Fuzzy Logic provides a framework for dealing quantitatively, mathematically, and logically with semantic, ambiguous, elastic, and vague concepts. It is a well proven and well established logic of degrees.
In fuzzy logic a data point’s membership in a set is not crisp (that is, either in or out of the set), but can be specified as a degree of membership.

Fuzzy logic has a wide spectrum of applicability in expert system, neural networks, clustering, decision trees, and many forms of machine learning.

Decision Trees use a form of data mining to find the rules that classify a collection of data values based on an objective measurement or value.
The classification scheme is expressed in a tree that actually implements a set of nested if-then-else rules. Decision trees find the rule orderings that classify the objective in the least number of rules.

Cluster Analysis organizes data into sets according their degrees of similarity. Unlike conventional cluster analysis that assigns a value to a single cluster, fuzzy clustering can assign a data point to multiple clusters with varying degrees of membership.

Automatic cluster detection and quantification finds patterns in data and then produces the if-then-else rules that turn the analysis into prediction and classification models.

Bayes Theorem implements a form of probabilistic logic that accumulates evidence for and against some objective or proposition. Bayes Theorem is a way of rigorously combining new evidence to decide whether some assertion is true or false (or whether some element is a member of a particular set.)

Genetic Algorithms and Evolutionary Programming are search and optimization techniques that work in a manner similar to natural selection and survival of the fittest in the theory of evolution.

From a large population of random possible solutions, new generations of solutions are created by breeding and occasionally mutating the current population. The solutions that give better and better answers (have a greater “goodness of fit”) are retained. This process continues until a final best answer is developed.

Machine Learning uses past errors and principles from adaptive control theory to automatically learn and predict the behavior of a system.
While neural and self-organizing maps are a form of machine learning, the underlying mechanism are much broader involving statistical learning theory, pattern induction, linear ad non-linear regression, decision trees, and support vector machines.

Neural Networks are highly nonlinear classification machines that work in a manner analogous to a collection of artificial neurons.
A neural network learns its classifications from examples, in the same way that biological neural systems (like the brain) learn from experience. Because they learn from examples, neural networks are excellent candidates for data mining, fault prediction, problem diagnosis, and similar applications where sufficient historical examples are available.

Rule-Induction or rule discovery uses a form of deep data mining to isolate patterns in data and then quantify them as if-then rules. It often forms the core of a regenerative learning system.
Rule induction is a powerful method of creating expert-like knowledge bases and coding patterns in rules that can be easily understood, modified and combined with subject matter expert rules.

Genetic algorithms can be used to reduce, tune, and optimize discovered rules.

Self-Organizing Maps(SOM’s) automatically learn and expose the relationships in high dimensional collections of data. Combining computational efficiency, ease of use, and powerful pattern discovery, self-organizing maps identify common properties among data and also generate a collection of description (classification) rules.

Statistical Learning Theory comprises a closely related set of techniques for learning system behavior form the statistical characteristics of the data. Developed by Vapnik and Chervonenkis, statistical learning theory (SLT) provides a powerful tool in building models from time-varying data. STL models can discover and quantify multiple periodicity patterns (such as seasonality trends), differentiate abrupt changes from spikes, associate confidence degrees to predictions, and work with a minimum of historical data.

Linear and Non-Linear Regression is a machine learning technique for fitting a curve to a collection of data. The algebraic formula for the curve is a model of the trend through the data and can be used to predict future values of the trend with varying degrees of certainty.

Linear regression is the most common technqiue and finds a straight line for the equation y = a + bx (where “y” is the dependent value and “x” is the independent variable, often time. The value “a” is the intercept, and “b” is the slope – run versus rise).

Non-linear regression models, as the name implies, model curves that fit data with underlying patterns that are not linear (such as data with seasonalities or other periodic behaviors).

Adaptive Control Theory combines a variety of disciplines from continuous and non-continuous control theory (such as regularization, vector quantization, support vector machines, and ordinary PID control) Adaptive control measures the response error in the system outcome and adjusts the numerical controls (the “coefficients”) to improve the underlying model (thus continuing to reduce the error rate).