C++ Neural Networks and Fuzzy Logic: Preface

Matrix Representation of a Fuzzy Relation

A fuzzy relation can be given as a matrix also when the underlying sets, call them domains, are finite. For

example, let the set of men be S = { Jeff, Steve, Mike }, and let us use the same relation,

much_more_educated. For each element of the Cartesian product S×S, we need the degree of membership in

this relation. We already have two such values, m

much_more_educated

(Jeff, Steve) = 0.2, and

m

much_more_educated

(Jeff, Mike) = 0.7. What degree of membership in the set should we assign for the pair (Jeff,

Jeff)? It seems reasonable to assign a 0. We will assign a 0 whenever the two members of the ordered pair are

the same. Our relation much_more_educated is given by a matrix that may look like the following:

                      0/(Jeff, Jeff)   0.2/(Jeff, Steve)  0.7/(Jeff, Mike)

 much_more_educated = 0.4/(Steve, Jeff)  0/(Steve, Steve) 0.3/(Steve, Mike)

                      0.1/(Mike, Jeff) 0.6/(Mike, Steve)    0/(Mike, Mike)

NOTE:  Note that the first row corresponds to ordered pairs with Jeff as the first member,

second column corresponds to those with Steve as the second member, and so on. The main

diagonal has ordered pairs where the first and second members are the same.

Previous Table of Contents Next

Copyright ©

 IDG Books Worldwide, Inc.

C++ Neural Networks and Fuzzy Logic:Preface

Matrix Representation of a Fuzzy Relation

384

---