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A novel approach to decision engineering, with a verified framework for modeling human reasoning

Soft Computing Evaluation Logic provides an in-depth examination of evaluation decision problems and presents comprehensive guidance toward the use of the Logic Scoring of Preference (LSP) method in modeling complex decision criteria. Fully aligned with current developments in computational intelligence, the discussion covers the design and use of LSP criteria for evaluation and comparison in diverse areas, such as search engines, medical conditions, real estate, space management, habitat mitigation projects in ecology, and land use and residential development suitability maps, with versatile transfer to other similar decision-modeling contexts.

Human decision making is rife with fuzziness, imprecision, uncertainty, and half-truths-yet humans make evaluation decisions every day. In this book, such decision processes are observed, analyzed, and modeled. The result is graded logic, a soft computing mathematical infrastructure that provides both formal logic and semantic generalizations of classical Boolean logic. Graded logic is used for logic aggregation in the context of evaluation models consistent with observable properties of human reasoning. The LSP method, based on graded logic and logic aggregation, is a vital component of an industrial-strength decision engineering framework. Thus, the book:

Provides detailed theoretical background for graded logic
Provides a theory of logic aggregators
Explains the LSP method for designing complex evaluation criteria and their use
Shows techniques for evaluation, comparison, and selection of complex systems, as well as the cost/suitability analysis, optimization, sensitivity analysis, tradeoff analysis, and missingness-tolerant aggregation
Includes a survey of available LSP software tools, including ISEE, ANSY and LSP.NT.
With quantitative modeling of human reasoning, novel approaches to modeling decision criteria, and a verified decision engineering framework applicable to a broad array of applications, this book is an invaluable resource for graduate students, researchers, and practitioners working within the decision engineering realm.



Preface xvii

About the Companion Website xxiii

Previous Publications xxiv

Acknowledgments xxv

List of Symbols and Abbreviations xxvii

Part One EVALUATION DECISION PROBLEMS 1

1.1 Intuitive Evaluation as a Logic Decision Process 5

1.1.1 Main Observable Steps of the Intuitive Evaluation Process 6

1.1.2 Subjective and Objective Components in Evaluation 18

1.2 Quantitative Evaluation-An Introductory Example 21

1.2.1 Stakeholders and Their Goals 21

1.2.2 Attributes 22

1.2.3 Attribute Criteria 23

1.2.4 Simple Direct Ranking 27

1.2.5 Aggregation of Attribute Suitability Degrees 29

1.2.6 Using Cost and Suitability to Compute the Overall Value 32

1.3 Drawbacks of Simple Additive and Multiplicative Scoring and Utility Models 35

1.3.1 Simple Additive Scoring: The Irresistible Attractiveness of Simplicity 36

1.3.2 Simple Multiplicative Scoring 45

1.3.3 Logic Unsuitability of Scoring and Utility Theory Models in Professional Evaluation 47

1.4 Introduction to Professional Quantitative Evaluation 51

1.4.1 Five Fundamental Types of Professional Evaluation Problems 51

1.4.2 A Survey of Typical Professional Evaluation Problems 54

1.4.3 Components of Methodology for Professional Quantitative Evaluation 58

Part Two GRADED LOGIC AND AGGREGATION 63

2.1 Graded Logic as a Generalization of Classical Boolean Logic 69

2.1.1 Aggregators and Their Classification 70

2.1.1.1 Means 71

2.1.1.2 General Aggregation Functions 71

2.1.1.3 Logic Aggregators 73

2.1.1.4 Triangular Norms and Conorms 73

2.1.2 How Do Human Beings Aggregate Subjective Categories? 75

2.1.3 Definition and Classification of Logic Aggregators 85

2.1.4 Logic Bisection, Trisection, and Quadrisection of the Unit Hypercube 92

2.1.5 Propositions, Value Statements, Graded Logic, and Fuzzy Logic 95

2.1.6 Classical Bivalent Boolean Logic 100

2.1.7 Six Generalizations of Bivalent Boolean Logic 108

2.1.7.1 Expansion of Function Domain 109

2.1.7.2 Expansion of Logic Domain 111

2.1.7.3 Expansion of Annihilator Adjustability 112

2.1.7.4 Expansion of Semantic Domain 115

2.1.7.5 Expansion of Compensative Logic Functions 117

2.1.7.6 Expansion of the Range of Andness/Orness from Drastic Conjunction to Drastic Disjunction 118

2.1.8 GL Conjecture: Ten Necessary and Sufficient GL Functions 123

2.1.9 Basic Idempotent GL Aggregators 127

2.1.10 A Summary of Differences between Graded Logic and Bivalent Boolean Logic 134

2.1.11 Relationships between Graded Logic, Perceptual Computing, and Fuzzy Logic 136

2.1.12 A Brief History of Graded Logic 142

2.2 Observable Properties of Human Evaluation Logic 147

2.2.1 Perceptual Computer and Its Basic Properties 152

2.2.2 Simultaneity and Substitutability in Evaluation Models 177

2.2.3 Basic Semantic Aspects of Evaluation Logic Reasoning 190

2.2.4 Multipolarity: Grouping and Aggregation of Semantically Heterogeneous Inputs 212

2.2.5 Grouping and Aggregation of Semantically Homogeneous Inputs 218

2.2.6 Imprecision, Incompleteness, Logic Inconsistency, and Errors 222

2.3 Andness and Orness 237

2.3.1 A General Definition of Andness/Orness 237

2.3.2 Local Andness and Orness in the Simplest Case of Two Variables 239

2.3.3 Variability of Local Andness 242

2.3.4 Mean Local Andness and Orness in the Case of Two Variables 248

2.3.5 Local and Mean Local Andness and Orness in the Case of n Variables 251

2.3.6 Global Andness and Orness 253

2.3.7 Mean Global Andness/Orness Theorems and Their Applications 272

2.3.8 Geometric Interpretations of Andness and Orness 275

2.4 Graded Conjunction/Disjunction and Logic Modeling of Simultaneity and Substitutability 283

2.4.1 Definitions and Basic Mathematical Properties of Logic Aggregators 284

2.4.2 Classification of Conjunctive and Disjunctive Logic Aggregators 295

2.4.3 Properties of Means Used in Logic Aggregation 298

2.4.4 Algebraic Properties of Aggregators Based on Weighted Power Means 304

2.4.5 Logic Aggregators Based on Weighted Means with Adjustable Andness/Orness 313

2.4.6 Selection and Use of the Threshold Andness Aggregator 318

2.4.7 Andness-Directed Interpolative GCD Aggregators 327

2.4.8 Uniform and Nonuniform Interpolative GCD Aggregators 334

2.4.8.1 The Uniform Interpolative GCD Aggregator (UGCD) 334

2.4.8.2 An Extremely Soft Interpolative Aggregator 338

2.4.8.3 An Extremely Hard Interpolative Aggregator 338

2.4.9 Extending GCD to Include Hyperconjunction and Hyperdisjunction 342

2.4.10 From Drastic Conjunction to Drastic Disjunction: A General GCD Aggregator 347

2.4.11 Gamma Aggregators versus Extended GCD Aggregators 348

2.4.11.1 Multiplicative an