Introduction to Set Theory and Fuzzy Logic

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.