Fuzzy neurons and fuzzy multilinear mappings

There are several mathematical models of fuzzy neurons. Usually, input values of them are fuzzy numbers (that is, fuzzy sets in one-dimensional space) with triangular membership functions. The aggregating operations may be one of the T-norms or T-conorms. There are currently few, if any, learning methods proposed in the literature. We propose to consider fuzzy linear spaces as fuzzy inputs of fuzzy neurons and offer mathematical theory to work with this notions. In particular, we study fuzzy multilinear maps of fuzzy linear spaces. If the neuron model were to carry out only linear operations, the method would lose its mathematical attractiveness, but this is overcome by considering multidimensional linear spaces