Wolfram Mathematica Fuzzy Logic

Category Intelligent Software>Fuzzy Logic Systems/Tools

Abstract Wolfram Mathematica Fuzzy Logic (WMFL) brings you an essential set of tools for creating, modifying, and visualizing fuzzy sets and fuzzy logic-based systems.

Ideal for engineers, researchers, and educators, WMFL provides practical examples that introduce you to basic concepts of fuzzy logic and demonstrate how to effectively apply the tools in the package to a wide variety of fuzzy system design tasks.

Experienced fuzzy logic designers will find it easy to use the package to research, model, test, and visualize highly complex systems.

The package's built-in functions help you at every stage of the fuzzy logic design process as you define inputs and outputs, create fuzzy set membership functions, manipulate and combine fuzzy sets and relations, apply inferencing functions to system models, and incorporate defuzzification routines.

Ready-to-use graphics routines make it easy to visualize defuzzification strategies, fuzzy sets, and fuzzy relations.

WMFL also takes advantage of Mathematica (see Note 1) notebooks, letting you combine fuzzy design settings, computations, 2D and 3D graphics, and even text in a single document on screen.

This interactive document format Not only is useful to professionals working on a complex fuzzy model but also is ideal for presenting concepts to students and allows them to turn in completed homework assignments and lab reports either electronically or on paper as a printed notebook.

The package comes with electronic documentation, which is fully integrated with the Mathematica Help Browser.

Wolfram Mathematica Fuzzy Logic New features/capabilities in ‘Version 2’:

1) Universal space is now defined with three (3) numbers that specify the start and end of the universal space and the increment between elements, giving users a greater flexibility in choosing the universal space.

2) Membership functions to create special types of fuzzy sets, including bell-shaped, sigmoidal, two-sided Gaussian, and digital fuzzy sets.

3) Visualization tool, fuzzy graph, to show what a set of fuzzy rules looks like.

4) Functions to find the smallest of maximum defuzzification and the bisector of area defuzzification of a fuzzy set.

5) Operators to return the fuzzy cardinality of a fuzzy set, the degree of subset-hood between fuzzy sets or relations, the Hamming distance from one fuzzy set or relation to another, and the set of all alpha levels that represent distinct alpha cuts of a fuzzy set or relation.

6) Yu and Weber union and intersection operations;

7) Introduction of alpha cuts for fuzzy relations;

8) Fuzzy relation equations;

9) Random fuzzy sets and fuzzy relations functions;

10) Fuzzy inferencing functions for rule-based inference;

11) Fuzzy arithmetic functions for fuzzy multiplication and division;

12) Fuzzy c-means clustering function that returns a list of cluster centers, a partition matrix indicating the degree to which each data point belongs to a particular cluster center, and a list containing the progression of cluster centers found during the run.

Wolfram Mathematica Fuzzy Logic features/capabilities include:

1) Membership Functions --

Triangular; Trapezoidal; Gaussian; Bell-Shaped; Double-Sided Gaussian; Sigmoidal; Digital; and User-Defined.

2) Compositions and Inferencing --

Compositions - Max-Min, Max-Dot, Max-Star; Rule-Based Inferencing for Multiple-Input/Single-Output Systems with Mamdani, Model, and Scaled Options; and Composition-Based Inferencing.

3) Standard and Parameterized Fuzzy Aggregators --

Intersections and Unions - Min, Max, Hamacher, Frank, Yager, Dubois- Prade, Dombi, Yu, Weber; Products and Sums - Drastic, Bounded, Algebraic, Einstein, Hamacher; Means - Arithmetic, Geometric, Harmonic, Generalized; and User-Defined Aggregators.

4) Fuzzy Operators --

Complements - Standard, Sugeno, Yager; Defuzzifiers - Center of Area, Mean of Max, Smallest of Max, Largest of Max, Bisector of Area; and Normalization, Concentration, Dilation, Fuzzy Cardinality, Subsethood, Hamming Distance, Level Set, Alpha Cuts.

Visualization of Fuzzy Sets and Relations --

Discrete, Line, and Crisp Plots of Fuzzy Sets; Discrete 3D, Surface, and Wire-Frame Plots of Fuzzy Relations; Fuzzy Graph; Membership Matrices; and Defuzzification Results.

Fuzzy System Modeling and Design Applications --

Fuzzy Modeling - System Definition; Inferencing; and Model Building.

Fuzzy Logic Control - Fuzzy Inputs and Outputs; Control Surfaces; Linguistic Rules; and Animated Examples.

Fuzzy Arithmetic - Fuzzy Numbers; Fuzzy Addition, Subtraction, Multiplication, and Division.

Approximate Reasoning - Linguistic Variables; Hedges; Modifiers; and Connectives.

Lukasiewicz Sets and Logic --

Fuzzy C-Means Clustering --

Note 1: Mathematica is a computer program used mainly in scientific, engineering and mathematical fields. It was originally conceived by Stephen Wolfram and developed by a team of mathematicians and programmers that he assembled and led. It is sold by Wolfram Research and its distributors.

Mathematica provides cross-platform support for tasks such as symbolic or numerical calculations, arbitrary precision arithmetic, data processing, and plotting. Mathematica offers a programming language which supports functional and procedural programming styles.

System Requirements

Wolfram Mathematica Neural Networks 1.0.2 requires Mathematica 5.0.1 - 5.2 and is available for all Mathematica platforms.

Mathematica platforms


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