with vague preferential statements, and Multi-Objective Optimization (MOO) with weighted degrees of satisfaction. New items are: Fuzzy PERT using activity durations with triangular membership functions, Fuzzy SMART with a sensitivity analysis based upon Fuzzy Logic, the Additive and the Multiplicative AHP with a similar feature, ELECTRE using the ideas of the AHP and SMART, and a comparative study of the ideal-point methods for MOO. Finally, earlier studies of colour perception illustrate the attempts to find a physiological basis for the set-theoretical and the algorithmic operations in Fuzzy Logic. The last chapter also discusses some key issues in linguistic categorization and the prospects of Fuzzy Logic as a multi-disciplinary research activity. Audience: Researchers and students working in applied mathematics, operations research, management science, business administration, econometrics, industrial engineering, information systems, artificial intelligence, mathematical psychology, and psycho-physics.
Multi criteria Decision Making Methods
Release on 2013-03-09 | by Evangelos Triantaphyllou
Lootsma, F.A., (1999), "Multi-Criteria Decision Analysis via Ratio and Difference Judgment." Kluwer Academic Publishers, Applied Optimization Series, Vol. 29, Dordrecht, The Netherlands. Lootsma, F.A., (1997), "Fuzzy Logic for Planning ...
Multi-Criteria Decision Making (MCDM) has been one of the fastest growing problem areas in many disciplines. The central problem is how to evaluate a set of alternatives in terms of a number of criteria. Although this problem is very relevant in practice, there are few methods available and their quality is hard to determine. Thus, the question `Which is the best method for a given problem?' has become one of the most important and challenging ones. This is exactly what this book has as its focus and why it is important. The author extensively compares, both theoretically and empirically, real-life MCDM issues and makes the reader aware of quite a number of surprising `abnormalities' with some of these methods. What makes this book so valuable and different is that even though the analyses are rigorous, the results can be understood even by the non-specialist. Audience: Researchers, practitioners, and students; it can be used as a textbook for senior undergraduate or graduate courses in business and engineering.
Release on 2016-04-15 | by Gert de Roo
The Role of Actors in a Fuzzy Governance Environment Gert de Roo, Geoff Porter. Byrne, D. (1998) Complexity Theory and the Social ... Lootsma, F.A. (1997) 'Fuzzy Logic for Planning and Decision Making', Applied Optimization Series nr.
Many of the key notions associated with spatial planning are essentially ’fuzzy’ in their nature. For example, while almost everyone accepts ’sustainability’ as an important goal of planning, the actions of the actors involved can render the achieved ’sustainability’ minimal, or even counterproductive. Putting forward an innovative way of looking at planning problems and policies, this volume suggests actor-consulting is important in addressing the fuzzy nature of planning. A tool to address differences in understanding, actor-consulting is based on an analysis of actor motives, perceptions and contributions. By inviting all actors to express their desired, actual and potential contributions to achieving an agreed outcome to a local policy issue, decision-makers have a means to develop their goals in line with the roles, motivation, perception and behaviour of the various actors involved. Including contributions from Patsy Healy, Johan Woltjer, Don Miller and Karel Martens, the book presents a variety of case studies which demonstrate the use of the actor-consulting model in addressing planning issues.
A Planner s Encounter with Complexity
Release on 2016-03-16 | by Gert de Roo
Lootsma, F.A. (1997) 'Fuzzy logic for planning and decision making', Applied Optimization Series no. 8, Kluwer Academic Publishers, Dordrecht. Lorenz, E.N. (1963) 'Deterministic nonperiodic flow', Journal of the Atmospheric Sciences, ...
Spatial planning is about dealing with our 'everyday' environment. In A Planner's Encounter with Complexity we present various understandings of complexity and how the environment is considered accordingly. One of these considerations is the environment as subject to processes of continuous change, being either progressive or destructive, evolving non-linearly and alternating between stable and dynamic periods. If the environment that is subject to change is adaptive, self-organizing, robust and flexible in relation to this change, a process of evolution and co-evolution can be expected. This understanding of an evolving environment is not mainstream to every planner. However, in A Planner's Encounter with Complexity, we argue that environments confronted with discontinuous, non-linear evolving processes might be more real than the idea that an environment is simply a planner's creation. Above all, we argue that recognizing the 'complexity' of our environment offers an entirely new perspective on our world and our environment, on planning theory and practice, and on the raison d'être of the planners that we are. A Planner's Encounter with Complexity is organized into 17 chapters. It begins with the interplay of planning and complexity from the perspective of contemporary planning theory. It continues by critically assessing planning theory and practice in the light of the interdisciplinary debate regarding complexity thinking. As the book progresses, it positions itself ever closer to the perspective of complexity thinking, looking at the planning discipline 'from the outside in', clarifying the facets of complexity and its importance in planning. Finally, conceptual and theoretical developments towards more applied examples are identified in order to see the interplay of planning and complexity in practice. This book emphasizes the importance of complexity in planning, clarifies many of the concepts and theories, presents examples on planning and complexity, and proposes new ideas and methods for planning.
Decision Making Recent Developments and Worldwide Applications
Release on 2013-04-17 | by Stelios H. Zanakis
Applied Optimization 10. 11. 12. 13. 14. 15. 16. 17. ... 1996 ISBN 0-7923–4201-1 B. Jansen: Interior Point Techniques in Optimization. ... 1997 ISBN 0-7923-4583–5 F.A. Lootsma: Fuzzy Logic for Planning and Decision Making.
This chapter describes a study conducted at the Swinburne University of Technology in Australia, in their School of Business. The study was to explore the applicability of a judgment-analytic decision support system to the assessment of the likelihood of an applicant being selected for admission to the School's Graduate Certificate in Business Administration (GCBA) program. The likelihood of a program administrator selecting a particular applicant is directly linked to the assessment of the likelihood of that applicant's success in the GCBA program. The purpose of this study, in effect, was to analyze the administrative judgment process in assessment of an applicant's likelihood of success in the program. THE PROCESS OF HUMAN JUDGMENT Human judgment is a process through which an individual uses social infonnation to make decisions. The social infonnation is obtained from an individual's environment and is interpreted through the individual's cognitive image of the environment. The. cognitive image provides a representation of the environment based on past experiences and training, and essentially predisposes the person to respond to social infonnation in predictable ways. An individual's policies or beliefs about the environment represent these patterns. Human judgments are based then upon one's interpretation of available infonnation. They are probability statements about one's environment and how one reacts to it. This condition leads to the human judgment process being inherently limited. It is fundamentally a covert process. It is seldom possible for an individual to accurately describe his or her judgment process accurately.
Fuzzy Reasoning in Decision Making and Optimization
Release on 2012-08-27 | by Christer Carlsson
This book starts with the basic concepts of fuzzy arithmetics and progresses through the analysis of sup-t-norm-extended arithmetic operations, possibilistic linear systems and fuzzy reasoning approaches to fuzzy optimization.
Many decision-making tasks are too complex to be understood quantitatively, however, humans succeed by using knowledge that is imprecise rather than precise. Fuzzy logic resembles human reasoning in its use of imprecise informa tion to generate decisions. Unlike classical logic which requires a deep under standing of a system, exact equations, and precise numeric values, fuzzy logic incorporates an alternative way of thinking, which allows modeling complex systems using a higher level of abstraction originating from our knowledge and experience. Fuzzy logic allows expressing this knowledge with subjective concepts such as very big and a long time which are mapped into exact numeric ranges. Since knowledge can be expressed in a more natural by using fuzzy sets, many decision (and engineering) problems can be greatly simplified. Fuzzy logic provides an inference morphology that enables approximate human reasoning capabilities to be applied to knowledge-based systems. The theory of fuzzy logic provides a mathematical strength to capture the un certainties associated with human cognitive processes, such as thinking and reasoning. The conventional approaches to knowledge representation lack the means for representating the meaning of fuzzy concepts. As a consequence, the approaches based on first order logic do not provide an appropriate con ceptual framework for dealing with the representation of commonsense knowl edge, since such knowledge is by its nature both lexically imprecise and non categorical.
Trends in Industrial and Applied Mathematics
Release on 2013-12-01 | by Abul Hasan Siddiqi
Complementarity, Sensitivity and Algorithms. 1997 ISBN 0-7923–4430-8 A. Migdalas, P.M. Pardalos and S. Storøy (eds.). Parallel Computing in Optimization. 1997 ISBN 0-7923–4583–5 F.A. Lootsma: Fuzzy Logic for Planning and Decision Making ...
An important objective of the study of mathematics is to analyze and visualize phenomena of nature and real world problems for its proper understanding. Gradually, it is also becoming the language of modem financial instruments. To project some of these developments, the conference was planned under the joint auspices of the Indian Society of Industrial and Applied mathematics (ISlAM) and Guru Nanak Dev University (G. N. D. U. ), Amritsar, India. Dr. Pammy Manchanda, chairperson of Mathematics Department, G. N. D. U. , was appointed the organizing secretary and an organizing committee was constituted. The Conference was scheduled in World Mathematics Year 2000 but, due one reason or the other, it could be held during 22. -25. January 2001. How ever, keeping in view the suggestion of the International Mathematics union, we organized two symposia, Role of Mathematics in industrial development and vice-versa and How image of Mathematics can be improved in public. These two symposia aroused great interest among the participants and almost everyone participated in the deliberations. The discussion in these two themes could be summarized in the lengthy following lines: "Tradition of working in isolation is a barrier for interaction with the workers in the other fields of science and engineering, what to talk of non-academic areas, specially the private sector of finance and industry. Therefore, it is essential to build bridges within in stitutions and between institutions.
Large scale Optimization
Release on 2013-03-09 | by Vladimir Tsurkov
Applied. Optimization. 10. 11. 12. 13. 14. 15. 16. 17. D.-Z. Du and D.F. Hsu (eds.): Combinatorial Network Theory. 1996 ISBN 0-7923-3777-8 M.J. ... 1997 ISBN 0-7923-4583–5 F.A. Lootsma: Fuzzy Logic for Planning and Decision Making.
Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms. Audience: This book is addressed to specialists in operations research, optimization, and optimal control.
Nonlinear Optimization and Related Topics
Release on 2013-06-29 | by Gianni Pillo
Applied Optimization 10. 11. 12. 13. 14. 15. 16. 17. ... 1996 ISBN 0-7923-4201-1 B. Jansen: Interior Point Techniques in Optimization. ... 1997 ISBN 0-7923-4583-5 F.A. Lootsma: Fuzzy Logic for Planning and Decision Making.
This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume.
Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization
Release on 2000 | by Dan Butnariu
Applied Optimization 1. D.-Z. Du and D.F. Hsu ( eds . ) ... 1996 ISBN 0-7923-4201-1 B. Jansen : Interior Point Techniques in Optimization . ... 1997 ISBN 0-7923-4583-5 F.A. Lootsma : Fuzzy Logic for Planning and Decision Making .
Its properties are deeply explored, and a comprehensive theory is presented, bringing together previously unrelated ideas from Banach space geometry, finite dimensional convex optimization and functional analysis. For making our general approach possible we had to improve over classical results like the Holder-Minkowsky inequality in [actual symbol not reproducible]. All the material is either new or very recent, and has never before been organized in a book." "This book will be of interest to both researchers in nonlinear analysis and to applied mathematicians dealing with numerical solution of integral equations, equilibrium problems, image reconstruction, optimal control, etc."--BOOK JACKET.
Type: BOOK - Published: 2007 - Publisher: ISTE (Interntl Soc Tech Educ
In 2004 a traditional Colorado elementary school became National School Library Media Program of the Year. How did they do it? In IT's Elementary! Integrating Technology in the Primary Grades instructional technology specialist Boni Hamilton offers an insider's view of her school's award-winning makeover. Guiding readers through the process of