## Complexity Management in Fuzzy Systems: A Rule Base Compression ApproachDoing research is a great adventure As any adventure sometimes it is hard You may feel alone and with no idea where to go But if you have courage and press onwards You will eventually stand where no one has stood And see the world as no one has seen it There can be no better feeling than this! Adaptation from ‘Introduction to Research’, Tom Addis (2004) The idea about this book has been on the author’s mind for almost a decade but it was only about a couple of years ago when the underlying research process was actually started. The reason for this delay has been the insufficient spare time for research being a lecturer in a ‘new’ UK university where the emphasis is mainly on teaching. And maybe this book would have never been written if the author had not been presented with the chance of developing new teaching modules in fuzzy logic that have given him food for thought in a research related context and have helped him combine efficiently his teaching and research activities. The title of this book may sound too specialised but it has a much wider meaning. Fuzzy systems are any systems for modelling, simulation, control, prediction, diagnosis, decision making, pattern recognition, image processing, etc. which use fuzzy logic. Although fuzzy logic is an advanced extension of binary logic, the latter is still used predominantly today. |

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### Contents

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22 Conjunctive and Disjunctive Systems | 9 |

62 Manipulation with Identity Rule Bases | 119 |

63 Manipulation with Transpose Rule Bases | 127 |

64 Manipulation with Permutation Rule Bases | 138 |

65 Specific Cases with Special Rule Bases | 144 |

66 Analysis of Manipulation Techniques with Special Rule Bases | 150 |

Formal Transformation of Fuzzy Rule Based Systems | 152 |

73 Combined Merging Manipulations | 158 |

74 Self Standing Inputs and Outputs | 164 |

23 Multiple Output and Single Output Systems | 10 |

24 Feedforward and Feedback Systems | 11 |

25 Single Rule Base and Multiple Rule Base Systems | 12 |

26 Complexity Analysis in Fuzzy Systems | 14 |

Rule Base Reduction Methods for Fuzzy Systems | 17 |

32 Removal and Fusion of Inputs | 19 |

33 Singular Value Decomposition of Output Matrix | 21 |

34 Conversion into Union Rule Configuration | 23 |

35 Spatial Decomposition into Subsystems | 25 |

36 Decomposition into Multilayer Hierarchical Structure | 26 |

37 Comparative Analysis of Reduction Methods | 29 |

Formal Presentation of Fuzzy Rule Based Systems | 32 |

42 Analysis of Rule Base Properties | 36 |

43 Presentation of Rule Bases by Boolean Matrices | 39 |

44 Presentation of Rule Bases by Binary Relations | 46 |

45 Comparative Analysis of Formal Presentation Techniques | 53 |

46 Application Range of Formal Presentation Techniques | 55 |

Formal Manipulation of Fuzzy Rule Based Systems | 65 |

53 Vertical Splitting Manipulation of Rule Bases | 73 |

54 Horizontal Merging Manipulation of Rule Bases | 81 |

55 Horizontal Splitting Manipulation of Rule Bases | 87 |

56 Output Merging Manipulation of Rule Bases | 92 |

57 Output Splitting Manipulation of Rule Bases | 102 |

58 Comparative Analysis of Formal Manipulation Techniques | 112 |

59 Application Range of Formal Manipulation Techniques | 113 |

Formal Manipulation with Special Rule Bases | 115 |

75 Total and Partial Identity Lines | 173 |

76 Comparative Analysis of Formal Transformation Techniques | 181 |

77 Application Range of Formal Transformation Techniques | 182 |

Formal Transformation of Feedback Rule Bases | 185 |

83 Transformation of Rule Bases with Local Feedback | 190 |

84 Transformation of Rule Bases with Global Feedback | 201 |

85 Transformation of Rule Bases with Nested Feedback | 211 |

86 Transformation of Rule Bases with Overlapping Feedback | 226 |

87 Transformation of Rule Bases with Crossed Feedback | 234 |

88 Transformation of Rule Bases with Multiple Feedback | 249 |

89 Feedback Rule Base Design | 257 |

810 Canonical Rule Base Networks | 264 |

811 Analysis of Transformation Techniques for Feedback Rule Bases | 268 |

Formal Simplification of Fuzzy Rule Based Systems | 269 |

92 Rule Base Simplification by Aggregation of Inconsistent Rules | 274 |

93 Rule Base Simplification by Filtration of Nonmonotonic Rules | 287 |

94 Complexity Evaluation of Formal Simplification Techniques | 328 |

95 Comparative Analysis of Formal Simplification Techniques | 338 |

96 Application Range of Formal Simplification Techniques | 339 |

Conclusion | 341 |

103 Application Framework for Fuzzy Rule Base Compression | 342 |

104 Future Directions for Related Research in Fuzzy Systems | 343 |

105 Overall Book Evaluation | 344 |

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### Other editions - View all

Complexity Management in Fuzzy Systems: A Rule Base Compression Approach Alexander Gegov No preview available - 2007 |

Complexity Management in Fuzzy Systems: A Rule Base Compression Approach Alexander Gegov No preview available - 2009 |

Complexity Management in Fuzzy Systems: A Rule Base Compression Approach Alexander Gegov No preview available - 2010 |

### Common terms and phrases

aggregation Algorithm base in level binary relation block matrix consistent defuzzification Equation equivalent MRB system Example FB function feedback following Boolean matrix following matrix formal manipulation function F2 fuzzy logic fuzzy membership function fuzzy rule base fuzzy system horizontal merging incomplete inconsistent rules initial MRB system input i1 Inputs/Outputs 11 12 integer table layer 1 layer layer 1 level level 1 o1 level/layer layer Mamdami maplets mapped matrix and binary merging manipulations monotonic non-exhaustive number of rules o2 level operand matrix operand rule bases output merging output o1 Output surface output-input interconnections parameters permutations of linguistic product matrix product rule base quantitative complexity RB presented RB RB RBE2 RBF1 RBF2 RBS1 RBS2 RBT1 RBT2 represented rule base RB rule based system Rule number Linguistic shows simple FB single equivalent rule substage Sugeno system are given system is presented value of i1 whereas