A Fuzzy Model Of Nervous System

Year 2017, Volume: 5 Issue: 1, 46 - 52, 01.05.2017

Timur Karacay

Abstract

Still there is no model of mathematics that is able to represent the true biological process, which can transform the signals, obtained from the nervous system to logical reasoning. However, some mathematical models may approximate to the process of logical reasoning. This paper assumes the set of inputs as fuzzy propositions and uses a LCA (locally compact abelian) group structure to characterize knowledges as Fourier series. The representation used in the study enables us to introduce the notions of logical bases and logical dependencies of knowledges. Also, this makes possible to compare the truthfulness of propositions and define maximal truthfulness that corresponds to the true value in the Boolean logic. Finally, the axiom False ⇒ True of the Boolean logic results

Keywords

Nervous system, neurons, Fuzzy Systems, Locally Compact Abelian Group, Fourier Series

Sinir Sistemi için Bir Fuzzy Modeli

Abstract

Sinir sistemi tarafından algılanan sinyallerin mantıksal akıl yürütmeye nasıl dönüştüğünü temsil eden bir matematiksel model yoktur. Ancak bu yönde önerilecek bazı modeller akıl yürütme sürecine yaklaşımı sağlayabilir. Bu yazı, sinir sistemine yapılan uyarıları birer fuzzy önermesi olarak alıyor ve onları LCA (yerel compact abelian) gruplar üzerindeki Fourier dönüşümleri ile karakterize ediyor. Bu temsil, bilginin mantıksal bir tabana dayalı olmasını sağlıyor ve bilginin, bool mantığına göre maximal doğruluğunu tanımlıyor. Son olarak bool mantığındaki False ⇒ True aksiyomu bir yan ürün olarak ispatlanıyor

Keywords

Sinir sistemi, nöronlar, Fuzzy Sistemler, Lokal Kompakt Abel Grubu, Fourier Serileri

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