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Fuzzy Logic

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The Most Flexible Environment for Exploring This Emerging New Field!

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Fuzzy Logic 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, the practical examples provided 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.

About Fuzzy Logic

Since its introduction nearly 30 years ago, fuzzy logic has established a place in engineering, proving to be especially useful in enabling designers and researchers to model complex, nonlinear systems quickly and effectively. Implemented most commonly in control system design, fuzzy logic-based systems can be found in a rapidly growing number of consumer appliances (from dishwashers to video cameras), as well as in automobile engines and transmissions and industrial equipment. The intuitive nature of the fuzzy-based system design saves engineers time and reduces costs by shortening product development cycles and making system maintenance and adjustments easier.

Also present in an ever broadening range of applications, the use of fuzzy logic for creating decision-support and expert systems has grown in popularity among management and financial decision-modeling experts. Still others are putting it to work in pattern recognition, economics, data analysis, and other areas that involve a high level of uncertainty, complexity, or nonlinearity.

Who Uses Fuzzy Logic?

The Fuzzy Logic package is ideally suited for the following professionals:

Engineers at all levels of experience with fuzzy logic. You can use it as you research, model, test, and visualize real systems, from the most basic to the highly complex.

Researchers who wish to investigate applications of and new ideas in fuzzy theory. The package's comprehensive set of fuzzy logic tools are all completely customizable and extensible.

Educators who are introducing fuzzy logic to students. Cover concepts, basic theory, and applications of fuzzy logic using the package alone or as a complement to your class text. Examples in the package show students how to solve a variety of problems in step-by-step detail. The package takes advantage of Mathematica notebooks, letting you combine fuzzy design settings, computations, 2D and 3D graphics, and even text in a single document on screen as you use it. This interactive document format is ideal for presenting concepts to students and having them turn in completed homework assignments and lab reports, either electronically or on paper as a printed notebook.


Features

Membership Functions
  • Triangular
  • Trapezoidal
  • Gaussian
  • User-Defined
Compositions and Inferencing
  • Compositions--Max-min, Max-dot, Max-star
  • Inferencing--Rule-Based, Composition-Based
Standard and Parameterized Fuzzy Aggregators
  • Intersections and Unions--Min, Max, Hamacher, Frank, Yager, Dubois-Prade, Dombi
  • Products and Sums--Drastic, Bounded, Algebraic, Einstein, Hamacher
  • Means--Arithmetic, Geometric, Harmonic, Generalized
  • User-Defined Aggregators
Fuzzy Operators
  • Complements--Standard, Sugeno, Yager
  • Defuzzifiers--Center of Area, Mean of Max
  • Normalization, Concentration, Dilation, Alpha-Cuts, and More
Visualization of Fuzzy Sets and Relations
  • Discrete, Line, and Crisp Plots of Fuzzy Sets
  • Discrete 3D, Surface, and Wire-Frame Plots of Fuzzy Relations
  • Membership Matrices
  • Defuzzification Results


Fuzzy System Modeling and Design Applications

Fuzzy Modeling
  • System definition
  • Inferencing
  • Model building
Fuzzy Logic Control
  • Fuzzy inputs and outputs
  • Control surfaces
  • Linguistic rules
  • Animated examples
Fuzzy Arithmetic
  • Fuzzy numbers
  • Fuzzy addition, subtraction, and multiplication
Approximate Reasoning
  • Linguistic variables
  • Hedges
  • Modifiers
  • Connectives


System Requirements:
Fuzzy Logic is compatible with Mathematica 2.2 only and is available for Windows 95/98/NT & Macintosh

Fuzzy Logic
Fuzzy Logic Windows Version $695
Fuzzy Logic MAC Version $695


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