Standard fuzzy arithmetic (SFA)

1
Standard fuzzy arithmetic (SFA)

• introduced by Zadeh, 1975
• basic aim to extend the operations , - , , /
  to the domain of fuzzy quantities
• How to evaluate AB?
• 1) a-cut representation a(AB) aA aB
• 2) extension principle
• (AB)(z) sup min(A(x), B(y)) x, y ? R, x
  y z

A
B
AB
2
SFA - questionable examples
A
B
A - A ? 0
A - A A - A ? 0
A / A ? 1
B . B
3
Constrained fuzzy arithmetic (CFA)

• introduced by G.J.Klir, 1997
• motivation
• to reduce the increase of vagueness
• to satisfy more of the classical laws of
  arithmetic
• equality constraint
• when one variable occurs more than once in the
  same expression
• different evaluations of A