Multicriteria Decision-Making Under Conditions of Uncertainty

A Fuzzy Set Perspective

Inbunden, Engelska, 2019

1 503 kr

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Beskrivning

A guide to the various models and methods to multicriteria decision-making in conditions of uncertainty presented in a systematic approachMulticriteria 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 models), construction and analysis of 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 transformationsDescribes models of multiobjective decision-making ( 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 resourcesInvestigates models of multiattribute decision-making ( 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 problemsExplores 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.

Produktinformation

Utgivningsdatum:2019-12-12
Mått:158 x 234 x 23 mm
Vikt:703 g
Format:Inbunden
Språk:Engelska
Antal sidor:368
Förlag:John Wiley & Sons Inc
ISBN:9781119534921

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Mer om författaren

PETR EKEL, DSc (habil.), PhD, is a Full Professor in the Graduate Program of Electrical Engineering, Pontifical Catholic University of Minas Gerais, Belo Horizonte, Brazil. WITOLD PEDRYCZ, DSc (habil.), PhD, is a Full Professor and Canada Research Chair (CRC) in Computational Intelligence in the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada. JOEL PEREIRA, JR., PhD, is a Researcher in ASOTECH Advanced System Optimization Technologies Ltda., Belo Horizonte, Brazil.

Innehållsförteckning

Preface xi1 Decision-Making in Problems of System Design, Planning, Operation, and Control: Motivation, Objectives, and Basic Notions 11.1 Decision-Making and Its Support 11.2 Problems of Optimization and Decision-Making 71.3 Uncertainty Factor and Its Consideration 111.4 Multicriteria Decision-Making: Multiobjective and Multiattribute Problems 121.5 Group Decision-Making: Basic Notions 151.6 Fuzzy Sets in Problems of Decision-Making 191.7 Conclusions 23References 242 Notions and Concepts of Fuzzy Sets: An Introduction 292.1 Sets and Fuzzy Sets: A Fundamental Departure from the Principle of Dichotomy 292.2 Interpretation of Fuzzy Sets 332.3 Membership Functions and Classes of Fuzzy Sets 352.4 Information Granules and Granular Computing 372.4.1 Image Processing 382.4.2 Processing and Interpretation of Time Series 382.4.3 Granulation of Time 382.4.4 Data Summarization 392.4.5 Design of Software Systems 392.5 Formal Platforms of Information Granularity 392.5.1 Symbolic Perspective 412.5.2 Numeric Perspective 422.6 Intervals and Calculus of Intervals 422.6.1 Set-Theoretic Operations 432.6.2 Algebraic Operations on Intervals 442.6.3 Distance Between Intervals 452.7 Fuzzy Numbers and Intervals 452.8 Linguistic Variables 462.9 A Generic Characterization of Fuzzy Sets: Some Fundamental Descriptors 482.10 Coverage of Fuzzy Sets 582.11 Matching Fuzzy Sets 592.12 Geometric Interpretation of Sets and Fuzzy Sets 602.13 Fuzzy Set and Its Family of α-Cuts 612.14 Fuzzy Sets of Higher Type and Fuzzy Order 642.14.1 Fuzzy Sets of Type −2 642.14.2 Fuzzy Sets of Order-2 652.15 Operations on Fuzzy Sets 652.16 Triangular Norms and Triangular Conorms as Models of Operations on Fuzzy Sets 682.17 Negations 702.18 Fuzzy Relations 712.19 The Concept of Relations 712.20 Fuzzy Relations 742.21 Properties of the Fuzzy Relations 762.21.1 Domain and Codomain of Fuzzy Relations 762.21.2 Representation of Fuzzy Relations 762.21.3 Equality of Fuzzy Relations 762.21.4 Inclusion of Fuzzy Relations 772.21.5 Operations on Fuzzy Relations 772.21.6 Union of Fuzzy Relations 772.21.7 Intersection of Fuzzy Relations 772.21.8 Complement of Fuzzy Relations 782.21.9 Transposition of Fuzzy Relations 782.21.10 Cartesian Product of Fuzzy Relations 782.21.11 Projection of Fuzzy Relations 782.21.12 Cylindrical Extension 802.21.13 Reconstruction of Fuzzy Relations 812.21.14 Binary Fuzzy Relations 812.21.15 Transitive Closure 822.21.16 Equivalence and Similarity Relations 832.21.17 Compatibility and Proximity Relations 842.22 Conclusions 85Exercises 85References 893 Design and Processing Aspects of Fuzzy Sets 913.1 The Development of Fuzzy Sets: Elicitation of Membership Functions 913.1.1 Semantics of Fuzzy Sets: Some General Observations 923.1.2 Fuzzy Set as a Descriptor of Feasible Solutions 933.1.3 Fuzzy Set as a Descriptor of the Notion of Typicality 953.1.4 Vertical and Horizontal Schemes of Membership Function Estimation 963.1.5 Saaty’s Priority Approach of Pairwise Membership Function Estimation 993.1.6 Fuzzy Sets as Granular Representatives of Numeric Data – The Principle of Justifiable Granularity 1033.1.7 From Type-0 to Type-1 Information Granules 1073.2 Weighted Data 1083.3 Inhibitory Data 1093.3.1 Design of Fuzzy Sets Through Fuzzy Clustering: From Data to Their Granular Abstraction 1103.4 Quality of Clustering Results 1163.4.1 Cluster Validity Indexes 1173.4.2 Classification Error 1183.4.3 Reconstruction Error 1183.5 From Numeric Data to Granular Data 1193.5.1 Unlabeled Data 1193.5.2 Labeled Data 1193.5.3 Fuzzy Equalization as a Way of Building Fuzzy Sets Supported by Experimental Evidence 1213.5.4 Several Design Guidelines for the Formation of Fuzzy Sets 1223.6 Aggregation Operations 1233.6.1 Averaging Operations 1243.7 Transformations of Fuzzy Sets 1253.7.1 The Extension Principle 1253.7.2 Fuzzy Numbers and Fuzzy Arithmetic 1283.7.3 Interval Arithmetic and α-Cuts 1303.7.4 Fuzzy Arithmetic and the Extension Principle 1313.7.5 Computing with Triangular Fuzzy Numbers 1363.7.6 Addition 1363.7.7 Multiplication 1383.7.8 Division 1393.8 Conclusions 140Exercises 140References 1444 <X, F> Models of Multicriteria Decision-Making and Their Analysis 1474.1 Models of Multiobjective Decision-Making 1474.2 Pareto Optimal Solutions 1484.3 Approaches to Incorporating Decision-Maker Information 1504.4 Methods of Multiobjective Decision-Making 1524.4.1 Normalization of Objective Functions 1524.4.2 Choice of the Principle of Optimality 1524.4.3 Consideration of Priorities of Objective Functions 1524.5 Bellman–Zadeh Approach to Decision-Making in a Fuzzy Environment and Its Application to Multicriteria Decision-Making 1594.6 OWA Operator Applied to Multiobjective Decision-Making 1624.7 Multiobjective Allocation of Resources and Their Shortages 1664.7.1 Model 1: Allocation of Available Resources 1704.7.2 Model 2: Allocation of Resource Shortages with Unlimited Cuts 1704.7.3 Model 3: Allocation of Resource Shortages with Limited Cuts 1714.8 Practical Examples of Analyzing Multiobjective Problems 1784.9 Conclusions 189Exercises 190References 1925 <X, R> Models of Multicriteria Decision-Making and Their Analysis 1995.1 Introduction to Preference Modeling with Binary Fuzzy Relations 2005.2 Construction of Fuzzy Preference Relations 2055.3 Preference Formats 2155.3.1 Ordering of Alternatives 2165.3.2 Utility Values 2165.3.3 Fuzzy Estimates 2195.3.4 Multiplicative Preference Relations 2205.4 Transformation Functions and Their Application to Unifying Different Preference Formats 2225.4.1 Transformation of the Ordered Array into the Additive Reciprocal Fuzzy Preference Relation 2235.4.2 Transformation of the Utility Values into the Additive Reciprocal Fuzzy Preference Relation 2245.4.3 Transformation of the Multiplicative Preference Relation into the Additive Reciprocal Fuzzy Preference Relation 2255.4.4 Transformation of the Nonreciprocal Fuzzy Preference Relation into the Additive Reciprocal Fuzzy Preference Relation 2265.4.5 Transformation of the Additive Reciprocal Fuzzy Preference Relation into the Nonreciprocal Fuzzy Preference Relation 2285.4.6 Transformation of the Ordered Array into the Nonreciprocal Fuzzy Preference Relation 2295.4.7 Transformation of the Utility Values into the Nonreciprocal Fuzzy Preference Relation 2305.4.8 Transformation of the Multiplicative Preference Relation into the Nonreciprocal Fuzzy Preference Relation 2325.4.9 Transformation of the Quantitative Information into the Fuzzy Preference Relation 2325.5 Optimization Problems with Fuzzy Coefficients and Their Analysis 2335.6 <X, R> Models of Multicriteria Decision-Making 2415.7 Techniques for Analyzing <X, R> Models 2425.8 Practical Examples of Analyzing <X, R> Models 2515.9 Conclusions 264Exercises 265References 2686 Dealing with Uncertainty of Information: A Classic Approach 2756.1 Characterization of the Classic Approach to Dealing with Uncertainty of Information 2756.2 Payoff Matrices and Characteristic Estimates 2766.3 Choice Criteria and Their Application 2816.4 Elements of Constructing Representative Combinations of Initial Data, States of Nature, or Scenarios 2836.5 Application Example 2856.6 Conclusions 288Exercises 288References 2907 Generalization of the Classic Approach to Dealing with Uncertainty of Information and General Scheme of Multicriteria Decision-Making under Conditions of Uncertainty 2917.1 Generalization of the Classic Approach to Dealing with Uncertainty of Information in Multicriteria Decision Problems 2927.2 Consideration of Choice Criteria of the Classic Approach to Dealing with Uncertainty of Information as Objective Functions within the Framework of <X, F> Models 2997.3 Construction of Objectives and Elaboration of Representative Combination of Initial Data, States of Nature, or Scenarios using Qualitative Information 3097.3.1 Elicitation of Preferences 3107.3.2 Representation of Preferences Within Multiplicative Preference Relations 3127.3.3 Definition of Preference Vectors on the Basis of Applying the AHP 3147.3.4 Aggregation of Preferences and Generation of Representative Combinations of Initial Data, States of Nature, or Scenarios 3147.4 General Scheme of Multicriteria Decision-Making under Conditions of Uncertainty 3157.5 Application Studies 3177.6 Conclusions 333Exercises 333References 335Index 339

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