Fuzzy Logic in Chemistry
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Table of contents
- Cover
- Contentsv
- Contributorsxiii
- Forewordxv
- Prefacexix
- Chapter 1. The Treatment of Uncertainty in the Physical Sciences1
- I. General Introduction1
- II. The Quest for Certainty4
- III. Probabilistic Panaceas7
- IV. Quantum Indeterminacy10
- V. Chaotic Phenomena13
- VI. The Approach to Uncertainty15
- VII. Multivalued Logics19
- VIII. Possibilistic Paradigms21
- IX. Concluding Remarks24
- References26
- Chapter 2. From Classical Mathematics to Fuzzy Mathematics: Emergence of a New Paradigm for Theoreti31
- I. Introduction31
- II. Types of Uncertainty32
- Ill. Fuzzy Sets and Fuzzy Logic: An Overview34
- IV. Scientific Paradigms and Paradigm Shifts47
- V. From Classical Sets to Fuzzy Sets: A Grand Paradigm Shift48
- VI. Stages in the Paradigm Shift56
- VII. Conclusions61
- Acknowledgment62
- References62
- Chapter 3. Fuzzy Restrictions and Inherent Uncertainties in Chirality Studies65
- I. Introduction65
- II. Manifestations of Chirality and the Choice of Models66
- Ill. The Homochirality Problem72
- Acknowledgments88
- References88
- Chapter 4. Fuzzy Classical Structures in Genuine Quantum Systems91
- I. Introduction91
- II. Strange States of Molecules98
- III. Chemical Concepts Are Fuzzy Classical Concepts101
- IV. Statistical versus Individual Formalisms of Quantum Mechanics103
- V. The Decomposition of a Nonpure State into Pure States Is Not Unique107
- VI. Decompositions of a Thermal State into Continuously Many Pure States111
- VII. Chemical versus Quantum-Mechanical Point of View115
- VIII. Effective Thermal States118
- IX. Stochastic Dynamics on the Level of Pure States120
- X. A Canonical Decomposition of Thermal States into Pure States124
- XI. Fuzzy Classical Observables and Large Deviation Theory126
- XII. The Structure of Single Molecules130
- XIII. Concluding Remarks135
- Acknowledgments136
- References136
- Chapter 5. Fuzzy Measures of Molecular Shape and Size139
- I. Introduction139
- II. A Brief Review of Some Fuzzy Set Concepts Relevant to the Molecular Shape Problem141
- III. A Generalization of the Hausdorff Metric for Fuzzy Sets142
- IV. Fuzzy Symmetry Deficiency Measures, Fuzzy Chirality Measures, and Fuzzy Symmetry Groups Based on155
- V. Another Fuzzy Symmetry Approach: Syntopy and Syntopy Groups164
- VI. A Third Fuzzy Symmetry Approach: Symmorphy and Fuzzy Symmorphy Groups Based on Fuzzy Hausdorff-T166
- VII. Proof of the Metric Properties of the Symmetric Scaling–Nesting Dissimilarity Measure172
- VIII. Chirality Measures and Symmetry Deficiency Measures for Continua Using the SNDSM Metric176
- IX. A Fuzzy Scaling–Nesting Similarity Measure and the Fuzzy Scaling–Nesting Dissimilarity Metri177
- X. Fuzzy Measures of Chirality and Symmetry Deficiency, Fuzzy Symmetry Groups, and Fuzzy Symmorphy G179
- XI. The Center of Mass of a Fuzzy Set, the Center of Molecular Electron Density, and Fuzzy Central M183
- XII. The Fuzzy Average of Crisp Sets, the Fuzzy Average of Fuzzy Sets, the Crisp Average of Crisp Se185
- XIII. Two Generalizations of the ZPA Folding–Unfolding Continuous Symmetry Measures for Continua U188
- XIV. Fuzzy Set Generalizations of ZPA Folding–Unfolding Continuous Symmetry Measures Based on the193
- XV. The Chiral Racemization Path Problem in n-Dimensions and Mislow's Label Paradox195
- XVI. Some Developments in the Computation of Properties of Fuzzy Electron Densities200
- Appendix218
- Acknowledgment220
- References220
- Chapter 6. Linguistic Variables in the Molecular Recognition Problem225
- I. Introduction225
- II. Transformation of Molecular Scenarios to a Three-Dimensional World227
- III. Fuzzy Logic Strategies and Molecular Recognition234
- IV. Matching of Molecular Surfaces with Fuzzy Logic Strategies239
- V. Conclusions245
- Acknowledgments245
- References246
- Chapter 7. The Use of Fuzzy Graphs in Chemical Structure Research249
- I. Introduction249
- II. Fuzzy Graph Theory251
- III. Fuzzy Graph Theory Applications in Computer-Assisted Biopolymer NMR Assignment260
- IV. Structure Elucidation Research Based upon Multiple Spectra270
- V. Summary280
- Acknowledgments281
- References281
- Chapter 8. Fuzzy Logic in Computer-Aided Structure Elucidation283
- I. Why Is Fuzzy Logic Necessary?283
- II. Computer-Aided Structure Elucidation Strategies292
- III. Fuzzy Sets, Fuzzy Logic, and Fuzzy Graphs297
- IV. A Novel Strategy for Computer-Aided Structure Elucidation300
- Acknowledgments317
- References318
- Chapter 9. Fuzzy Hierarchical Classification Methods in Analytical Chemistry321
- I. Introduction321
- II. Fuzzy Partition of a Fuzzy Class324
- III. Cluster Substructure in a Fuzzy Class327
- IV. Fuzzy Divisive Hierarchical Clustering339
- V. Fuzzy Cross-Classification342
- VI. Fuzzy Hierarchical Classification Techniques in Analytical Chemistry347
- References355
- Index357
Fuzzy Logic has gained increasing acceptance as a way to deal with complexity and uncertainty in many areas of science and engineering. This book is the first to address its practical applications to chemical systems. Ten distinguished authors discuss the role of fuzzy logic in the characterization of a variety of chemical concepts, including chirality, quantum systems, molecular engineering and design, and hierarchical classification methods. Fuzzy Logic in Chemistry will appeal to both students and professionals who are seeking to learn more about theory and applications in an area of growing importance to the physical sciences.
Key Features
* The first book on the applications of fuzzy logic in chemistry
* Covers a topic relevant to many disciplines, including molecular design
* Discusses applications of fuzzy logic to the physical sciences, a rapidly growing area
* Features chapters from highly distinguished authors in the physical sciences
Key Features
* The first book on the applications of fuzzy logic in chemistry
* Covers a topic relevant to many disciplines, including molecular design
* Discusses applications of fuzzy logic to the physical sciences, a rapidly growing area
* Features chapters from highly distinguished authors in the physical sciences