Multicriteria Decision-Making Under Conditions of Uncertainty

A Fuzzy Set Perspective

Petr Ekel, Witold Pedrycz, Joel Pereira, Jr.

• Publisher: Wiley
• Year: 2019
• Print ISBN: 9781119534921
• eBook ISBN: 9781119534907
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

A guide to the various models and methods to multicriteria decision-making in conditions of uncertainty presented in a systematic approach

Multicriteria Decision-Making under Conditions of Uncertainty presents approaches that help to answer the fundamental questions at the center of all decision-making problems: "What to do?" and "How to do it?" The book explores methods of representing and handling diverse manifestations of the uncertainty factor and a multicriteria nature of problems that can arise in system design, planning, operation, and control. The authors—noted experts on the topic—and their book covers essential questions, including notions and fundamental concepts of fuzzy sets, models and methods of multiobjective as well as multiattribute decision-making, the classical approach to dealing with uncertainty of information and its generalization for analyzing multicriteria problems in condition of uncertainty, and more.

This comprehensive book contains information on "harmonious solutions" in multiobjective problem-solving (analyzing X, F> models), construction and analysis of X, R > models, results aimed at generating robust solutions in analyzing multicriteria problems under uncertainty, and more. In addition, the book includes illustrative examples of various applications, including real-world case studies related to the authors' various industrial projects. This important resource:

• Explains the design and processing aspect of fuzzy sets, including construction of membership functions, fuzzy numbers, fuzzy relations, aggregation operations, and fuzzy sets transformations
• Describes models of multiobjective decision-making ( X. M > models), their analysis on the basis of using the Bellman-Zadeh approach to decision-making in a fuzzy environment, and their diverse applications, including multicriteria allocation of resources
• Investigates models of multiattribute decision-making ( X, R > models) and their analysis on the basis of the construction and processing of fuzzy preference relations as well as demonstrating their applications to solve diverse classes of multiattribute problems
• Explores notions of payoff matrices and fuzzy-set-based generalization and modification of the classic approach to decision-making under conditions of uncertainty to generate robust solutions in analyzing multicriteria problems

Written for students, researchers and practitioners in disciplines in which decision-making is of paramount relevance, Multicriteria Decision-Making under Conditions of Uncertainty presents a systematic and current approach that encompasses a range of models and methods as well as new applications.

1
Decision‐Making in Problems of System Design, Planning, Operation, and Control: Motivation, Objectives, and Basic Notions

The main objective of this chapter is to offer the reader a broad perspective on the fundamentals of decision‐making problems, provide their general taxonomy in terms of criteria, objectives, and attributes involved, emphasize the objectivity and relevance of the uncertainty factor, classify the types of uncertainty, discuss ways of considering the uncertainty factor, and highlight the aspects of rationality of decision‐making processes. This chapter also highlights the fundamental differences between optimization and decision‐making problems, between the concepts of optimal solutions and robust solutions as well as between approaches to their construction. The main objectives and characteristics of group decision‐making are discussed. The role of fuzzy sets is stressed in the general framework of decision‐making processes. The most important advantages of their application to individual as well as group decision‐making are discussed. The chapter also clarifies necessary notations and terminology (for instance, <X, F > models and <X, R > models) used throughout the book.

1.1 Decision‐Making and Its Support

The life of each person is filled with alternatives. From the moment of conscious thought to a venerable age, from morning awakening to nightly sleeping, a person is faced with the need to make certain decisions. This need is associated with the fact that any situation may have two or more mutually exclusive alternatives and it is necessary to choose one among them. The decision‐making process, in the majority of cases, consists of the evaluation of alternatives and the choice of the most preferable from them.

Pospelov and Pushkin (1972) indicate that making the “correct” decision means choosing such an alternative from a possible set of alternatives, in which, by considering all the diversified factors and contradictory requirements, an overall value will be optimized. That is, it will be favorable in achieving the goal sought to the maximal possible degree.

If the diverse alternatives met by a person are considered as a set, then this set usually includes at least three intersecting subsets of alternatives related to personal life, social life, and professional life. As possible examples, we can indicate, for instance, deciding where to study, where to work, how to spend time on a vacation, who to elect, and many others.

At the same time, if we speak about any organization, it faces different goals and achieves them through the use of diverse types of resources (material, energy, financial, human, etc.), and the performance of managerial functions such as organizing, planning, operating, controlling, and so on (Lu et al. 2007). To fulfill these functions, managers need to participate in the continuous decision‐making process. Since each decision supposes a reasonable and justified choice realized among different alternatives, the manager can be called a decision‐maker (DM). DMs can be managers at various levels, from a technological process manager to a chief executive officer of a large company, and their decision problems can vary in nature. Besides, decisions can be made by individuals or groups (individual decisions are usually made at lower managerial levels and in small organizations and group decisions are usually made at high managerial levels and in large organizations). As possible examples, we can indicate, for instance, deciding what to buy, where to buy, when to begin a production process, whom to employ, and many others. These problems can concern logistics management, customer relationship management, production planning, and so on.

A person makes simple, habitual decisions easily and frequently in an automatic and subconscious way, without too much intensive thinking. However, in many cases, alternatives are related to complex situations that are characterized by a contradiction of requirements and multiple criteria, ambiguity in evaluating situations, errors in the choice of priorities, and so on. All these factors substantially complicate a way in which decisions are being made.

Furthermore, various facets of uncertainty are commonly encountered in a wide range of problems of an optimization character, which are inherently present in the design, planning, operation, and control of complex systems (engineering, economical, ecological, etc.). In particular, diverse manifestations of the uncertainty factor are associated, for instance, with (Ekel 1999; Pedrycz et al. 2011):

• the impossibility or inexpediency of obtaining sufficient amounts of information with the necessary degree of reliability;
• the lack of reliable predictions of the characteristics, properties, and behavior of complex systems that reflect their responses to external and internal actions;
• poorly defined goals and constraints in the design, planning, operation, and control tasks;
• the infeasibility of formalizing a number of factors and criteria and the need to take into account qualitative (semantic) information.

Considering the essence of the manifestations of the uncertainty factor listed here, more concisely, it is possible (Stewart 2005; Durbach and Stewart 2012) to talk about internal uncertainties (related to DM values and judgments) and external uncertainties (defined by environmental conditions lying beyond the control of a DM).

The described situation with the uncertainty involved is to be considered as natural and unavoidable in the context of problems of complex systems. In principle, it is impossible to reduce these problems to exact and well‐formulated mathematical problems; to do this, it is necessary, in one way or another, to “discard” the uncertainty and accept some hypothesis (Pedrycz et al. 2011). However, the construction of hypotheses is a prerogative of the substantial analysis; in reality, this is the formalization of informal situations. One of the ways to address the problem is the formation of subjective estimates based on knowledge, experience, and intuition of involved experts, managers, and DMs in general, and the definition of the corresponding preferences.

Thus, DMs are forced to rely on their own subjective ideas of the efficiency of possible alternatives and importance of diverse criteria. Sometimes, this subjective estimation is the only possible basis for combining the heterogeneous physical parameters of a problem to be solved into a unique model, which permits decision alternatives to be evaluated (Larichev 1987). At the same time, there is nothing unusual and unacceptable in the subjectivity itself. For instance, experienced managers perceive, in a broad and well‐informed manner, how many personal and subjective considerations they have to bring into the decision‐making process. On the other hand, successes and failures of the majority of decisions can be judged by people on the basis of their subjective preferences.

However, the most complicated aspect is associated with the fact that the essence of problems solved by humans in diverse areas has been changed in recent decades (Trachtengerts 1998). New, more complicated and unusual problems have emerged. For many centuries, people made decisions by considering one or two main factors, while ignoring others that were perceived to be marginal to the essence of the problem. They lived in a world where changes in the surroundings were few and new phenomena arose “in turn” but not simultaneously.

Presently, this situation has changed. A considerable number of problems, or probably the majority of them, are multic...

Table of contents

• Cover
• Table of Contents
• Preface
• 1 Decision‐Making in Problems of System Design, Planning, Operation, and Control
• 2 Notions and Concepts of Fuzzy Sets
• 3 Design and Processing Aspects of Fuzzy Sets
• 4 <X, F> Models of Multicriteria Decision‐Making and Their Analysis
• 5 <X, R> Models of Multicriteria Decision‐Making and Their Analysis
• 6 Dealing with Uncertainty of Information
• 7 Generalization of the Classic Approach to Dealing with Uncertainty of Information and General Scheme of Multicriteria Decision‐Making under Conditions of Uncertainty
• Index
• End User License Agreement