Fuzzy logic s From Wikipedia, the free encyclopedia Contents 1 Adaptive neuro fuzzy inference system 1 1.1 References ............................................... 1 2 Bate’s chip 2 2.1 References ............................................... 2 3 BL (logic) 3 3.1 Syntax ................................................. 3 3.1.1 Language ........................................... 3 3.1.2 Axioms ............................................ 4 3.2 Semantics ............................................... 4 3.3 Bibliography ............................................. 5 3.4 References .............................................. 5 4 Combs method 6 4.1 Equality proof ............................................. 6 4.2 Combinatorial explosion ....................................... 6 4.3 Example ............................................... 6 4.4 References .............................................. 7 5 Construction of t-norms 8 5.1 Generators of t-norms ........................................ 8 5.1.1 Additive generators ...................................... 8 5.1.2 Multiplicative generators ................................... 9 5.2 Parametric classes of t-norms ..................................... 9 5.2.1 Schweizer–Sklar t-norms ................................... 10 5.2.2 Hamacher t-norms ...................................... 10 5.2.3 Frank t-norms ........................................ 11 5.2.4 Yager t-norms ........................................ 11 5.2.5 Aczél–Alsina t-norms .................................... 11 5.2.6 Dombi t-norms ........................................ 12 5.2.7 Sugeno–Weber t-norms ................................... 12 5.3 Ordinal sums ............................................. 13 5.3.1 Ordinal sums of continuous t-norms ............................. 14 i ii CONTENTS 5.4 Rotations ............................................... 14 5.5 See also ................................................ 15 5.6 References .............................................. 16 6 Defuzzification 17 6.1 Methods ................................................ 17 6.2 Notes ................................................. 18 6.3 See also ................................................ 18 7 Degree of truth 19 7.1 See also ................................................ 19 7.2 Bibliography ............................................. 19 8 European Society for Fuzzy Logic and Technology 20 8.1 History ................................................. 20 8.2 Conferences .............................................. 20 8.3 Publications .............................................. 21 8.4 Presidents ............................................... 21 8.5 References ............................................... 21 8.6 External links ............................................. 21 9 Fuzzy architectural spatial analysis 22 9.1 Overview ............................................... 22 9.2 References ............................................... 22 9.3 Further reading ............................................ 22 9.4 See also ................................................ 23 10 Fuzzy associative matrix 24 11 Fuzzy classification 25 11.1 Classification ............................................. 25 11.2 See also ................................................ 26 11.3 References ............................................... 26 12 Fuzzy cognitive map 27 12.1 Details ................................................. 27 12.2 References .............................................. 29 12.3 External links ............................................. 29 13 Fuzzy Control Language 30 13.1 External links ............................................. 30 14 Fuzzy control system 31 14.1 Overview ............................................... 31 14.2 History and applications ....................................... 31 CONTENTS iii 14.3 Fuzzy sets ............................................... 32 14.3.1 Fuzzy control in detail .................................... 33 14.3.2 Building a fuzzy controller .................................. 37 14.4 Antilock brakes ............................................ 38 14.5 Logical interpretation of fuzzy control ................................ 39 14.6 See also ................................................ 39 14.7 References ............................................... 40 14.8 Further reading ............................................ 40 14.9 External links ............................................. 40 15 Fuzzy electronics 41 15.1 See also ................................................ 41 15.2 Bibliography ............................................. 41 15.3 External links ............................................. 41 16 Fuzzy finite element 42 16.1 See also ................................................ 42 16.2 References ............................................... 42 17 Fuzzy logic 43 17.1 Overview ............................................... 43 17.1.1 Applying truth values ..................................... 43 17.1.2 Linguistic variables ...................................... 44 17.2 Early applications ........................................... 44 17.3 Example ................................................ 44 17.3.1 Hard science with IF-THEN rules .............................. 44 17.3.2 Define with multiply ..................................... 45 17.3.3 Define with sigmoid ..................................... 45 17.4 Logical analysis ............................................ 45 17.4.1 Propositional fuzzy logics .................................. 45 17.4.2 Predicate fuzzy logics .................................... 45 17.4.3 Decidability issues for fuzzy logic ............................... 46 17.5 Fuzzy databases ............................................ 46 17.6 Comparison to probability ....................................... 46 17.7 Relation to ecorithms ......................................... 47 17.8 Compensatory fuzzy logic ...................................... 47 17.9 See also ................................................ 47 17.10References ............................................... 48 17.11Bibliography ............................................. 49 17.12External links ............................................. 51 18 Fuzzy markup language 52 18.1 Overview ............................................... 52 iv CONTENTS 18.2 FML at work: syntax, grammar and hardware synthesis ........................ 52 18.2.1 FML Syntax .......................................... 53 18.2.2 FML Grammar ........................................ 55 18.2.3 FML Synthesis ........................................ 56 18.3 References ............................................... 56 18.4 Further reading ............................................ 57 19 Fuzzy mathematics 58 19.1 Some fields of mathematics using fuzzy set theory .......................... 58 19.2 See also ................................................ 59 19.3 References ............................................... 59 19.4 External links ............................................. 60 20 Fuzzy measure theory 61 20.1 Definitions ............................................... 61 20.2 Properties of fuzzy measures ..................................... 61 20.3 Möbius representation ......................................... 62 20.4 Simplification assumptions for fuzzy measures ............................ 62 20.4.1 Sugeno λ-measure ....................................... 62 20.4.2 k-additive fuzzy measure ................................... 63 20.5 Shapley and interaction indices .................................... 63 20.6 See also ................................................ 63 20.7 References ............................................... 63 20.8 External links ............................................. 63 21 Fuzzy number 64 21.1 See also ................................................ 64 21.2 References ............................................... 64 21.3 External links ............................................. 64 21.4 Applications .............................................. 64 22 Fuzzy pay-off method for real option valuation 65 22.1 Method ................................................ 65 22.2 Use of the method ........................................... 66 22.3 References ............................................... 66 22.4 External links ............................................. 66 23 Fuzzy routing 67 23.1 See also ................................................ 67 23.2 External links ............................................. 67 24 Fuzzy rule 68 24.1 Comparison between Boolean and fuzzy logic rules ......................... 68 24.2 Comparison between computational verb and fuzzy logic rules .................... 68 CONTENTS v 24.3 See also ................................................ 68 25 Fuzzy set 69 25.1 Definition ............................................... 69 25.2 Fuzzy logic .............................................. 69 25.3 Fuzzy number ............................................. 70 25.4 Fuzzy interval ............................................. 70 25.5 Fuzzy relation equation ........................................ 70 25.6 Axiomatic definition of credibility ................................... 70 25.7 Credibility inversion theorem ..................................... 70 25.8 Expected Value ............................................ 71 25.9 Entropy ................................................ 71 25.10Generalizations