Explains for the first time how "computing with words" can aid in making subjective judgmentsLotfi Zadeh, the father of fuzzy logic, coined the phrase "computing with words" (CWW) to describe a methodology in which the objects of computation are words and propositions drawn from a natural language. Perceptual Computing explains how to implement CWW to aid in the important area of making subjective judgments, using a methodology that leads to an interactive device—a "Perceptual Computer"—that propagates random and linguistic uncertainties into the subjective judgment in a way that can be modeled and observed by the judgment maker.This book focuses on the three components of a Perceptual Computer—encoder, CWW engines, and decoder—and then provides detailed applications for each. It uses interval type-2 fuzzy sets (IT2 FSs) and fuzzy logic as the mathematical vehicle for perceptual computing, because such fuzzy sets can model first-order linguistic uncertainties whereas the usual kind of fuzzy sets cannot. Drawing upon the work on subjective judgments that Jerry Mendel and his students completed over the past decade, Perceptual Computing shows readers how to:Map word-data with its inherent uncertainties into an IT2 FS that captures these uncertaintiesUse uncertainty measures to quantify linguistic uncertaintiesCompare IT2 FSs by using similarity and rankCompute the subsethood of one IT2 FS in another such setAggregate disparate data, ranging from numbers to uniformly weighted intervals to nonuniformly weighted intervals to wordsAggregate multiple-fired IF-THEN rules so that the integrity of word IT2 FS models is preservedFree MATLAB-based software is also available online so readers can apply the methodology of perceptual computing immediately, and even try to improve upon it. Perceptual Computing is an important go-to for researchers and students in the fields of artificial intelligence and fuzzy logic, as well as for operations researchers, decision makers, psychologists, computer scientists, and computational intelligence experts.
Author(s): Jerry Mendel, Dongrui Wu
Edition: 1
Year: 2010
Language: English
Pages: 320
PERCEPTUAL COMPUTING......Page 4
Contents......Page 10
Preface......Page 16
1.1 Perceptual Computing......Page 20
1.2.1 Investment Decision Making......Page 22
1.2.2 Social Judgment Making......Page 24
1.2.3 Hierarchical Decision Making......Page 26
1.2.4 Hierarchical and Distributed Decision Making......Page 28
1.3 Historical Origins of Perceptual Computing......Page 30
1.4 How to Validate the Perceptual Computer......Page 34
1.5 The Choice of Fuzzy Set Models for the Per-C......Page 35
1.6 Keeping the Per-C as Simple as Possible......Page 38
1.7 Coverage of the Book......Page 39
1.8.1 Chapter 2: Interval Type-2 Fuzzy Sets......Page 43
1.8.2 Chapter 3: Encoding: From a Word to a Model—The Codebook......Page 45
1.8.3 Chapter 4: Decoding: From FOUs to a Recommendation......Page 46
1.8.5 Chapter 6: If–Then Rules as a CWW Engine......Page 48
References......Page 50
2.1 A Brief Review of Type-1 Fuzzy Sets......Page 54
2.2 Introduction to Interval Type-2 Fuzzy Sets......Page 57
2.3 Definitions......Page 61
2.5 Set-Theoretic Operations......Page 64
2.6.1 General Results......Page 65
2.6.2 Properties of the Centroid......Page 69
2.7.1 Derivation of KM Algorithms......Page 71
2.7.2 Statements of KM Algorithms......Page 72
2.7.3 Properties of KM Algorithms......Page 73
2.8 Cardinality and Average Cardinality of an IT2 FS......Page 75
Appendix 2A. Derivation of the Union of Two IT2 FSs......Page 77
Appendix 2B. Enhanced KM (EKM) Algorithms......Page 78
References......Page 80
3.1 Introduction......Page 84
3.2 Person FOU Approach for a Group of Subjects......Page 86
3.3.1 Methodology......Page 96
3.3.2 Establishing End-Point Statistics For the Data......Page 100
3.4 Interval End-Points Approach......Page 101
3.5 Interval Approach......Page 102
3.5.1 Data Part......Page 103
3.5.2 Fuzzy Set Part......Page 108
3.5.3 Observations......Page 118
3.5.4 Codebook Example......Page 120
3.5.5 Software......Page 123
3.6 Hedges......Page 124
3A.2 Description of the Methods......Page 126
3A.3 Discussion......Page 129
Appendix 3B. Derivation of Reasonable Interval Test......Page 130
References......Page 133
4.1 Introduction......Page 136
4.2.1 Definitions......Page 137
4.2.2 Desirable Properties for an IT2 FS Similarity Measure Used as a Decoder......Page 138
4.2.3 Problems with Existing IT2 FS Similarity Measures......Page 139
4.2.4 Jaccard Similarity Measure for IT2 FSs......Page 140
4.2.5 Simulation Results......Page 141
4.3 Ranking Method Used as a Decoder......Page 142
4.3.2 Mitchell’s Method for Ranking IT2 FSs......Page 147
4.3.4 Simulation Results......Page 148
4.4.1 Desirable Properties for Subsethood Measure as a Decoder......Page 149
4.4.3 Vlachos and Sergiadis’s IT2 FS Subsethood Measure......Page 150
4.4.4 Simulation Results......Page 151
4A.1 Compatibility Measures for T1 FSs......Page 154
4B.1 Proof of Theorem 4.1......Page 156
4B.3 Proof of Theorem 4.3......Page 159
References......Page 161
5.1 Introduction......Page 164
5.2 Novel Weighted Averages......Page 165
5.3 Interval Weighted Average......Page 166
5.4.1 α-cuts and a Decomposition Theorem......Page 168
5.4.2 Functions of T1 FSs......Page 170
5.4.3 Computing the FWA......Page 171
5.5.1 Introduction......Page 173
5.5.2 Computing the LWA......Page 176
5.5.3 Algorithms......Page 179
5.6 A Special Case of the LWA......Page 182
5.7 Fuzzy Extensions of Ordered Weighted Averages......Page 184
5.7.2 Ordered Linguistic Weighted Averages (OLWAs)......Page 185
5A.1 Extension Principle......Page 186
5A.2 Decomposition of a Function of T1 FSs Using α-cuts......Page 188
5A.3 Proof of Theorem 5.2......Page 190
References......Page 192
6.1 Introduction......Page 194
6.2.1 Firing Interval......Page 196
6.2.4 Type-Reduction and Defuzzification......Page 197
6.2.5 Observations......Page 198
6.3 Perceptual Reasoning: Computations......Page 199
6.3.1 Computing Firing Levels......Page 200
6.3.2 Computing Ỹ(PR)......Page 201
6.4 Perceptual Reasoning: Properties......Page 203
6.4.1 General Properties About the Shape of Ỹ(PR)......Page 204
6.4.2 Properties of Ỹ(PR) FOUs......Page 205
6.5 Examples......Page 206
6A.3 Proof of Theorem 6.3......Page 210
6A.6 Proof of Theorem 6.6......Page 211
6A.7 Proof of Theorem 6.7......Page 212
6A.8 Proof of Theorem 6.8......Page 213
References......Page 214
7.1 Introduction......Page 218
7.2.1 Vocabulary......Page 221
7.2.2 Word FOUs and Codebooks......Page 222
7.3 Reduction of the Codebooks to User-Friendly Codebooks......Page 223
7.4 CWW Engine for the IJA......Page 233
7.5 Decoder for the IJA......Page 234
7.6.1 Example 1: Comparisons for Three Kinds of Investors......Page 235
7.6.2 Example 2: Sensitivity of IJA to the Linguistic Ratings......Page 240
7.8 Conclusions......Page 247
References......Page 252
8.2 Design an SJA......Page 254
8.2.1 Methodology......Page 255
8.2.3 Data Pre-Processing......Page 257
8.2.4 Rulebase Generation......Page 261
8.2.5 Computing the Output of the SJA......Page 264
8.3 Using an SJA......Page 265
8.3.1 Single Antecedent Rules: Touching and Flirtation......Page 266
8.3.2 Single Antecedent Rules: Eye Contact and Flirtation......Page 268
8.3.3 Two-Antecedent Rules: Touching/Eye Contact and Flirtation......Page 270
8.3.4 On Multiple Indicators......Page 272
8.4 Discussion......Page 274
8.5 Conclusions......Page 275
References......Page 276
9.1 Introduction......Page 278
9.2 Missile Evaluation Problem Statement......Page 279
9.3.1 Encoder......Page 282
9.3.2 CWW Engine......Page 284
9.4 Per-C for Missile Evaluation: Examples......Page 285
9.5.1 Comparison with Mon et al.’s Approach......Page 292
9.5.2 Comparison with Chen’s First Approach......Page 295
9.5.3 Comparison with Chen’s Second Approach......Page 297
9.5.4 Discussion......Page 298
Appendix 9A: Some Hierarchical Multicriteria Decision-Making Applications......Page 299
References......Page 301
10.1 Introduction......Page 302
10.2 The Journal Publication Judgment Advisor (JPJA)......Page 303
10.3.1 Modified Paper Review Form......Page 304
10.3.2 Encoder......Page 305
10.3.3 CWW Engine......Page 307
10.3.4 Decoder......Page 309
10.4.1 Aggregation of Technical Merit Subcriteria......Page 310
10.4.2 Aggregation of Presentation Subcriteria......Page 313
10.4.3 Aggregation at the Reviewer Level......Page 318
10.4.4 Aggregation at the AE Level......Page 319
10.4.5 Complete Reviews......Page 323
10.5 Conclusions......Page 328
Reference......Page 329
11.1 Perceptual Computing Methodology......Page 330
11.2 Proposed Guidelines for Calling Something CWW......Page 331
Index......Page 334
