Research
Kosko’s technical contributions have been in three main areas: fuzzy logic, neural networks, and noise.
In fuzzy logic, he introduced fuzzy cognitive maps, fuzzy subsethood, additive fuzzy systems, fuzzy approximation theorems, optimal fuzzy rules, fuzzy associative memories, various neural-based adaptive fuzzy systems, ratio measures of fuzziness, the shape of fuzzy sets, the conditional variance of fuzzy systems, and the geometric view of (finite) fuzzy sets as points in hypercubes and its relationship to the on-going debate of fuzziness versus probability.
In neural networks, Kosko introduced the unsupervised technique of differential Hebbian learning, sometimes called the “differential synapse,” and most famously the BAM or bidirectional associative memory family of feedback neural architectures, with corresponding global stability theorems.
In noise, Kosko introduced the concept of adaptive stochastic resonance, using neural-like learning algorithms to find the optimal level of noise to add to many nonlinear systems to improve their performance. He proved many versions of the so-called “forbidden interval theorem,” which guarantees that noise will benefit a system if the average level of noise does not fall in an interval of values.
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