FUZZY NONLINEAR ACTIVITY AND DYNAMICS OF FUZZY UNCERTAINTY IN THE NEURAL COMPLEX

The studies addressed in this paper refer to the following: (i) Deduci ng a functional relationship between the logistic output versus input values in a neural network when the boundaries of the input and output sets are fuzzy and developing a fuzzy Riccardi differential equation (FRDE) which governs the relevant nonlinear process(es) associated wit h the neural complex. (ii) Evolving the dynamics of learning associate d with a fuzzy neural network in terms of a fuzzy uncertainty paramete r via a fuzzy Fokker-Planck equation (FFPE). The logistic growth of ou tput versus input in the fuzzy neural complex as dictated by the FRDE, follows not only a generalized representation of a stochastically jus tifiable sigmoidal function (as decided by the spatial long-range orde r of neuronal state proliferation across the network), but it also cap tures the approximate nature of reasoning and perception associated wi th the ''granular information'' vis-a-vis the fuzzy set(s) of the vari ables involved. As regards to the solution of FRDE, it represents the function approximation of overlapping output clusters resulting from t he segments of input-space grouped into membership classes (each depic ting a certain range of input values). An architecture based on the fu zzy sigmoidal description of the nonlinear process(es) involved is pre sented and discussed. In reference to the dynamics of learning with an associated fuzzy uncertainty, the relevant stochasticity versus time discourse is described in terms of a FFPE. The fuzzy variable of the F FPE refers to the probability density function (pdf) of a (fuzzy) erro r between the network's output and a desired objective function. It is shown that the pdf is related to the grade membership function of the fuzzy attributes; and, the FFPE developed thereof offers a vivid, tem poral learning profile of the neural complex under fuzzy consideration s. (C) 1998 Elsevier Science B.V. All rights reserved.