Titlebook: Explainable Neural Networks Based on Fuzzy Logic and Multi-criteria Decision Tools; József Dombi,Orsolya Csiszár Book 2021 The Editor(s) (

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Equivalencesor applications in image processing, we define the overall equivalence of two grey level images and give an important semantic meaning of the aggregated equivalences. Finally, for applications in image processing, we define the overall equivalence of two grey level images and give an important semantic meaning to the aggregated equivalences.

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Book 2021odeling 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..

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Lotta Frändberg,Bertil Vilhelmsonough these operators have many properties in common with implications, we show that there is a subtle but important difference. After a profound examination of the main properties of the preference operator, our main goal is the implementation of this operator into neural networks.

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Modifiers and Membership Functions in Fuzzy Setslts. Now, we make a suggestion of how modifiers and membership functions can be linked to the logical operators of the system. This unified framework will be useful and aid better interpretability of neural computations in Chap. ..

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Squashing Functionsle parametrized family of functions that can not only be used for approximating piecewise linear membership functions but also Łukasiewicz-type logical operators. We show that the derivative of a squashing function is the difference of two sigmoid functions. This fact will come useful in gradient-based applications.

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Book 2021tools 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 m