Abstract
In fuzzy theory any degree to belong to a set can be considered as a positive distance from complementary set. So the distance moves from zero to one when the object belongs to the set. The extension theory considers a negative value of the distance. This is in conflict with the classical definition of the distance is a positive scalar. So we have a classical contradiction. To solve this conflict we define the distance as a vector with two different directions one positive and the other negative. The distances are vectors with positive norm. In this way we have positive norm for the two directions. In extension theory we define the dependent function and suitable transformations in a way to build a nonlinear neuron that can solve a very old conflicting problem in brain linear neural computation.
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Acknowledgments
This paper is sponsored by National Natural Science Foundation Project (61503085) and Science and Technology Planning Project of Guangdong Province (2016A040404015).
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Resconi, G., Yang, C. (2018). Solution of Brain Contradiction by Extension Theory. In: Shi, Z., Pennartz, C., Huang, T. (eds) Intelligence Science II. ICIS 2018. IFIP Advances in Information and Communication Technology, vol 539. Springer, Cham. https://doi.org/10.1007/978-3-030-01313-4_3
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DOI: https://doi.org/10.1007/978-3-030-01313-4_3
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