296 A.F. Shapiro, R. Paul Gorman Insurance: Mathematics and Economics 26 2000 289–307
fuzzy NN can be constructed where the NN possesses fuzzy signals andor has fuzzy weights. Conversely,
FL can use technologies from other fields, like NNs or GAs, to deduce or to tune, from observed data, the
membership functions in fuzzy rules, and may also structure or learn the rules themselves.
4. Functional classes
ANM technologies also can be grouped into func- tional classes. Broadly, these classes include:
• Generalized nonlinear function approximation,
which adaptively constructs a nonlinear relation- ship between observed variables and dependent
variables. Technologies in this class include NNs and generalized regression networks.
• Domain segmentation, which involves finding sub-
domains in the observation space where the rela- tionships between observed variables and dependent
variables are consistent. This is a very crucial step in the development of nonlinear models. This class
includes rule induction and technologies for analyz- ing data and for inducing decision trees from data.
• Generalized knowledge encoding, which uses do-
main knowledge to creatively bias more general adaptive methods. This is an important component
in the evolution of robust nonlinear models. Tech- nologies in this category includes expert systems,
neuro-fuzzy models and case-based reasoning tech- nologies.
• Dimension reduction, which uses variable selection
and aggregation to lower the dimensionality of the problem. This group includes Kohonen networks
and fuzzy clustering Zimmermann, 1991, Section 11.2, which seeks to divide objects into categori-
cally homogeneous subsets called “clusters”.
• Numerical optimization, which allows the numeri-
cal estimation of model parameters based on a sam- ple of data. These optimization technologies are
an indispensable element of an adaptive nonlinear modeling toolkit. Technologies in this class include
gradient descent, simulated annealing Aarts and Van Laarhoven, 1987, and GAs. Gradient descent
iteratively updates the weight vector in the direc- tion of the greatest decrease in the network error
and simulated annealing is a stochastic algorithm that minimizes numerical functions, whose distin-
guishing feature is that it uses a random process to elude local minimums.
5. The team approach
Given this wide range of technologies, it often is ad- vantageous to approach a problem with a team whose
members have diverse backgrounds and experiences. Thus, for example, an ideal team may be composed of
members whose backgrounds include not only math- ematics, economics and statistics, but physics, and
computational and computer science, as well. It is the ability of the team to craft a solution by integrating
complementary advanced technologies that makes this methodology so powerful.
6. Modeling considerations
