# Introduction to Set Theory and Fuzzy Logic

• Ian S. Shaw
Chapter
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 457)

## Abstract

Given a multi-input multi-output system with m input and p output terminals. Applied to these terminals is a set of possible input and output values respectively. In order to obtain the combined input to the system, one must be able to know how to combine the m input sets. A similar reasoning applies to the p outputs where at every output terminal a different set of output values can arise. To determine the total output, one must be able to know how to combine the p output sets. For this reason, one must study the appropriate set-theoretical operations whereby to combine two or more sets.In systems analysis and design one is also interested in how the input affects the output; in other words, how the input is mapped into the output by the given system. In other words, how the system transforms the combined m input sets into the p output sets. The set-theoretical operations that provide this information establish an input-output mapping analogous to the transfer function of linear system theory.

## Keywords

Membership Function Fuzzy Logic Fuzzy Number Fuzzy Control Fuzzy Term
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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