Preface ......................................................... 9
Chapter 1. Generalized Nets in Modeling Relational Database
Management Systems .................................. 11
1.1. Overview of database server processes ..................... 11
1.1.1. Query processing ................................... 11
1.1.2. Relational algebra operations ...................... 12
1.1.2.1. Selection operation σсondition(R) ........... 12
1.1.2.2. Join operation R×сonditionS ................. 13
1.1.2.3. Projection operation П(attribute list)(R) ..... 13
1.2. GN model of query execution ............................... 13
1.3. GN representation of query execution plan ................. 17
1.4. GN models of some relational algebra operations ........... 21
1.4.1. Sort-merge join .................................... 21
1.4.2. Linear search selection ............................ 24
1.5. Transaction processing and concurrency control ............ 25
1.6. GN model of transaction processing and concurrency
control ................................................... 27
1.6.1. Brief description of the model ..................... 27
1.6.2. Tokens and memory elements description ............. 29
1.6.3. Detailed description of the model .................. 30
1.7. Conclusions, application and future work .................. 34
Chapter 2. Intuitionistic fuzzy generalized net analysis
of concurrency control with deadlock detection
in database systems ................................. 37
2.1. Periodic deadlock detection ............................... 38
2.2. Continuous deadlock detection ............................. 47
2.3. General model ............................................. 56
2.4. Conclusions ............................................... 63
Chapter 3. Intuitionistic Fuzzy Relational Databases ........... 65
3.1. Introduction .............................................. 65
3.2. Intuitionistic fuzzy relational model ..................... 66
3.3. Physical representation of the intuitionistic fuzzy
relational model .......................................... 67
3.3.1. Database template ifs template ..................... 67
3.3.2. Type ifs.bool ..................................... 68
3.3.3. Predicates ......................................... 68
3.3.4. Modifiers .......................................... 68
3.4. Intuitionistic fuzzy SQL .................................. 68
3.4.1. Create database .................................... 68
3.4.2. Create table ....................................... 69
3.4.3. Create predicate ................................... 69
3.4.4. Create modifier .................................... 69
3.4.5. Select ............................................. 69
3.4.5.1. Target list ............................... 70
3.4.5.2. FROM clause ............................... 70
3.4.5.3. WHERE clause .............................. 71
3.4.5.4. GROUP BY clause ........................... 71
3.4.5.5. HAVING clause ............................. 71
3.4.5.6. MODIFY BY clause .......................... 71
3.4.5.7. Set operations - UNION and INTERSECT ...... 71
3.4.6. UPDATE ............................................. 72
3.4.7. Crisp relations .................................... 72
3.5. Enabling IFSQL support .................................... 72
3.6. Translation of the Intuitionistic Fuzzy SQL ............... 73
3.7. An example ................................................ 77
3.8. Conclusions and application ............................... 82
Chapter 4. Intuitionistic Fuzzy Mediator ....................... 83
4.1. Introduction .............................................. 83
4.2. Uncertainty in relational databases ....................... 85
4.3. The intuitionistic fuzzy tabular (ifrdb) model -
the mediator level ........................................ 87
4.4. Probabilistic data & intuitionistic fuzzy
representation - binder level ............................. 88
4.4.1. Performing selection operation using IFRDBMS ....... 89
4.4.2. Performing join using IFRDBMS ...................... 90
4.5. Null values intuitionistic fuzzy representation-binder
level ..................................................... 91
4.6. Fuzzy data and its intuitionistic fuzzy representation-
binder level .............................................. 93
4.7. Concluding remark on the binder level ..................... 94
4.8. Enhanced query model constraints utilization .............. 95
4.9. GN representation of the intuitionistic fuzzy mediator .... 97
4.9.1 Description of the places ........................... 99
4.9.2. Description of the GN .............................. 99
Chapter 5. Generalized Net Model of an Expert System with
Temporal Components ................................ 103
5.1. Introduction ............................................. 103
5.2. On two previous GN-models ................................ 104
5.3. Main results: tenth GN-model of ESS ...................... 118
5.3.1. The Intuitionistic Fuzzy logics of the Tenth
GN Model .......................................... 119
5.3.2. The Specification of the Tenth GN Model ........... 121
5.4. Conclusion ............................................... 131
Appendix A. Generalized Nets .................................. 133
Appendix B. Intuitionistic Fuzzy Logic ........................ 151
Bibliography .................................................. 155
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