C++ Neural Networks and Fuzzy Logic: Preface

Fuzzy Sets Revisited

We will illustrate the concept of fuzziness in the case where the database and the queries have fuzziness in

them. Our discussion is guided by the reference Terano, Asai, and Sugeno. First, let us review and recast the

concept of a fuzzy set in a slightly different notation.

If a, b, c, and d are in the set A with 0.9, 0.4, 0.5, 0, respectively, as degrees of membership, and in B with

0.9, 0.6, 0.3, 0.8, respectively, we give these fuzzy sets A and B as A = { 0.9/a, 0.4/b, 0.5/c} and B = {0.9/a,

0.6/b, 0.3/c, 0.8/d}. Now A[cup]B = {0.9/a, 0.6/b, 0.5/c, 0.8/d} since you take the larger of the degrees of

membership in A and B for each element. Also, A[cap]B = {0.9/a, 0.4/b, 0.3/c} since you now take the

smaller of the degrees of membership in A and B for each element. Since d has 0 as degree of membership in