Explainable Neural Networks Based on Fuzzy Logic and Multi-criteria Decision ToolsThe research presented in this book shows how combining deep neural networks with a special class of fuzzy logical rules and multi-criteria decision tools can make deep neural networks more interpretable – and even, in many cases, more efficient. Fuzzy logic together with multi-criteria decision-making tools provides very powerful tools for modeling human thinking. Based on their common theoretical basis, we propose a consistent framework for modeling human thinking by using the tools of all three fields: fuzzy logic, multi-criteria decision-making, and deep learning to help reduce the black-box nature of neural models; a challenge that is of vital importance to the whole research community. |
Contents
| 1 | |
| 2 | |
| 3 | |
2 Implications | 29 |
3 Equivalences | 43 |
4 Modifiers and Membership Functions in Fuzzy Sets | 63 |
Decision Operators | 82 |
5 Aggregative Operators | 85 |
6 Preference Operators | 101 |
Learning and Neural Networks | 119 |
7 Squashing Functions | 120 |
8 Learning Rules | 135 |
9 Interpretable Neural Networks Based on ContinuousValued Logic and Multicriteria Decision Operators | 147 |
10 Conclusions | 170 |
Other editions - View all
Explainable Neural Networks Based on Fuzzy Logic and Multi-criteria Decision ... József Dombi,Orsolya Csiszár No preview available - 2021 |
Explainable Neural Networks Based on Fuzzy Logic and Multi-criteria Decision ... József Dombi,Orsolya Csiszár No preview available - 2022 |
Common terms and phrases
activation functions aggregated equivalences arithmetic mean binary relation bounded system chapter classification property continuous logical Csiszár cutting function decision tools Definition direct calculation Dombi ec(x ed(x equivalence operators equivalence relations examples fa(x fa(y fc(x fc(y fd(x Fodor follows from direct Fuzziness and Soft fuzzy implication fuzzy logic Fuzzy Sets Syst hidden layers increasing bijection input isomorphic ISSN Jayaram Let us define Logic and Multi-criteria logical operators Łukasiewicz logic machine learning membership functions monotonicity Morgan law Morgan property Multi-criteria Decision Tools natural negations nc(x nd(x nd(y negation operator neural model nilpotent connective system nilpotent logical systems nilpotent neural nilpotent operators normalized generator functions optimization parameters perceptron preference modeling preference operator Proof Proposition Remark S-implication Sect sigmoid function Soft Computing squashing function strictly increasing strong negation Studies in Fuzziness t-norm Table triangular Trillas unary operators uninorms values weighted aggregative operator weighted general operator