Artificial neural networks models with fuzziness and chaos phenomena

Abstract

We consider a generalized model of neural network with a fuzziness and chaos. The origin of the fuzzy signals lies in complex biochemical and electrical processes of the synapse and dendrite membrane excitation and the inhibition mechanism, The mathematical operations included into fuzzy neural network modeling are: the scalar product between inputs of layers and synaptic weights is replaced by a fuzzy logic multiplication, the sum of products changes to the fuzzy logic sums, and the operators such as suprenium, maximum, and minimum are presented for a fuzzy description. The algorithm of varying membership functions, built basing on a backpropagation paradigm and a method of fuzzy neural optimization, has been considered. Both fuzzy properties and a chaos phenomenon are analyzed basing upon experimental computations.

Nagrinėjamas apibendrintas neurotinklų modelis atsižvelgiant į parametrų neryškumą (neapibrėžtumą) ir chaosą. Neryškumas susietas su sinapsių biocheminiais procesais ir dendritų membranų mechanizmų atsitiktiniais reiškiniais bei galimais įėjimų signalų neapibrėžtumais. Pateikti neryškios logikos algoritmai dirbtinio neurotinklo plotmėje bei chaoso interpretacijoje, duoti skaitinio chaoso pasireiškimo eksperimento rezultatai.