| Over the last decade fuzzy sets and fuzzy logic introduced in 1965 by
Lotfi Zadeh [113] have been used in a wide range of problem domains
including process control, image processing, pattern recognition and
classification, management, economics and decision making. Specific
applications include washing-machine automation, camcorder focusing, TV
colour tuning, automobile transmissions and subway operations [29]. We
have also been witnessing a rapid development in the area of neural networks
(see e.g. [93, 94, 135]). Both fuzzy systems and neural networks, along with
probabilistic methods [1, 20, 67], evolutionary algorithms [23, 59], rough
sets [69, 70] and uncertain variables [6, 7, 8], constitute a consortium of soft
computing techniques [1, 39, 42]. These techniques are often used in
combination. For example, fuzzy inference systems are frequently converted
into connectionist structures called neuro-fuzzy systems which exhibit
advantages of neural networks and fuzzy systems. In literature various neuro
fuzzy systems have been developed (see e.g. [11, 12, 13, 15, 18, 24, 25, 26,
34, 35, 37, 40, 49, 50, 52, 53, 54, 55, 60, 61, 65, 72, 75, 76, 80-85, 100]).
They combine the natural language description of fuzzy systems and the
learning properties of neural networks. Some of them are known in literature
under short names such as ANFIS [33], ANNBFIS [15], DENFIS [41],
FALCON [51], GARIC [3], NEFCLASS [62], NEFPROX [62, 64],
SANFIS [99] and others. |
