Mathematical Models For Decision Making With Multiple Perspectives

This book brings together, in a single volume, the fields of multicriteria decision making and multiobjective optimization that are traditionally covered separately. Both fields have in common the presence of multiple perspectives of looking at and evaluating decisions to be taken but they differ in the number of available alternatives. Multicriteria approaches deal with decision processes where a finite number of alternatives have to be evaluated while, in multiobjective optimization, this number is infinite and the space of alternatives continuous. This book is written for students of applied mathematics, engineering, and economics and management, with no assumed previous knowledge on the subject, as well as for practitioners in industry looking for techniques to support decision making. The mathematical formalism is very low, so that all materials are accessible to most readers. Nonetheless, a rich bibliography allows interested readers to access more technical literature. The textbook is organized in eleven chapters, each corresponding to a class of about two hours. A comprehensive set of examples is presented, allowing for a didactic approach when presenting the methodologies. Each chapter ends with exercises that are designed to develop problem-solving skills and to promote concepts retention.

This volume is devoted to models and methods in multiple objectives decision making. The importance of the multiple dimensions of decision making was first recognised during the 1960s and since then progress has been made in that theoretical or application oriented contributions may now be categorized under two main headings:- Multiattribute Decision Making (MADM) which concerns the sorting, the ranking or the evaluation of objects of choice according to several criteria and Multiobjective Decision Making (MODM) which deals with the vector optimization in mathematical programming. The above are also presented in the context of various applications, namely banking, environment, health, manpower, media, portfolio and traffic control, resulting in a book for a wide variety of readers.

Among the various multi-level formulations of mathematical models in decision making processes, this book focuses on the bi-level model. Being the most frequently used, the bi-level model addresses conflicts which exist in multi-level decision making processes. From the perspective of bi-level structure and uncertainty, this book takes real-life problems as the background, focuses on the so-called random-like uncertainty, and develops the general framework of random-like bi-level decision making problems. The random-like uncertainty considered in this book includes random phenomenon, random-overlapped random (Ra-Ra) phenomenon and fuzzy-overlapped random (Ra-Fu) phenomenon. Basic theory, models, algorithms and practical applications for different types of random-like bi-level decision making problems are also presented in this book.

Decision making is an omnipresent, most crucial activity of the human being, and also of virtually all artificial broadly perceived “intelligent” systems that try to mimic human behavior, reasoning and choice processes. It is quite obvious that such a relevance of decision making had triggered vast research effort on its very essence, and attempts to develop tools and techniques which would make it possible to somehow mimic human decision making related acts, even to automate decision making processes that had been so far reserved for the human beings. The roots of those attempts at a scientific analysis can be traced to the ancient times but – clearly – they have gained momentum in the recent 50 or 100 years following a general boom in science. Depending on the field of science, decision making can be viewed in different ways. The most general view can be that decision making boils down to some cognitive, mental process(es) that lead to the selection of an option or a course of action among several alternatives. Then, looking in a deeper way, from a psychological perspective this process proceeds in the context of a set of needs, preferences, rational choice of an individual, a group of individuals, or even an organization. From a cognitive perspective, the decision making process proceeds in the context of various interactions with the environment.

It is quite an onerous task to edit the proceedings of a two week long institute with learned contributors from many parts of the world. All the same, the editorial team has found the process of refereeing and reviewing the contributions worthwhile and completing the volume has proven to be a satisfying task. In setting up the institute we had considered models and methods taken from a number of different disciplines. As a result the whole institute - preparing for it, attending it and editing the proceedings - proved to be an intense learning experience for us. Here I speak on behalf of the committee and the editorial team. By the time the institute took place, the papers were delivered and the delegates exchanged their views, the structure of the topics covered and their relative positioning appeared in a different light. In editing the volume I felt compelled to introduce a new structure in grouping the papers. The contents of this volume are organised in eight main sections set out below: 1 . Abstracts. 2. Review Paper. 3. Models with Multiple Criteria and Single or Multiple Decision Makers. 4. Use of Optimisation Models as Decision Support Tools. 5. Role of Information Systems in Decision Making: Database and Model Management Issues. 6. Methods of Artificial Intelligence in Decision Making: Intelligent Knowledge Based Systems. 7. Representation of Uncertainty in Mathematical Models and Knowledge Based Systems. 8. Mathematical Basis for Constructing Models and Model Validation.

This book offers a simple introduction to the theory and practice of the Analytic Hierarchy Process (AHP) without a pre-requisite for a sophisticated mathematical background. AHP is an intuitive and mathematically simple methodology in the field of multi-criteria decision making in Operational Research (OR). Using Super Decisions v3, the newly developed software by the Creative Decisions Foundations, this book provides a quick and intuitive understanding of AHP using spreadsheet examples and step-by-step software instructions. Super Decisions v3 marks a drastic departure from the previous version 2 in terms of interface and ratings model development. In addition to a concise guide, instructional videos are also available to demonstrate how to use the different features of Super Decisions v3. Most AHP books assume the reader has basic OR mathematical background; however, AHP was developed with the goal that decision makers can take advantage of this methodology without struggling with the mathematics behind it. For this reason, only basic arithmetic knowledge is required from the readers. In conclusion, this book delivers a quick and practical understanding of the AHP methodology that can be useful for corporate executives and decision-makers in all fields.

The volume delivers a wealth of effective methods to deal with various types of uncertainty inherently existing in human-centric decision problems. It elaborates on comprehensive decision frameworks to handle different decision scenarios, which help use effectively the explicit and tacit knowledge and intuition, model perceptions and preferences in a more human-oriented style. The book presents original approaches and delivers new results on fundamentals and applications related to human-centered decision making approaches to business, economics and social systems. Individual chapters cover multi-criteria (multiattribute) decision making, decision making with prospect theory, decision making with incomplete probabilistic information, granular models of decision making and decision making realized with the use of non-additive measures. New emerging decision theories being presented as along with a wide spectrum of ongoing research make the book valuable to all interested in the field of advanced decision-making. The volume, self-contained in its nature, offers a systematic exposure to the concepts, design methodologies, and detailed algorithms. A prudent balance between the theoretical studies and applications makes the material suitable for researchers and graduate students in information, computer sciences, psychology, cognitive science, economics, system engineering, operation research and management science, risk management, public and social policy.