Table of Contents
Preface vii
About the Author xi
Chapter 1 Preliminary Information on Fuzzy Logic 1
1.1 Fuzzy sets 1
1.2 Fuzzy numbers 14
1.3 Fuzzy inference rules and reasoning 36
1.4 Fuzzy Modeling 40
1.5 Z-numbers 45
1.6 Fuzzy decision making 56
Chapter 2 State-of-the-Art of Material Selection and Synthesis 59
2.1 Literature review on material selection 59
2.1.1 Multi-criteria decision-making methods (MCDM) and the related techniques 60
2.1.2 Fuzzy logic and soft computing based methods 65
2.2 Literature review on synthesis of materials with characteristics required 68
2.2.1 Classical approaches 68
2.2.2 Modern computational approaches 70
Chapter 3 Fuzzy Material Selection Methodology 83
3.1 Factors affecting material selection 83
3.2 Fuzzy Big database on candidate materials (alloys) 90
3.3 Fuzzy rules mining by clustering for material synthesis 98
3.3.1 Main principles of data mining 98
3.3.2 Fuzzy rules mining from big database of materials by clustering 101
3.3.2.1 Fuzzy K-means clustering algorithm 101
3.3.2.2 Fuzzy C-means algorithm 103
3.3.2.3 Adaptive Network Based Fuzzy Inference System 106
3.4 Decision making for material selection by fuzzy inference 108
3.4.1 Statement of the problem of multiattribute decision making on alloy selection 108
3.4.2 Multiattribute decisions on selection of titanium alloys on the basis of the Z-number-valued weighted arithmetic mean 109
3.4.3 Multiattribute decisions on selection of alloys for pressure vessel on the basis of the VIKOR method 116
3.4.4 Decision making on alloy selection for drive shaft by using Z-valued If-Then rules 122
3.5 Material selection methodology on the basis of fuzzy expert systems 133
3.5.1 Expert System ESPLAN 133
3.5.2 Statement of the problem 138
3.6 Comparative analysis of material selection methodologies 146
Chapter 4 Intelligent System for Synthesis of Materials with Characteristics Required 149
4.1 Statement of the material synthesis problem 149
4.2 Z-clustering of materials data 150
4.2.1 State-of-the-art 150
4.2.2 Z-clustering using a new compound function 154
4.2.3 Z-rule base construction using general fuzzy type-2 clustering 156
4.3 Synthesis of new materials 159
4.3.1 Synthesis of Ti-Ni-Pd alloys with given characteristics 159
4.3.2 Synthesis of TiNiPt alloys with given characteristics 162
4.3.3 Synthesis of TiNiZr alloys with given characteristics 165
4.3.4 Computational synthesis of TiNiHf alloys with given characteristics 168
4.4 Fuzzy material synthesis by expert system for pressure vessel 172
4.4.1 Statement of the problem 172
4.4.2 Modelling by FCM 173
4.5 A Fuzzy approach to estimation of phase diagram under uncertain thermodynamic data 184
Chapter 5 Case Study 191
5.1 Case study for material selection. Application of Fuzzy Analytic Hierarchy Process to alloy selection problem 191
5.2 Computational synthesis of TiNi alloys by using fuzzy rules and big data concepts 197
5.3 Validity of the suggested approach. Evaluation of alloy performance by using Z-rules 201
Appendix A Fuzzy Big Database on Candidate Materials (Alloys) 207
Appendix B Fuzzy Big Database on Material Synthesis 217
Appendix C Documentation of ZNCalc Software for Computation with Z-numbers 229
Bibliography 245
Index 257
